Approches multivaluées et supervisées en morphologie mathématique et applications en analyse d'image. (Multivalued and Supervised Approaches within Mathematical Morphology, and Applications in Image Analysis)

Ce memoire presente une synthese des activites de recherche en morphologie mathematique menees au LSIIT (UMR 7005 CNRS–UDS) depuis 2003. La morphologie mathematique est une theorie introduite il y a quarante ans par les chercheurs francais Georges Matheron et Jean Serra. Elle connait depuis un vif succes dans la communaute de l'analyse et du traitement des images, puisqu'elle permet l'analyse des structures spatiales (le plus souvent au travers d'un voisinage defini par le terme d'element structurant) dans un cadre non-lineaire. Son application aux images binaires et aux images en niveaux de gris s'effectue tres simplement en s'appuyant sur la theorie des ensembles ou mieux, celle des treillis. Cependant, son extension au cas des images multivaluees (ou chaque pixel est represente par un vecteur et non plus par un scalaire) n'est pas triviale et reste un probleme ouvert. Ainsi, nous nous sommes interesses aux approches morphologiques vectorielles basees sur des ordres totaux (aux fondements theoriques les plus valides), en cherchant a attenuer, a l'aide de differentes methodes de quantification, leur caractere fortement asymetrique afin de mieux exploiter l'ensemble des donnees disponibles. Nous avons egalement etudie une autre strategie consistant a eviter l'appel explicite a un ordre vectoriel, et a decomposer l'image en un ensemble de composantes binaires ou a niveaux de gris, traitees independemment ou conjointement. Independamment de la nature des images considerees, la creation des systemes d'analyse d'image par morphologie mathematique necessite le plus souvent une expertise du domaine et une connaissance tres fine du probleme pour pouvoir choisir, combiner, et parametrer les operateurs morphologiques a bon escient. De ce fait, les methodes morphologiques ne peuvent generalement pas etre reutilisees dans un contexte different de celui pour lequel elles ont ete elaborees, et ne respectent que tres peu la contrainte de genericite souhaitee en analyse d'image. Ce probleme n'est bien sur pas specifique a la morphologie mathematique et est recurrent en traitement d'image, et nous l'avons aborde selon deux axes principaux. D'une part, nous avons etudie les connaissances pouvant etre formalisees au sein des elements structurants dans le contexte de la detection d'objet. D'autre part, nous avons exploite des procedures de classification supervisee (ou des ensembles d'apprentissage sont fournis par l'expert) ou non-supervisee (ou seul le nombre d'objets ou de classes d'interet est connu) au sein du processus de segmentation d'image en regions. L'objectif sous-jacent a ces travaux fondamentaux est d'aboutir a terme a des approches morphologiques multivaluees et guidees par les connaissances, aptes a traiter tout type d'information, dans tout contexte. Nous avons donc cherche a appliquer ces developpements theoriques et methodologiques dans differents domaines, en particulier l'analyse d'images couleur (dans un but d'annotation et de recherche par le contenu), ainsi que la teledetection (a tres haute resolution spatiale) et l'imagerie astronomique (ou les donnees peuvent etre particulierement bruitees). Ces domaines d'application, ou les images sont de nature multivaluee et ou l'integration de connaissances pour guider les traitements est necessaire, sont particulierement pertinents puisque l'information spatiale y est cruciale, la morphologie mathematique prenant alors tout son sens. Les problemes recurrents rencontres dans ces differents domaines sont la detection, la segmentation, et la description des images. En complement a ces travaux relatifs a la morphologie mathematique, nous presentons le projet PELICAN, une plate-forme generique et extensible pour le traitement d'image. Ce memoire se termine par une presentation de quelques perspectives de recherche envisagees dans le cadre de differentes collaborations. Ainsi, l'apport des proprietes d'invariance et d'imprecision dans le contexte de la morphologie mathematique aurait des repercussions en imagerie du vivant. L'analyse morphologique de sequences video, et l'elaboration de descripteurs morphologiques locaux offriraient des solutions alternatives en indexation multimedia. Enfin, la morphologie mathematique n'etant par definition pas limitee a des donnees de type image, son application a des donnees de differentes natures merite d'etre etudiee avec une attention particuliere.

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