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Bridge Simulation and Metric Estimation on Landmark Manifolds

  • Stefan Sommer
  • Alexis Arnaudon
  • Line Kuhnel
  • Sarang Joshi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10551)

Abstract

We present an inference algorithm and connected Monte Carlo based estimation procedures for metric estimation from landmark configurations distributed according to the transition distribution of a Riemannian Brownian motion arising from the Large Deformation Diffeomorphic Metric Mapping (LDDMM) metric. The distribution possesses properties similar to the regular Euclidean normal distribution but its transition density is governed by a high-dimensional PDE with no closed-form solution in the nonlinear case. We show how the density can be numerically approximated by Monte Carlo sampling of conditioned Brownian bridges, and we use this to estimate parameters of the LDDMM kernel and thus the metric structure by maximum likelihood.

Keywords

Landmarks Brownian motion Brownian bridges MLE 

Notes

Acknowledgements

We are grateful for the use of the cardiac ventricle dataset provided by Jens Chr. Nilsson and Bjørn A. Grønning, Danish Research Centre for Magnetic Resonance (DRCMR).

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Stefan Sommer
    • 1
  • Alexis Arnaudon
    • 2
  • Line Kuhnel
    • 1
  • Sarang Joshi
    • 3
  1. 1.Department of Computer Science (DIKU)University of CopenhagenCopenhagenDenmark
  2. 2.Department of MathematicsImperial College LondonLondonUK
  3. 3.Department of Bioengineering, Scientific Computing and Imaging InstituteUniversity of UtahSalt Lake CityUSA

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