TY - CONF A1 - Hanik, Martin A1 - Hege, Hans-Christian A1 - von Tycowicz, Christoph T1 - A Nonlinear Hierarchical Model for Longitudinal Data on Manifolds T2 - 2022 IEEE 19th International Symposium on Biomedical Imaging (ISBI) N2 - Large longitudinal studies provide lots of valuable information, especially in medical applications. A problem which must be taken care of in order to utilize their full potential is that of correlation between intra-subject measurements taken at different times. For data in Euclidean space this can be done with hierarchical models, that is, models that consider intra-subject and between-subject variability in two different stages. Nevertheless, data from medical studies often takes values in nonlinear manifolds. Here, as a first step, geodesic hierarchical models have been developed that generalize the linear ansatz by assuming that time-induced intra-subject variations occur along a generalized straight line in the manifold. However, this is often not the case (e.g., periodic motion or processes with saturation). We propose a hierarchical model for manifold-valued data that extends this to include trends along higher-order curves, namely Bézier splines in the manifold. To this end, we present a principled way of comparing shape trends in terms of a functional-based Riemannian metric. Remarkably, this metric allows efficient, yet simple computations by virtue of a variational time discretization requiring only the solution of regression problems. We validate our model on longitudinal data from the osteoarthritis initiative, including classification of disease progression. Y1 - 2022 UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/8540 SP - 1 EP - 5 ER -