Learning landmark geodesics using the ensemble Kalman filter. (English) Zbl 1478.68281
Summary: 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.
MSC:
| 68T05 | Learning and adaptive systems in artificial intelligence |
| 58D05 | Groups of diffeomorphisms and homeomorphisms as manifolds |
| 58E10 | Variational problems in applications to the theory of geodesics (problems in one independent variable) |
| 62F15 | Bayesian inference |
| 65C05 | Monte Carlo methods |
| 65D18 | Numerical aspects of computer graphics, image analysis, and computational geometry |
| 65K10 | Numerical optimization and variational techniques |
| 68T10 | Pattern recognition, speech recognition |
Keywords:
ensemble Kalman filter; large deformation diffeomorphic metric mapping; Bayesian inverse problem; landmark matching; derivative-free optimisationReferences:
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