Learning the spatiotemporal variability in longitudinal shape data sets
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Learning the spatiotemporal variability in longitudinal shape data sets Alexandre Bône1,2,3,4,5 · Olivier Colliot1,2,3,4,5 · Stanley Durrleman1,2,3,4,5 for the Alzheimer’s Disease Neuroimaging Initiative
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Received: 12 April 2019 / Accepted: 19 May 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this paper, we propose a generative statistical model to learn the spatiotemporal variability in longitudinal shape data sets, which contain repeated observations of a set of objects or individuals over time. From all the short-term sequences of individual data, the method estimates a long-term normative scenario of shape changes and a tubular coordinate system around this trajectory. Each individual data sequence is therefore (i) mapped onto a specific portion of the trajectory accounting for differences in pace of progression across individuals, and (ii) shifted in the shape space to account for intrinsic shape differences across individuals that are independent of the progression of the observed process. The parameters of the model are estimated using a stochastic approximation of the expectation–maximization algorithm. The proposed approach is validated on a simulated data set, illustrated on the analysis of facial expression in video sequences, and applied to the modeling of the progressive atrophy of the hippocampus in Alzheimer’s disease patients. These experiments show that one can use the method to reconstruct data at the precision of the noise, to highlight significant factors that may modulate the progression, and to simulate entirely synthetic longitudinal data sets reproducing the variability of the observed process. Keywords Longitudinal data · Statistical shape analysis · Large deformation diffeomorphic metric mapping · Medical imaging · Disease progression modeling
1 Introduction 1.1 Motivation
Data used in preparation of this article were partly obtained from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database. As such, the investigators within the ADNI contributed to the design and implementation of ADNI and/or provided data but did not participate in analysis or writing of this report. A complete listing of ADNI investigators can be found at: adni.loni.usc.edu.
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Alexandre Bône [email protected] Olivier Colliot [email protected] Stanley Durrleman [email protected]
1
Institut du Cerveau, ICM, F-75013 Paris, France
2
Inserm, U 1127, F-75013 Paris, France
3
CNRS, UMR 7225, F-75013 Paris, France
4
Sorbonne Université, F-75013 Paris, France
5
Inria, Aramis project-team, F-75013 Paris, France
Video sequences of smiling faces, repeated measurements of growing plants or developing cells, medical images collected at multiple visits from a population of patients affected by a chronic disease: all these examples can be understood as data collections where individual instances of a common underlying process are observed at multiple time-points. Such collections are called longitudinal data sets. The in
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