Abstract
In the study of shapes of human organs using computational anatomy, variations are found to arise from inter-subject anatomical differences, disease-specific effects, and measurement noise. This paper introduces a stochastic model for incorporating random variations into the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework. By accounting for randomness in a particular setup which is crafted to fit the geometrical properties of LDDMM, we formulate the template estimation problem for landmarks with noise and give two methods for efficiently estimating the parameters of the noise fields from a prescribed data set. One method directly approximates the time evolution of the variance of each landmark by a finite set of differential equations, and the other is based on an Expectation-Maximisation algorithm. In the second method, the evaluation of the data likelihood is achieved without registering the landmarks, by applying bridge sampling using a stochastically perturbed version of the large deformation gradient flow algorithm. The method and the estimation algorithms are experimentally validated on synthetic examples and shape data of human corpora callosa.
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Acknowledgements
We are grateful to M. Bruveris, M. Bauer, N. Ganaba C. Tronci and T. Tyranowski for helpful discussions of this material. AA acknowledges partial support from an Imperial College London Roth Award. AA and DH are partially supported by the European Research Council Advanced Grant 267382 FCCA held by DH. DH is also grateful for support from EPSRC Grant EP/N023781/1. SS is partially supported by the CSGB Centre for Stochastic Geometry and Advanced Bioimaging funded by a grant from the Villum foundation.
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Arnaudon, A., Holm, D.D., Pai, A., Sommer, S. (2017). A Stochastic Large Deformation Model for Computational Anatomy. In: Niethammer, M., et al. Information Processing in Medical Imaging. IPMI 2017. Lecture Notes in Computer Science(), vol 10265. Springer, Cham. https://doi.org/10.1007/978-3-319-59050-9_45
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DOI: https://doi.org/10.1007/978-3-319-59050-9_45
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