Abstract
Matching of images and analysis of shape differences is traditionally pursued by energy minimization of paths of deformations acting to match the shape objects. In the large deformation diffeomorphic metric mapping (LDDMM) framework, iterative gradient descents on the matching functional lead to matching algorithms informally known as Beg algorithms. When stochasticity is introduced to model stochastic variability of shapes and to provide more realistic models of observed shape data, the corresponding matching problem can be solved with a stochastic Beg algorithm, similar to the finite-temperature string method used in rare event sampling. In this paper, we apply a stochastic model compatible with the geometry of the LDDMM framework to obtain a stochastic model of images and we derive the stochastic version of the Beg algorithm which we compare with the string method and an expectation-maximization optimization of posterior likelihoods. The algorithm and its use for statistical inference is tested on stochastic LDDMM landmarks and images.
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Acknowledgements
Alexis Arnaudon acknowledges partial support from an Imperial College London Roth Award and the EPSRC through award EP/N014529/1 funding the EPSRC Centre for Mathematics of Precision Healthcare. Alexis Arnaudon and Darryl Holm are partially supported by the European Research Council Advanced Grant 267382 FCCA held by Darryl Holm. Darryl Holm is also grateful for support from EPSRC Grant EP/N023781/1. Stefan Sommer is partially supported by the CSGB Centre for Stochastic Geometry and Advanced Bioimaging funded by a grant from the Villum Foundation. We thank the anonymous reviewers for insightful comments that have substantially improved the manuscript.
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Arnaudon, A., Holm, D. & Sommer, S. String Methods for Stochastic Image and Shape Matching. J Math Imaging Vis 60, 953–967 (2018). https://doi.org/10.1007/s10851-018-0823-z
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DOI: https://doi.org/10.1007/s10851-018-0823-z