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Riemannian Geometry Learning for Disease Progression Modelling

Maxime Louis 1, 2 Raphäel Couronné 1, 2 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 longstandingproblem in medical imaging which is often tackled in the context ofRiemannian geometry: the set of observations is assumed to lie on an apriori known Riemannian manifold. When dealing with high-dimensionalor complex data, it is in general not possible to design a Riemanniangeometry of relevance. In this paper, we perform Riemannian manifoldlearning in association with the statistical task of longitudinal trajectoryanalysis. After inference, we obtain both a submanifold of observationsand a Riemannian metric so that the observed progressions are geodesics.This is achieved using a deep generative network, which maps trajectoriesin a low-dimensional Euclidean space to the observation space.
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https://hal.inria.fr/hal-02429839
Contributor : Stanley Durrleman <>
Submitted on : Monday, January 6, 2020 - 9:22:12 PM
Last modification on : Monday, March 29, 2021 - 2:45:41 PM

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Maxime Louis, Raphäel Couronné, Igor Koval, Benjamin Charlier, Stanley Durrleman. Riemannian Geometry Learning for Disease Progression Modelling. Information Processing in Medical Imaging - IPMI 2019, Jun 2019, Hong-Kong, China. pp.542-553, ⟨10.1007/978-3-030-20351-1_42⟩. ⟨hal-02429839⟩

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