The morphology observed in the brain of patients a ected by Alzheimer's disease (AD) is the contribution of di erent biological processes such as the normal aging and the AD-speci c pathological matter loss. The ability to di erentiate these complementary biological factors is fundamental in order to reliably evaluate the pathological AD related structural changes, especially at the earliest phase of the disease, at prodromal and pre-clinical stages. We propose a method based on non-rigid registration to estimate the di erent contributions of these complementary factors, and to identify the brain structural changes which are speci c for the pathological component. The experimental results provide a description of the anatomical changes observed across the AD time span: normal aging, normal aging at risk, conversion to MCI and latest AD stages. More advanced AD stages are associated to "virtually older" brains, and to increased speci c morphological changes that are not related to the normal aging. These results provide new insights that can lead to new understandings of the AD dynamics, and to novel techniques for the modeling and the early detection of the disease.