Learning the spatiotemporal variability in longitudinal shape data sets

Abstract

In this paper, we propose a generative statistical model to learn the spatiotemporal variability in longitudinal shape data sets, which contain repeated observations of a set of objects or individuals over time. From all the short-term sequences of individual data, the method estimates a long-term normative scenario of shape changes and a tubular coordinate system around this trajectory. Each individual data sequence is therefore (i) mapped onto a specific portion of the trajectory accounting for differences in pace of progression across individuals, and (ii) shifted in the shape space to account for intrinsic shape differences across individuals that are independent of the progression of the observed process. The parameters of the model are estimated using a stochastic approximation of the expectation–maximization algorithm. The proposed approach is validated on a simulated data set, illustrated on the analysis of facial expression in video sequences, and applied to the modeling of the progressive atrophy of the hippocampus in Alzheimer’s disease patients. These experiments show that one can use the method to reconstruct data at the precision of the noise, to highlight significant factors that may modulate the progression, and to simulate entirely synthetic longitudinal data sets reproducing the variability of the observed process.