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Bayesian Point Set Registration

  • Adam Spannaus
  • Vasileios Maroulas
  • David J. Keffer
  • Kody J. H. Law
Chapter
Part of the MATRIX Book Series book series (MXBS, volume 2)

Abstract

Point set registration involves identifying a smooth invertible transformation between corresponding points in two point sets, one of which may be smaller than the other and possibly corrupted by observation noise. This problem is traditionally decomposed into two separate optimization problems: (1) assignment or correspondence, and (2) identification of the optimal transformation between the ordered point sets. In this work, we propose an approach solving both problems simultaneously. In particular, a coherent Bayesian formulation of the problem results in a marginal posterior distribution on the transformation, which is explored within a Markov chain Monte Carlo scheme. Motivated by Atomic Probe Tomography (APT), in the context of structure inference for high entropy alloys (HEA), we focus on the registration of noisy sparse observations of rigid transformations of a known reference configuration. Lastly, we test our method on synthetic data sets.

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Notes

Acknowledgements

A.S. would like to thank ORISE as well as Oak Ridge National Laboratory (ORNL) Directed Research and Development funding. In addition, he thanks the CAM group at ORNL for their hospitality. K.J.H.L. gratefully acknowledges the support of Oak Ridge National Laboratory Directed Research and Development funding.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Adam Spannaus
    • 1
  • Vasileios Maroulas
    • 1
  • David J. Keffer
    • 2
  • Kody J. H. Law
    • 3
    • 4
  1. 1.Department of MathematicsUniversity of TennesseeKnoxvilleUSA
  2. 2.Department of Materials Science and EngineeringUniversity of TennesseeKnoxvilleUSA
  3. 3.Computer Science and Mathematics DivisionOak Ridge National LaboratoryOak RidgeUSA
  4. 4.School of MathematicsUniversity of ManchesterManchesterUK

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