Representation of time-varying shapes in the large deformation diffeomorphic framework

Tracking and representation of shape change over time is of great interest in the field of computational anatomy. We propose a longitudinal growth model which estimates the diffeomorphic flow of a baseline image passing through a series of time-points that are the observed evolution of the template over time. We optimize the full space-time flow for the sequence of images, providing a linear space representation of the shape-change via a time-dependent velocity vector field, thus application of linear techniques becomes straightforward. We test our longitudinal growth model on both synthetic and real data-sets and demonstrate flexibility in time- point spacing, generation of average growth, and robust interpolation of missing time-points.