1 - Les équations aux dérivées partielles en traitement des images et vision par ordinateur

For some time now we have been witnessing an increased interest in a number of problems based within the domain of imag e processing . This is for a number of reasons, of which the first is for an increased demand of efficient algorithms and bette r performance, within image enhancement, restoration, multi-scale analysis . . .The second reason is the emergence of a ne w methodology within the algorithmic framework of Partial Differential Equations (PDE) for the resolution of such problems . This PD E based methodology, whose introduction within image processing has occurred only recently, allows to handle efficiently a numbe r of non linear problems (existence and uniqueness of solution, efficient numerical schemes for the implementation part . . ) Some of the ideas developped within the context of image processing have also started to be applied to a certain number o f problems in the domain of computer vision, such as in low-level vision, stereovision, motion analysis, shape from shading, etc . This article is a non-exhaustive review of the state-of-the-art research within this domain . It shows how the most recent technique s of the theory of PDE's succeed in solving some of the most difficult problems in image processing and computer vision .