Section: New Results
Parallel transport in shape analysis : a scalable numerical scheme
Participants : Maxime Louis, Alexandre Bône, Benjamin Charlier, Stanley Durrleman.
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 work, we adapted a generic numerical scheme recently introduced for computing parallel transport along geodesics in a Riemannian manifold to finite-dimensional manifolds of diffeomorphisms. We provided a qualitative and quantitative analysis of its behavior on high-dimensional manifolds, and investigated an application with the prediction of brain structures progression.
More details in [32].