In medicine, large scale population analysis aim to obtain statistical information in order to understand better diseases, identify their risk factors, develop preventive and curative treatments and improve the quality of life of the patients. In this thesis, we first introduce the medical context of Alzheimer's disease, recall some concepts of statistical learning and the challenges that typically occur when applied in medical imaging. The second part focus on cross-sectional studies, i.e. at a single time point. We present an efficient method to classify white matter lesions based on support vector machines. Then we discuss the use of manifold learning techniques for image and shape analysis. Finally, we present extensions of Laplacian eigenmaps to improve the low-dimension representations of patients using the combination of imaging and clinical data. The third part focus on longitudinal studies, i.e. between several time points. We quantify the hippocampus deformations of patients via the large deformation diffeomorphic metric mapping framework to build disease progression classifiers. We introduce novel strategies and spatial regularizations for the classification and identification of biomarkers.
Mathematical methods of image analysis for cross-sectional and longitudinal population studies.