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In many applications, geodesic hierarchical models are adequate for the studyof temporal observations. We employ such a model derived for manifold-valueddata to Kendall's shape space. In particular, instead of the Sasaki metric, weadapt a functional-based metric, which increases the computational efficiencyand does not require the implementation of the curvature tensor. We propose thecorresponding variational time discretization of geodesics and employ theapproach for longitudinal analysis of 2D rat skulls shapes as well as 3D shapesderived from an imaging study on osteoarthritis. Particularly, we performhypothesis test and estimate the mean trends.

A Hierarchical Geodesic Model for Longitudinal Analysis on Manifolds