Learning landmark geodesics using Kalman ensembles

TL;DR

This paper introduces a novel derivative-free Bayesian inverse approach using the ensemble Kalman filter to learn optimal landmark geodesics in diffeomorphometric matching, improving efficiency and accuracy.

Contribution

It applies the ensemble Kalman filter to landmark matching, providing a new method for learning diffeomorphic mappings without derivatives.

Findings

Effective numerical results on various target shapes

Demonstrated efficiency of the ensemble Kalman filter approach

Improved landmark matching accuracy

Abstract

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.