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{\bf Abstract : } What is a texture? It is impossible to answer this question in an intensive way, but it is possible to show examples: a field, the sea, a reptile skin...
The goal of this thesis is to formalize mathematically the {\it texture discrimination} knowing the Julesz Texton Theory (psychophysical).

We formalize both aspects of that theory :

On one hand, the definition of local geometrical features called {\it textons}.
By using the Julesz axiomatic, we show that these features can be computed with a multiscale analysis coming from a parabolic partial differential equation which is geometrically invariant.

On the other hand, we have to perform the {\it grouping} process: How can we segment an image knowing the texton density images. We propose a variationnal
method which achieves this segmentation.    

At the end, we make the numerical of both basic tools (multichannel segmentation, geometrical PDE) of the Julesz theory. Then, it is possible to verify it and to discuss it numerically.



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