Infinitesimal Drift Diffeomorphometry Models for Population Shape Analysis

Abstract

Describing longitudinal morphometric differences between populations and individuals is a critical task in computational anatomy. In the context of the random orbit model of computational anatomy, this often implies study of the variation of individual shape trajectories associated to some mean field, as well as longitudinal morphological differences as encoded by similar subjects from representative populations. In this paper, we present a new method for computing the deviation of individual subjects from models of flow. We demonstrate estimation of the infinitesimal drift representing the mean flow of a population and its entrance into the Eulerian vector field controlling that flow. Each individual is studied longitudinally by modeling another associated individual drift which acts as the personalized control of the flow. We provide an augmentation of the classic LDDMM equations to generate "biased geodesics" for trajectory shooting algorithms, allowing for direct computation of the individual’s deviation under the influence of a mean drift. Our new model is inspired by diffusion models from stochastic processes in which the personalized control is a non-stochastic term representing the additive Brownian component on top of the infinitesimal drift representing the population. We present results of our model on entorhinal cortical surfaces extracted from a patient population of the Alzheimer’s Disease Neuroimaging Initiative.