Abstract
A parallel distributed relaxation labeling (RL) method, called the Lagrange-Hopfield (LH) method, is presented. RL is treated as a constrained optimization problem. The LH method solves the problem using the augmented Lagrangian multiplier technique and the graded Hopfield network. The LH method effectively overcomes instabilities that are inherent in the penalty method (e.g. Hopfield network) or the Lagrange multiplier method in constrained optimization. Due to the use of Lagrangian multipliers, the normalization operation in traditional RL methods is dispensed with. This makes the LH algorithm fully parallel and distributed and is suitable for analog implementation. Experiments also show that the method is able to produce good solutions in terms of the optimized objective values.
This work is supported by NTU project ARC-1/94.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
E. H. L. Aarts. Simulated annealing and Boltzmann machines: a stochastic approach to combinatorial optimization and neural computing. Wiley, 1989.
K. J. Arrow, L. Hurwicz, and H. Uzawa. Studies in Linear and Nonlinear Programming. Stanford University Press, 1958.
J. Besag. “On the statistical analysis of dirty pictures” (with discussions). Journal of the Royal Statistical Society, Series B, 48:259–302, 1986.
O. D. Faugeras and M. Berthod. “Improving consistency and reducing ambiguity in stochastic labeling: An optimization approach”. IEEE Transactions on Pattern Analysis and Machine Intelligence, 3:412–423, April 1981.
S. Geman and D. Geman. “Stochastic relaxation, Gibbs distribution and the Bayesian restoration of images”. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6(6):721–741, November 1984.
B. S. Gottfried. Introduction to Optimization Theory. Prentice-Hall, 1973.
R. M. Haralick. “Decision making in context”. IEEE Transactions on Pattern Analysis and Machine Intelligence, 5(4):417–428, July 1983.
M. R. Hestenes. “Multipler and gradient methods”. Journal of Optimization Theory and Applications, 4:303–320, 1969.
J. J. Hopfield. “Neurons with graded response have collective computational properties like those of two state neurons”. Proceedings of National Academic Science, USA, 81:3088–3092, 1984.
R. A. Hummel and S. W. Zucker. “On the foundations of relaxation labeling process”. IEEE Transactions on Pattern Analysis and Machine Intelligence, 5(3):267–286, May 1983.
S. Kirkpatrick, C. D. Gellatt, and M. P. Vecchi. “Optimization by simulated annealing”. Science, 220:671–680, 1983.
S. Z. Li. “A Markov random field model for object matching under contextual constraints”. In Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pages 866–869, Seattle, Washington, June 1994.
C. Peterson and B. Soderberg. “A new method for mapping optimization problems onto neural networks”. International Journal of Neural Systems, 1(1):3–22, 1989.
J. C. Platt and A. H. Barr. “Constrained differential optimization”. In Proceedings of the IEEE 1987 NIPS conference, 1988.
M. J. D. Powell. “A method of nonlinear constraints in minimization problems”. In R. Fletcher, editor, Optimization, London, 1969. Academic Press.
K. E. Price. “Relaxation matching techniques — A comparison”. IEEE Transactions on Pattern Analysis and Machine Intelligence, 7(5):617–623, September 1985.
A. Rosenfeld, R. Hummel, and S. Zucker. “Scene labeling by relaxation operations”. IEEE Transactions on Systems, Man and Cybernetics, 6:420–433, June 1976.
S. Ullman. “Relaxation and constraint optimization by local process”. Computer Graphics and Image Processing, 10:115–195, 1979.
E. Wacholder, J. Han, and R. C. Mann. “A neural network algorithm for the multiple traveling salesman problem”. Biological Cybernetics, 61:11–19, 1989.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Li, S.Z. (1996). Parallel distributed relaxation labeling. In: Li, S.Z., Mital, D.P., Teoh, E.K., Wang, H. (eds) Recent Developments in Computer Vision. ACCV 1995. Lecture Notes in Computer Science, vol 1035. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60793-5_90
Download citation
DOI: https://doi.org/10.1007/3-540-60793-5_90
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60793-9
Online ISBN: 978-3-540-49448-5
eBook Packages: Springer Book Archive