Diffeomorphic Random Sampling Using Optimal Information Transport

  • Martin Bauer
  • Sarang Joshi
  • Klas ModinEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10589)


In this article we explore an algorithm for diffeomorphic random sampling of nonuniform probability distributions on Riemannian manifolds. The algorithm is based on optimal information transport (OIT)—an analogue of optimal mass transport (OMT). Our framework uses the deep geometric connections between the Fisher-Rao metric on the space of probability densities and the right-invariant information metric on the group of diffeomorphisms. The resulting sampling algorithm is a promising alternative to OMT, in particular as our formulation is semi-explicit, free of the nonlinear Monge–Ampere equation. Compared to Markov Chain Monte Carlo methods, we expect our algorithm to stand up well when a large number of samples from a low dimensional nonuniform distribution is needed.


Density matching Information geometry Fisher–Rao metric Optimal transport Image registration Diffeomorphism groups Random sampling 


58E50 49Q10 58E10 


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of MathematicsFlorida State UniversityTallahasseeUSA
  2. 2.Department of Bioengineering, Scientific Computing and Imaging InstituteUniversity of UtahSalt Lake CityUSA
  3. 3.Mathematical SciencesChalmers and University of GothenburgGothenburgSweden

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