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Journal Articles SIAM Journal on Imaging Sciences Year : 2021

A coherent framework for learning spatiotemporal piecewise-geodesic trajectories from longitudinal manifold-valued data

Abstract

This paper provides a coherent framework for studying longitudinal manifold-valued data. We introduce a Bayesian mixed-effects model which allows estimating both a group-representative piecewise-geodesic trajectory in the Riemannian space of shape and inter-individual variability. We prove the existence of the maximum a posteriori estimate and its asymptotic consistency under reasonable assumptions. Due to the non-linearity of the proposed model, we use a stochastic version of the Expectation-Maximization algorithm to estimate the model parameters. Our simulations show that our model is not noise-sensitive and succeeds in explaining various paths of progression.
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Dates and versions

hal-01646298 , version 1 (23-11-2017)
hal-01646298 , version 2 (11-04-2019)
hal-01646298 , version 3 (29-05-2019)
hal-01646298 , version 4 (10-04-2020)

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Juliette Chevallier, Vianney Debavelaere, Stéphanie Allassonnière. A coherent framework for learning spatiotemporal piecewise-geodesic trajectories from longitudinal manifold-valued data. SIAM Journal on Imaging Sciences, 2021, 14 (1), pp.349-388. ⟨10.1137/20M1328026⟩. ⟨hal-01646298v4⟩
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