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.
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Contributor : Maxime Louis <>
Submitted on : Sunday, September 24, 2017 - 8:58:41 PM
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  • HAL Id : hal-01565478, version 1


Maxime Louis, Alexandre Bône, Benjamin Charlier, Stanley Durrleman. Parallel transport in shape analysis : a scalable numerical scheme. Geometric Science of Information, Nov 2017, Paris, France. ⟨hal-01565478⟩



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