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arXiv · 1711.08725

Parallel transport in shape analysis: a scalable numerical scheme

Maxime Louis·Alexandre Bône·Benjamin Charlier·Stanley Durrleman
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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.

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Maxime Louis, Alexandre Bône, Benjamin Charlier, Stanley Durrleman. 2017-11-23. Parallel transport in shape analysis: a scalable numerical scheme. https://doi.org/10.1007/978-3-319-68445-1_4

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