Fig. 1.

Schematics of transport in diffeomorphisms for studying longitudinal shape variation. There are three levels of analysis. In the first level, the initial momentum ${\alpha }_0^{\left(j\right)}$ encoding the deformation of the hippocampus between the baseline and follow-up within subject j is computed via LDDMM surface mapping. The geodesic $x_t^{\left(j\right)}$ connecting subject j at the baseline to the global template is also computed via LDDMM surface mapping in the second level of the analysis. Finally, ${\alpha }_0^{\left(j\right)}$ is parallel transported to the global template along $x_t^{\left(j\right)}$ via the technique described in Methods.