Learning landmark geodesics using Kalman ensembles
This work addresses landmark matching in computational anatomy, but it is incremental as it applies an existing method (ensemble Kalman filter) to a known optimization problem without broad SOTA impact.
The paper tackles the problem of diffeomorphometric geodesic landmark matching by learning optimal momenta using a derivative-free Bayesian inverse method, specifically the ensemble Kalman filter, and demonstrates efficient implementation with numerical results for various target shapes.
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 observation operators. We describe an efficient implementation of the algorithm and show several numerical results for various target shapes.