Mixed-Effects Shape Models for Estimating Longitudinal Changes in Anatomy

In this paper, we propose a new method for longitudinal shape analysis that fits a linear mixed-effects model, while simultaneously optimizing correspondences on a set of anatomical shapes. Shape changes are modeled in a hierarchical fashion, with the global population trend as a fixed effect and individual trends as random effects. The statistical significance of the estimated trends are evaluated using specifically designed permutation tests. We also develop a permutation test based on the Hotelling T2 statistic to compare the average shapes trends between two populations. We demonstrate the benefits of our method on a synthetic example of longitudinal tori and data from a developmental neuroimaging study.