Abstract
We derive reaction-diffusion approximations for simple models of neural networks. On the basis of this formal link we construct a non linear diffusion operator which combined with reaction allows to obtain non trivial asymptotic states. The efficiency of this model in terms of image processing is discussed on test images as well as medical images.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Berthomier, F. and al. ‘Asymptotic behavior of neural networks and image processing’, in A. Babloyantz (ed), Self-organization, Emerging properties and learning, Plenum Press, NATO Series (to appear).
Cottet, G.-H. (1991) ‘Modèles de reaction-diffusion pour des réseaux de neurones stochastiques et déterministes ’, C. R. Acad. Sci. Paris, 312, 217–221.
Cottet, G.-H. and Germain, L. (1992) ‘Non-linear diffusion combined to reaction for image processing ’, preprint.
De Masi, A. and al. (1986) ‘Reaction-diffusion equations for interacting particle systems’, Journal of Stat. Phys., 44, 589–627.
François, O. (1992) Thèse de l’Université Joseph Fourier, Grenoble
Hopfield, J. J. (1984) ‘Neurons with graded response have collective computational properties like those of two-states neurons’, Proc. Natl. Acad. Sci., 81, 3088–3092.
Alvarez, L. and al (1991) ‘Image selective smoothing by nonlinear diffusion’, preprint.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1992 Springer Fachmedien Wiesbaden
About this chapter
Cite this chapter
Cottet, GH. (1992). Diffusion approximation on neural networks and applications for image processing. In: Hodnett, F. (eds) Proceedings of the Sixth European Conference on Mathematics in Industry August 27–31, 1991 Limerick. European Consortium for Mathematics in Industry. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-09834-8_1
Download citation
DOI: https://doi.org/10.1007/978-3-663-09834-8_1
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-663-09835-5
Online ISBN: 978-3-663-09834-8
eBook Packages: Springer Book Archive