Title: Parallel transport in shape analysis: a scalable numerical scheme,
Abstract: The analysis of manifold-valued data requires efficient tools from Riemannian
geometry to cope with the computational complexity at stake. This complexity
arises from the always-increasing dimension of the data, and the absence of
closed-form expressions to basic operations such as the Riemannian logarithm.
In this paper, we adapt a generic numerical scheme recently introduced for
computing parallel transport along geodesics in a Riemannian manifold to
finite-dimensional manifolds of diffeomorphisms. We provide a qualitative and
quantitative analysis of its behavior on high-dimensional manifolds, and
investigate an application with the prediction of brain structures progression.