  Cortical surface registration is a fundamental tool for neuroimaging analysis
that has been shown to improve the alignment of functional regions relative to
volumetric approaches. Classically, image registration is performed by
optimizing a complex objective similarity function, leading to long run times.
This contributes to a convention for aligning all data to a global average
reference frame that poorly reflects the underlying cortical heterogeneity. In
this paper, we propose a novel unsupervised learning-based framework that
converts registration to a multi-label classification problem, where each point
in a low-resolution control grid deforms to one of fixed, finite number of
endpoints. This is learned using a spherical geometric deep learning
architecture, in an end-to-end unsupervised way, with regularization imposed
using a deep Conditional Random Field (CRF). Experiments show that our proposed
framework performs competitively, in terms of similarity and areal distortion,
relative to the most popular classical surface registration algorithms and
generates smoother deformations than other learning-based surface registration
methods, even in subjects with atypical cortical morphology.
