Biomarkers derived from brain magnetic resonance (MR) imaging have promise in being able to assist in the clinical diagnosis of brain pathologies. These have been used in many studies in which the goal has been to distinguish between pathologies such as Alzheimer's disease and healthy aging. However, other dementias, in particular, frontotemporal dementia, also present overlapping pathological brain morphometry patterns. Hence, a classifier that can discriminate morphometric features from a brain MRI from the three classes of normal aging, Alzheimer's disease (AD), and frontotemporal dementia (FTD) would offer considerable utility in aiding in correct group identification. Compared to the conventional use of multiple pair-wise binary classifiers that learn to discriminate between two classes at each stage, we propose a single three-way classification system that can discriminate between three classes at the same time. We present a novel classifier that is able to perform a three-class discrimination test for discriminating among AD, FTD, and normal controls (NC) using volumes, shape invariants, and local displacements (three features) of hippocampi and lateral ventricles (two structures times two hemispheres individually) obtained from brain MR images. In order to quantify its utility in correct discrimination, we optimize the three-class classifier on a training set and evaluate its performance using a separate test set. This is a novel, first-of-its-kind comparative study of multiple individual biomarkers in a three-class setting. Our results demonstrate that local atrophy features in lateral ventricles offer the potential to be a biomarker in discriminating among AD, FTD, and NC in a three-class setting for individual patient classification.