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The analysis of manifold-valued data requires efficient tools from Riemanniangeometry to cope with the computational complexity at stake. This complexityarises from the always-increasing dimension of the data, and the absence ofclosed-form expressions to basic operations such as the Riemannian logarithm.In this paper, we adapt a generic numerical scheme recently introduced forcomputing parallel transport along geodesics in a Riemannian manifold tofinite-dimensional manifolds of diffeomorphisms. We provide a qualitative andquantitative analysis of its behavior on high-dimensional manifolds, andinvestigate an application with the prediction of brain structures progression.

Parallel transport in shape analysis: a scalable numerical scheme