PDE with memory and image processing

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PDE with memory and image processing

Labo LJK
Equipe EDP
Encadrants georges-henri.cottet@imag.fr

General setting

Non linear Partial Differential equations are popular tools to address a wide range of applications in image processing.

In this internship we focus on a system [1] which combines a diffusion equation with a time-delay equation governing the diffusion tensor. This system is inspired from neural networks with memory terms and allows to filter efficiently grey level images [2]. See also the image processing section of my webpage.

Assignment

The goal is to extend the model to color images and to experiment it on benchmark images available at [1].

This internship allows to grasp some essential features of image processing by combining basic PDEs (it suffices to understand the heat equation), a little bit of programming (the whole code is less than 100 lines long) and experiments against state-of-the art models.

[1] G.-H. Cottet and M. El Ayyadi, A Volterra type model for image processing, IEEE Transactions on image processing, 7, 1998.

[2] G.-H. Cottet, Neural networks: continuous approach and applications to image processing, J. Biological Systems, 3, 1995.