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.
CITATION STYLE
Louis, M., Bône, A., Charlier, B., & Durrleman, S. (2017). Parallel transport in shape analysis: A scalable numerical scheme. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10589 LNCS, pp. 29–37). Springer Verlag. https://doi.org/10.1007/978-3-319-68445-1_4
Mendeley helps you to discover research relevant for your work.