Abstract

We develop a multi-scale model of shape based on a volu- metric representation of solids in 3D space. A signed energy function (SEF) derived from the model is designed to quantify the magnitude of regional shape changes that correlate well with local shrinkage and expansion. The methodology is applied to the analysis of longitudinal morphological data representing hippocampal volumes extracted from one-year repeat magnetic resonance scans of the brain of 381 sub jects collected by the Alzheimer’s Disease Neuroimaging Initiative. We first es- tablish a strong correlation between the SEFs and hippocampal volume loss over a one-year period and then use SEFs to characterize specific regions where hippocampal atrophy over the one-year period differ signif- icantly among groups of normal controls and sub jects with mild cognitive impairment and Alzheimer’s disease.