Abstract
Stochastic algorithms for solving constraint satisfaction problems with soft constraints that can be implemented on a parallel distributed network are discussed in a unified framework. The algorithms considered are: the Boltzmann machine, a Learning Automata network for Relaxation Labelling and a formulation of optimization problems based on Markov random field (mrf) models. It is shown that the automata network and themrf formulation can be regarded as generalisations of the Boltzmann machine in different directions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Banerjee S 1989On stochastic relaxation paradigms for computational vision, Ph D thesis, Dept. Elec. Eng., Indian Institute of Science, Bangalore
Banerjee K, Sastry P S, Ramakrishnan K R, Venkatesh Y V 1988 An SIMD machine for low-level vision.Inf. Sci. 44: 19–50
Billingsley P 1968Convergence of probability measures (New York: John Wiley)
Blake A 1989 Comparison of the efficiency of deterministic and stochastic algorithms for visual reconstruction.IEEE Trans. Pattern Anal. Mach. Intell. PAMI-11: 2–12
Blake A, Zisserman A 1987Visual reconstruction (Cambridge: MIT Press)
Davis L, Rosenfeld A 1981 Cooperating processes in low level vision.Artif. Intell. 17: 245–263
Geman S, Geman D 1984 Stochastic relaxation, Gibbs distribution and Bayesian restoration of images.IEEE Trans. Pattern Anal. Mach. Intell. PAMI-6: 721–741
Geman D, Geman S, Graffigne C, Dong P 1990 Boundary detection by constrained optimization.IEEE Trans. Pattern Anal. Mach. Intell. PAMI-12: 609–628
Geman S, Graffigne C 1987 Markov random field image models and their applications to computer vision.Proc. Intl. Congress of mathematicians (ed.) A M Gleason (Providence: Am. Math. Soc.)
Hinton G E, Sejnowsky T J, Ackley D H 1984 Boltzmann machines: Constraint satisfaction networks that learn, Tech. Rep.cmu-cs-84-119, Carnegie Mellon Univ. Pittsburgh
Hopfield J J, Tank D W 1985 Neural computation of decisions in optimization problems.Biol. Cybernet. 52: 141–152
Hummel R A, Zucker S W 1983 On the foundations of relaxation labelling processes.IEEE Trans. Pattern Anal. Mach. Intell. PAMI-5: 267–286
Kirkpatrick S, Gelatt C D, Vecchi M P 1983 Optimization by simulated annealing.Science 220: 671–680
Kushner H 1984Approximation and weak convergence methods for random processes (Cambridge: MIT Press)
Marroquin J, Mitter S, Poggio T 1987 Probabilistic solution of ill-posed problems in computational vision.J. Am. Stat. Assoc. 82 (397): 76–89
Mitra D, Fabio R, Vincentelli A S 1986 Convergence and finite-time behaviour of simulated annealing.Adv. Appl. Probab. 18: 747–771
Muralidharan S 1989Parallel distributed processing schemes for combinatorial optimisation, M Sc (Eng.) thesis, Dept. Elect. Eng., Indian Institute of Science, Bangalore
Narendra K S, Thathachar M A L 1989Learning automata: An introduction (Englewood Cliffs,NJ: Prentice-Hall)
Rumelhart D E, McClelland J L 1986Parellel distributed processing (Cambridge: MIT Press) Vols. 1 & 2
Sastry P S, Ramakrishnan K R, Banerjee S 1988 A local cooperative processing model for low level vision.Indo-US Workshop on Systems and Signal Processing (New Delhi: Oxford and IBH)
Thathachar M A L, Sastry P S 1986 Relaxation labelling with Learning Automata.IEEE Trans. Pattern Anal. Mach. Intell. PAMI-8: 256–268
Waltz L D 1975 Understanding of line drawings of scenes with shadows. In:Psychology of computer vision (ed.) P H Winston (New York: McGraw-Hill)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sastry, P.S. Stochastic networks for constraint satisfaction and optimization. Sadhana 15, 251–262 (1990). https://doi.org/10.1007/BF02811324
Issue Date:
DOI: https://doi.org/10.1007/BF02811324