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@article{Bock:2021:10.3934/fods.2021020,
author = {Bock, A and Cotter, CJ},
doi = {10.3934/fods.2021020},
journal = {Foundations of Data Science},
pages = {701--727},
title = {Learning landmark geodesics using the ensemble Kalman filter},
url = {http://dx.doi.org/10.3934/fods.2021020},
volume = {3},
year = {2021}
}

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TY  - JOUR
AB  - We study the problem of diffeomorphometric geodesic landmark matching where the objective is to find a diffeomorphism that, via its group action, maps between two sets of landmarks. It is well-known that the motion of the landmarks, and thereby the diffeomorphism, can be encoded by an initial momentum leading to a formulation where the landmark matching problem can be solved as an optimisation problem over such momenta. The novelty of our work lies in the application of a derivative-free Bayesian inverse method for learning the optimal momentum encoding the diffeomorphic mapping between the template and the target. The method we apply is the ensemble Kalman filter, an extension of the Kalman filter to nonlinear operators. We describe an efficient implementation of the algorithm and show several numerical results for various target shapes.
AU  - Bock,A
AU  - Cotter,CJ
DO  - 10.3934/fods.2021020
EP  - 727
PY  - 2021///
SN  - 2639-8001
SP  - 701
TI  - Learning landmark geodesics using the ensemble Kalman filter
T2  - Foundations of Data Science
UR  - http://dx.doi.org/10.3934/fods.2021020
UR  - https://www.aimsciences.org/article/doi/10.3934/fods.2021020
UR  - http://hdl.handle.net/10044/1/91395
VL  - 3
ER  -

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