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.