Eyes on the Prize: Improved Biological Surface Registration via Forward Propagation
This work addresses the challenge of robust and high-resolution surface registration for evolutionary biology, offering incremental improvements over existing methods.
The paper tackles the problem of accurately registering biological surfaces that are significantly nonisometric by proposing a novel algorithm that combines initial correspondences with manifold learning to improve correspondence accuracy. It demonstrates improved accuracy on a diverse dataset from evolutionary biology and shows how to compute consistent homeomorphisms between surfaces.
Many algorithms for surface registration risk producing significant errors if surfaces are significantly nonisometric. Manifold learning has been shown to be effective at improving registration quality, using information from an entire collection of surfaces to correct issues present in pairwise registrations. These methods, however, are not robust to changes in the collection of surfaces, or do not produce accurate registrations at a resolution high enough for subsequent downstream analysis. We propose a novel algorithm for efficiently registering such collections given initial correspondences with varying degrees of accuracy. By combining the initial information with recent developments in manifold learning, we employ a simple metric condition to construct a measure on the space of correspondences between any pair of shapes in our collection, which we then use to distill soft correspondences. We demonstrate that this measure can improve correspondence accuracy between feature points compared to currently employed, less robust methods on a diverse dataset of surfaces from evolutionary biology. We then show how our methods can be used, in combination with recent sampling and interpolation methods, to compute accurate and consistent homeomorphisms between surfaces.