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Front Neurosci. 2018 Nov 12;12:803. doi: 10.3389/fnins.2018.00803. eCollection 2018.

Statistical Shape Analysis of Large Datasets Based on Diffeomorphic Iterative Centroids.

Cury C1,2,3,4,5,6, Glaunès JA7, Toro R8,9, Chupin M1,2,3,4,5, Schumann G10, Frouin V11, Poline JB12, Colliot O1,2,3,4,5; Imagen Consortium.

Author information

Institut du Cerveau et de la Moelle épinire, ICM, Paris, France.
Inserm, U 1127, Paris, France.
CNRS,UMR 7225, Paris, France.
Sorbonne Université, Paris, France.
Inria, Aramis project-team, Paris, France.
Univ Rennes, Inria, CNRS, Inserm, IRISA UMR 6074, VISAGES ERL U 1228, Rennes, France.
MAP5, Université Paris Descartes, Sorbonne Paris Cité, Paris, France.
Human Genetics and Cognitive Functions, Institut Pasteur, Paris, France.
CNRS URA 2182 "Genes, Synapses and Cognition", Paris, France.
MRC-Social Genetic and Developmental Psychiatry Centre, Institute of Psychiatry, King's College London, London, United Kingdom.
Neurospin, Commissariat à l'Energie Atomique et aux Energies Alternatives, Paris, France.
Henry H. Wheeler Jr. Brain Imaging Center, University of California, Berkeley, California City, CA, United States.


In this paper, we propose an approach for template-based shape analysis of large datasets, using diffeomorphic centroids as atlas shapes. Diffeomorphic centroid methods fit in the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework and use kernel metrics on currents to quantify surface dissimilarities. The statistical analysis is based on a Kernel Principal Component Analysis (Kernel PCA) performed on the set of initial momentum vectors which parametrize the deformations. We tested the approach on different datasets of hippocampal shapes extracted from brain magnetic resonance imaging (MRI), compared three different centroid methods and a variational template estimation. The largest dataset is composed of 1,000 surfaces, and we are able to analyse this dataset in 26 h using a diffeomorphic centroid. Our experiments demonstrate that computing diffeomorphic centroids in place of standard variational templates leads to similar shape analysis results and saves around 70% of computation time. Furthermore, the approach is able to adequately capture the variability of hippocampal shapes with a reasonable number of dimensions, and to predict anatomical features of the hippocampus, only present in 17% of the population, in healthy subjects.


IHI; LDDMM; Morphometry; atlas; computational anatomy; hippocampus; riemannian barycentres; shape analysis

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