Bayesian Point Set Registration
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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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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