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Learning distributions of shape trajectories: a hierarchical model on a manifold of diffeomorphisms

Presented by: 
Alexandre Bône
Thursday 16th November 2017 - 11:00 to 11:30
INI Seminar Room 1
Co-authors: Olivier Colliot (CNRS), Stanley Durrleman (INRIA)

We propose a mixed effects statistical model to learn a distribution of shape trajectories from longitudinal data, i.e. the collection of individual objects repeatedly observed at multiple time-points. Shape trajectories and their variations are defined via the action of a group of deformations. The model is built on a generic statistical model for manifold-valued longitudinal data, for which we propose to use a finite-dimensional set of diffeomorphisms with a manifold structure, an efficient numerical scheme to compute parallel transport on this manifold and a specific sampling strategy for estimating shapes within a Markov Chain Monte Carlo (MCMC) method. The method allows the estimation of an average spatiotemporal trajectory of shape changes at the group level, and the individual variations of this trajectory in terms of shape and pace of shape changes. This estimation is obtained by a Stochastic Approximation of the Expectation-Maximization (MCMC-SAEM). We show that the algorithm recovers the optimal model parameters with simulated 2D shapes. We apply the method to estimate a scenario of alteration of the shape of the hippocampus 3D brain structure during the course of Alzheimer's disease.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons