Eyes on the Prize: Improved Registration via Forward Propagation

We develop a robust method for improving pairwise correspondences for a collection of shapes in a metric space. Given a collection $f_{ji}: S_{i} \to S_{j}$ of correspondences, we use a simple metric condition, which has a natural interpretation when considering the analogy of parallel transport, to construct a Gibbs measure on the space of correspondences between any pair of shapes that are generated by the $f_{ji}.$ We demonstrate that this measure can be used to more accurately compute correspondences between feature points compared to currently employed, less robust methods. As an application, we use our results to propose a novel method for computing homeomorphisms between pairs of shapes that are similar to one another after alignment.