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Theses

Equations aux dérivées partielles et réseaux de neurones pour le traitement d'images

Abstract : This work deals with mathematical tools based both on partial differential equations and neural networks for images processing. Approximation of neural network dynamics by reaction-diffusion equations enables us to introduce a new nonlinear anisotropic diffusion model of selective filters for image processing. This Volterra type equations allows the diffusion tensor to change dynamically in order to process the image by a combination of smoothing and contrast enhancement. Moreover, they exhibit strong stability properties which permit acquisition of the desired filtered image on the asymptotic (in time) state of the model. In other terms, their use requires only an (\em a priori) knowledge of a contrast parameter about the desired image. The experimental results on test and medical images shown in this thesis illustrate the ability of the model to detect fine objects in a highly degraded images.
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https://tel.archives-ouvertes.fr/tel-00004940
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Submitted on : Friday, February 20, 2004 - 4:01:18 PM
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  • HAL Id : tel-00004940, version 1

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Mohamed Elayyadi. Equations aux dérivées partielles et réseaux de neurones pour le traitement d'images. Interface homme-machine [cs.HC]. Université Joseph-Fourier - Grenoble I, 1997. Français. ⟨tel-00004940⟩

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