Estimation et analyse de champs denses de vitesses d'écoulements fluides. (Estimation and analysis of dense fluid flows)

Cette etude a pour cadre l'analyse de mouvements fluides dans des sequences d'images et s'articule autour de deux axes. Nous traitons en premier lieu le probleme de l'estimation du mouvement. Dans un contexte d'imagerie fluide, la luminance des images fait parfois apparaitre de fortes distorsions spatiales et temporelles, rendant delicate l'utilisation de techniques standard issues de la Vision par Ordinateur, originalement concues pour des mouvements rigides et reposant sur une hypothese d'invariance de la fonction de luminance. Nous proposons un estimateur de mouvement modelise au moyen d'une formulation energetique et specialement dedie a l'estimation du mouvement fluide. La fonctionnelle consideree est composee d'un terme d'attache aux donnees original issu de l'equation de continuite de la mecanique des fluides. Ce nouveau modele de donnees, specifie pour etre aisement integre dans un schema multiresolution, est associe a une regularisation de type ``div-curl''. Les performances de cet estimateur sont experimentalement demontrees sur des images synthetiques et reelles meteorologiques. Une validation de la methode sur un ecoulement experimental representant une ``couche de melange'' est par ailleurs presentee. L'interet de l'etude est en second lieu porte sur l'analyse d'un champ de deplacement prealablement estime, relatif a un mouvement fluide. Nous proposons une methode visant a extraire les vortex et puits/sources de l'ecoulement en s'appuyant sur le modele de Rankine. Ce probleme est essentiel dans de nombreuses applications comme par exemple la detection d'importants evenements meteorologiques (depressions, cellules convectives, ...) ou la caracterisation d'ecoulements experimentaux. La connaissance de telles structures autorise par ailleurs une representation parametrique de l'ecoulement. La methode que nous proposons s'appuie sur une representation analytique du champ des vitesses e permet d'extraire d'autres informations pertinentes relatives a l'ecoulement (fonctions de potentiels, decomposition selon Helmholtz de l'ecoulement, points singuliers, ...). L'approche presentee sera experimentalement etudiee sur des ecoulement representant divers phenomenes physiques.

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