Probabilistic Diffeomorphic Registration: Representing Uncertainty

  • Demian Wassermann
  • Matthew Toews
  • Marc Niethammer
  • William WellsIII
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8545)


This paper presents a novel mathematical framework for representing uncertainty in large deformation diffeomorphic image registration. The Bayesian posterior distribution over the deformations aligning a moving and a fixed image is approximated via a variational formulation. A stochastic differential equation (SDE) modeling the deformations as the evolution of a time-varying velocity field leads to a prior density over deformations in the form of a Gaussian process. This permits estimating the full posterior distribution in order to represent uncertainty, in contrast to methods in which the posterior is approximated via Monte Carlo sampling or maximized in maximum a-posteriori (MAP) estimation. The framework is demonstrated in the case of landmark-based image registration, including simulated data and annotated pre and intra-operative 3D images.


Gaussian Process Stochastic Differential Equation Deformable Image Registration Registration Problem Deformable Registration 
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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Demian Wassermann
    • 1
    • 3
  • Matthew Toews
    • 1
  • Marc Niethammer
    • 4
  • William WellsIII
    • 1
    • 2
  1. 1.Harvard Medical SchoolSPL, Brigham and Women’s HospitalBostonUSA
  2. 2.CSAILMassachusetts Institute of TechnologyBostonUSA
  3. 3.EPI AthenaINRIA Sophia Antipolis-MéditerranéeSophia AntipolisFrance
  4. 4.Department of Computer ScienceUniversity of North CarolinaChapel HillUSA

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