The aim of the present thesis is to provide an e ffective computational framework for the analysis and quantifi cation of the longitudinal structural changes in Alzheimer's disease (AD). The framework is based on the diffeomorphic non-rigid registration parameterized by stationary velocity fields (SVFs), and is hierachically developed to account for the diff erent levels of variability which characterize the longitudinal observations of T1 brain magnetic resonance images (MRIs). We developed an effi cient and robust method for the quantifi cation of the structural changes observed between pairs of MRIs. For this purpose, we propose the LCC-Demons registration framework which implements the local correlation coeffi cient as similarity metric, and we derived consistent and numerically stable measures of volume change and boundary shift for the regional assessment of the brain atrophy. In order to consistently analyze group-wise longitudinal evolutions, we then investigated the parallel transport of subject-specifi c deformation trajectories across di fferent anatomical references. Based on the SVF parametrization of diffeomorphisms, we relied on the Lie group theory to propose new and effective strategies for the parallel transport of SVFs, with particular interest into the practical application to the registration setting. These contributions are the basis for the defi nition of qualitative and quantitative analysis for the pathological evolution of AD. We proposed several analysis frameworks which addressed the di fferentiation of pathological evolutions between clinical populations, the statistically powered evaluation of regional volume changes, and the clinical diagnosis at the early/prodromal disease stages.
