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International Conference on Information Processing in Medical Imaging

IPMI 2015: Information Processing in Medical Imaging pp 261–272Cite as

Fast Optimal Transport Averaging of Neuroimaging Data

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Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9123))

Abstract

Knowing how the Human brain is anatomically and functionally organized at the level of a group of healthy individuals or patients is the primary goal of neuroimaging research. Yet computing an average of brain imaging data defined over a voxel grid or a triangulation remains a challenge. Data are large, the geometry of the brain is complex and the between subjects variability leads to spatially or temporally non-overlapping effects of interest. To address the problem of variability, data are commonly smoothed before performing a linear group averaging. In this work we build on ideas originally introduced by Kantorovich [18] to propose a new algorithm that can average efficiently non-normalized data defined over arbitrary discrete domains using transportation metrics. We show how Kantorovich means can be linked to Wasserstein barycenters in order to take advantage of the entropic smoothing approach used by [7]. It leads to a smooth convex optimization problem and an algorithm with strong convergence guarantees. We illustrate the versatility of this tool and its empirical behavior on functional neuroimaging data, functional MRI and magnetoencephalography (MEG) source estimates, defined on voxel grids and triangulations of the folded cortical surface.

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Notes

  1. 1.

    https://surfer.nmr.mgh.harvard.edu/.

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Acknowledgements

A. Gramfort was supported by the ANR grant THALAMEEG, ANR-14-NEUC-0002-01. M. Cuturi gratefully acknowledges the support of JSPS young researcher A grant 26700002, the gift of a K40 card from NVIDIA and fruitful discussions with K.R. Müller. The work of G. Peyré has been supported by the European Research Council (ERC project SIGMA-Vision).

Author information

Authors and Affiliations

  1. Institut Mines-Télécom, Telecom ParisTech, CNRS LTCI, Paris, France

    A. Gramfort

  2. NeuroSpin, CEA Saclay, Bat. 145, 91191, Gif-sur-Yvette, Cedex France

    A. Gramfort

  3. CNRS and CEREMADE, Université Paris-Dauphine, Paris, France

    G. Peyré

  4. Graduate School of Informatics, Kyoto University, Kyoto, Japan

    M. Cuturi

Authors
  1. A. Gramfort
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  2. G. Peyré
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  3. M. Cuturi
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Corresponding author

Correspondence to A. Gramfort .

Editor information

Editors and Affiliations

  1. Centre for Medical Image Computing, University College London, London, United Kingdom

    Sebastien Ourselin

  2. Centre for Medical Image Computing, University College London, London, United Kingdom

    Daniel C. Alexander

  3. Dept. of Radiology, Harvard Medical School Brigham and Women's Hospital, Boston, Massachusetts, USA

    Carl-Fredrik Westin

  4. Centre for Medical Image Computing, University College London, London, United Kingdom

    M. Jorge Cardoso

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© 2015 Springer International Publishing Switzerland

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Gramfort, A., Peyré, G., Cuturi, M. (2015). Fast Optimal Transport Averaging of Neuroimaging Data. In: Ourselin, S., Alexander, D., Westin, CF., Cardoso, M. (eds) Information Processing in Medical Imaging. IPMI 2015. Lecture Notes in Computer Science(), vol 9123. Springer, Cham. https://doi.org/10.1007/978-3-319-19992-4_20

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  • DOI: https://doi.org/10.1007/978-3-319-19992-4_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19991-7

  • Online ISBN: 978-3-319-19992-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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