Intrinsic analysis of time-varying shape data

Time-varying shapes exist in abundance especially in life sciences where shape changes within and between individuals are tracked over time to gain insights into dynamic processes, such as aging or disease progression. A major challenge in the digital age is to deal with the increasing amount of such data, for example from large-scale clinical studies. This requires the development of robust, efficient, and consistent analysis and processing tools.

In this talk we will discuss recent approaches for the analysis of longitudinal shape data using generative hierarchical models. Such models describe the inner-individual changes as smooth, parametric curves, which in turn are considered as perturbations of a population-average trend.

To this end, we present a principled way of comparing shape trends in terms of a novel Riemannian metric, which increases the computational efficiency and does not require the implementation of the curvature tensor. We propose the corresponding variational time discretization of geodesics and apply it to the estimation of group trends and statistical testing of 3D shapes derived from epidemiological imaging studies.