Mathematical methods of image analysis for cross-sectional and longitudinal population studies. (Méthodes mathématiques d'analyse d'image pour les études de population transversales et longitudinales.)

En medecine, les analyses de population a grande echelle ont pour but d’obtenir des informations statistiques pour mieux comprendre des maladies, identifier leurs facteurs de risque, developper des traitements preventifs et curatifs et ameliorer la qualite de vie des patients.Dans cette these, nous presentons d’abord le contexte medical de la maladie d’Alzheimer, rappelons certains concepts d’apprentissage statistique et difficultes rencontrees lors de l’application en imagerie medicale. Dans la deuxieme partie,nous nous interessons aux analyses transversales, c-a-d ayant un seul point temporel.Nous presentons une methode efficace basee sur les separateurs a vaste marge (SVM)permettant de classifier des lesions dans la matiere blanche. Ensuite, nous etudions les techniques d’apprentissage de varietes pour l’analyse de formes et d’images, et presentons deux extensions des Laplacian eigenmaps ameliorant la representation de patients en faible dimension grâce a la combinaison de donnees d’imagerie et cliniques. Dans la troisieme partie, nous nous interessons aux analyses longitudinales, c-a-d entre plusieurs points temporels. Nous quantifions les deformations des hippocampus de patients via le modele des larges deformations par diffeomorphismes pour classifier les evolutions de la maladie. Nous introduisons de nouvelles strategies et des regularisations spatiales pour la classification et l’identification de marqueurs biologiques.

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