A Random Riemannian Metric for Probabilistic Shortest-Path Tractography

  • Søren Hauberg
  • Michael Schober
  • Matthew Liptrot
  • Philipp Hennig
  • Aasa Feragen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9349)


Shortest-path tractography (SPT) algorithms solve global optimization problems defined from local distance functions. As diffusion MRI data is inherently noisy, so are the voxelwise tensors from which local distances are derived. We extend Riemannian SPT by modeling the stochasticity of the diffusion tensor as a “random Riemannian metric”, where a geodesic is a distribution over tracts. We approximate this distribution with a Gaussian process and present a probabilistic numerics algorithm for computing the geodesic distribution. We demonstrate SPT improvements on data from the Human Connectome Project.


Orientation Distribution Function Observation Likelihood Human Connectome Project Structural Brain Network Free Brownian Motion 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Søren Hauberg
    • 1
  • Michael Schober
    • 2
  • Matthew Liptrot
    • 1
    • 3
  • Philipp Hennig
    • 2
  • Aasa Feragen
    • 3
  1. 1.Cognitive SystemsTechnical University of DenmarkLyngbyDenmark
  2. 2.Max Planck Institute for Intelligent SystemsTübingenGermany
  3. 3.Department of Computer ScienceUniversity of CopenhagenCopenhagenDenmark

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