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Robust Fréchet Mean and PGA on Riemannian Manifolds with Applications to Neuroimaging

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Information Processing in Medical Imaging (IPMI 2017)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10265))

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Abstract

In this paper, we present novel algorithms to compute robust statistics from manifold-valued data. Specifically, we present algorithms for estimating the robust Fréchet Mean (FM) and performing a robust exact-principal geodesic analysis (ePGA) for data lying on known Riemannian manifolds. We formulate the minimization problems involved in both these problems using the minimum distance estimator called the L\(_2\)E. This leads to a nonlinear optimization which is solved efficiently using a Riemannian accelerated gradient descent technique. We present competitive performance results of our algorithms applied to synthetic data with outliers, the corpus callosum shapes extracted from OASIS MRI database, and diffusion MRI scans from movement disorder patients respectively.

This research was funded in part by, the NSF grant IIS-1525431 to BCV and the UFII fellowship to MB.

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Acknowledgements

Authors thank Drs. Vaillancourt, Okun and Ofori of the University of Florida, for providing us the movement disorder data used here.

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Authors and Affiliations

  1. University of Florida, Gainesville, USA

    Monami Banerjee & Baba C. Vemuri

  2. Google, Mountain View, CA, USA

    Bing Jian

Authors
  1. Monami Banerjee
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  2. Bing Jian
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  3. Baba C. Vemuri
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Corresponding author

Correspondence to Baba C. Vemuri .

Editor information

Editors and Affiliations

  1. University of North Carolina, Chapel Hill, North Carolina, USA

    Marc Niethammer

  2. University of North Carolina, Chapel Hill, North Carolina, USA

    Martin Styner

  3. Kitware Inc., Carrboro, North Carolina, USA

    Stephen Aylward

  4. University of North Carolina, Chapel Hill, North Carolina, USA

    Hongtu Zhu

  5. University of Pennsylvania, Philadelphia, Pennsylvania, USA

    Ipek Oguz

  6. University of North Carolina, Chapel Hill, North Carolina, USA

    Pew-Thian Yap

  7. University of North Carolina, Chapel Hill, North Carolina, USA

    Dinggang Shen

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Banerjee, M., Jian, B., Vemuri, B.C. (2017). Robust Fréchet Mean and PGA on Riemannian Manifolds with Applications to Neuroimaging. In: Niethammer, M., et al. Information Processing in Medical Imaging. IPMI 2017. Lecture Notes in Computer Science(), vol 10265. Springer, Cham. https://doi.org/10.1007/978-3-319-59050-9_1

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  • DOI: https://doi.org/10.1007/978-3-319-59050-9_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59049-3

  • Online ISBN: 978-3-319-59050-9

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