  Brain surface-based image registration, an important component of brain image
analysis, establishes spatial correspondence between cortical surfaces.
Existing iterative and learning-based approaches focus on accurate registration
of folding patterns of the cerebral cortex, and assume that geometry predicts
function and thus functional areas will also be well aligned. However,
structure/functional variability of anatomically corresponding areas across
subjects has been widely reported. In this work, we introduce a learning-based
cortical registration framework, JOSA, which jointly aligns folding patterns
and functional maps while simultaneously learning an optimal atlas. We
demonstrate that JOSA can substantially improve registration performance in
both anatomical and functional domains over existing methods. By employing a
semi-supervised training strategy, the proposed framework obviates the need for
functional data during inference, enabling its use in broad neuroscientific
domains where functional data may not be observed. The source code of JOSA will
be released to the public at https://voxelmorph.net.
