Statistical analysis of longitudinal data and applications to neuro-imaging

Abstract

Longitudinal data analysis is an often encountered problem in Medical Image Analysis. A differential geometric treatment of such problems has been reported in literature in the recent past. However, most of these methods require that the trajectory characterizing the evolution of features over time lie on a geodesic emanating from the initial time point on the manifold containing the trajectory. This is a stringent and not necessarily a meaningful requirement. Further, most of these methods impose the restriction that the number of samples on a trajectory be the same across the members of a group of trajectories. At times, this restriction is hard to meet from a practical view point. In this paper, we present a novel formulation of the trajectory analysis problem that overcomes the aforementioned limitations. We represent the trajectories by embedding them in a product Riemannian manifold and endowing it with a Riemannian metric, thereby facilitating the statistical analysis. Finally, we present real data (from MR brain scans of dementia patients) examples depicting the performance of our algorithms.