This paper proposes a novel fully automatic computer-aided diagnosis (CAD) system for the early detection of Alzheimer's disease (AD) based on supervised machine learning methods. The novelty of the approach, which is based on histogram analysis, is twofold: 1) a feature extraction process that aims to detect differences in brain regions of interest (ROIs) relevant for the recognition of subjects with AD and 2) an original greedy algorithm that predicts the severity of the effects of AD on these regions. This algorithm takes account of the progressive nature of AD that affects the brain structure with different levels of severity, i.e., the loss of gray matter in AD is found first in memory-related areas of the brain such as the hippocampus. Moreover, the proposed feature extraction process generates a reduced set of attributes which allows the use of general-purpose classification machine learning algorithms. In particular, the proposed feature extraction approach assesses the ROI image separability between classes in order to identify the ones with greater discriminant power. These regions will have the highest influence in the classification decision at the final stage. Several experiments were carried out on segmented magnetic resonance images from the Alzheimer's Disease Neuroimaging Initiative (ADNI) in order to show the benefits of the overall method. The proposed CAD system achieved competitive classification results in a highly efficient and straightforward way.