Riemannian geometry learning for disease progression modelling

Maxime Louis 1, 2 Raphael Couronne 1 Igor Koval 1, 2 Benjamin Charlier 3, 2 Stanley Durrleman 1, 2
1 ARAMIS - Algorithms, models and methods for images and signals of the human brain
SU - Sorbonne Université, Inria de Paris, ICM - Institut du Cerveau et de la Moëlle Epinière = Brain and Spine Institute
Abstract : The analysis of longitudinal trajectories is a longstanding problem in medical imaging which is often tackled in the context of Riemannian geometry: the set of observations is assumed to lie on an a priori known Riemannian manifold. When dealing with high-dimensional or complex data, it is in general not possible to design a Riemannian geometry of relevance. In this paper, we perform Riemannian manifold learning in association with the statistical task of longitudinal trajectory analysis. After inference, we obtain both a submanifold of observations and a Riemannian metric so that the observed progressions are geodesics. This is achieved using a deep generative network, which maps trajectories in a low-dimensional Euclidean space to the observation space.
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  • HAL Id : hal-02079820, version 2

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Maxime Louis, Raphael Couronne, Igor Koval, Benjamin Charlier, Stanley Durrleman. Riemannian geometry learning for disease progression modelling. 2019. ⟨hal-02079820v2⟩

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