Discrete Optimisation for Group-wise Cortical Surface Atlasing

This paper presents a novel method for cortical surface atlasing. Group-wise registration is performed through a discrete optimisation framework that seeks to simultaneously improve pairwise correspondences between surface feature sets, whilst minimising a global cost relating to the rank of the feature matrix. It is assumed that when fully aligned, features will be highly linearly correlated, and thus have low rank. The framework is regularised through use of multi-resolution control point grids and higher-order smoothness terms, calculated by considering deformation strain for displacements of triplets of points. Accordingly the discrete framework is solved through high-order clique reduction. The framework is tested on cortical folding based alignment, using data from the Human Connectome Project. Preliminary results indicate that group-wise alignment improves folding correspondences, relative to registration between all pair-wise combinations, and registration to a global average template.