The scale of medical imaging data is growing rapidly and automated computer algorithms are well suited to analyze such data. Shape information can distinguish diseased scans from normal controls, but analyzing the data is difficult due to the high dimensionality of shape information. With manifold learning, shape analysis becomes more tractable in a low dimensional space. Some manifold learning methods, including multidimensional scaling (MDS), require a distance measure to quantify pair-wise dissimilarities between scans of interest. In this study, we compared two different distance measures combined with MDS to distinguish patients with Alzheimer’s disease (AD) and mild cognitive impairment (MCI) from normal control patients. The first distance measure is based on the displacement field, and the second distance measure is based on mutual information (MI). Shape quantification was applied to the brain scans of 25 normal, 25 AD, and 25 MCI patients. Use of the first distance measure resulted in an 18% error rate while use of the second distance measure resulted in a 46% error rate for classifying between patients with AD and normal patients. Application of MDS leads to a feature space, and we compared the MDS-induced feature space with the feature space induced from hippocampus volume, a traditionally used feature for distinguishing AD/MCI patients from normal patients.