Abstract
An object extraction problem based on the Gibbs Random Field model is discussed. The Maximum a'posteriori probability (MAP) estimate of a scene based on a noise-corrupted realization is found to be computationally exponential in nature. A neural network, which is a modified version of that of Hopfield, is suggested for solving the problem. A single neuron is assigned to every pixel. Each neuron is supposed to be connected only to all of its nearest neighbours. The energy function of the network is designed in such a way that its minimum value corresponds to the MAP estimate of the scene. The dynamics of the network are described. A possible hardware realization of a neuron is also suggested. The technique is implemented on a set of noisy images and found to be highly robust and immune to noise.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Besag J (1974) Spatial interaction and statistical analysis of lattice systems. J R Statist Soc B36:192–236
Cohen FS, Cooper DB (1983) Real time textured image segmentation based on noncausal Markovian random field models. Proc SPIE Conf Intell Robots, Cambridge, Mass
Derin H, Elliott H (1987) Modeling and segmentation of noisy and textured images using Gibbs random fields. IEEE Trans Pattern Anal Machine Intell PAMI-9:39–55
Geman S, Geman D (1984) Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans Pattern Anal Machine Intell PAMI-6:721–741
Gonzalez RC, Wintz P (1977) Digital image processing. Addison-Wesley, Reading, Mass
Hopfield JJ (1982) Neural networks and physical systems with emergent computational abilities. Proc Natl Acad Sci USA 79:2554–2558
Hopfield JJ (1984) Neurons with graded response have collective computational properties like those of two state neurons. Proc Natl Acad Sci USA 81:3088–3092
Hopfield JJ, Tank DW (1985) Neural computation of decisions in optimization problems. Biol Cybern 52:141–152
Kinderman R, Snell JL (1980) Markov random fields and their applications. American Mathematical Society, Providence
Kirkpatric S, Gellat CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220:671–680
Kohonen T (1989) Self-organization and associative memory, 3rd edn. Springer, Berlin Heidelberg New York
Pal SK, Dutta Majumder D (1986) Fuzzy mathematical approach to pattern recognition. Wiley (Halsted Press), New York
Parsi BK, Parsi BK (1990), On problem solving with Hopfield neural networks. Biol Cybern 62:415–423
Rosenfeld A, Kak AC (1982) Digital picture processing. Academic Press, New York
Rumelhart DE, McClelland J, PDP Research Group (1986) Parallel distributed processing: explorations in the microstructure of cognition, vol 1. MIT Press, Cambridge, Mass
Splitzer F (1971) Markov random fields and Gibbs ensembles. Am Math Mon 78:142–154
Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ghosh, A., Pal, N.R. & Pal, S.K. Image segmentation using a neural network. Biol. Cybern. 66, 151–158 (1991). https://doi.org/10.1007/BF00243290
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00243290