  The reconstruction of cortical surfaces is a prerequisite for quantitative
analyses of the cerebral cortex in magnetic resonance imaging (MRI). Existing
segmentation-based methods separate the surface registration from the surface
extraction, which is computationally inefficient and prone to distortions. We
introduce Vox2Cortex-Flow (V2C-Flow), a deep mesh-deformation technique that
learns a deformation field from a brain template to the cortical surfaces of an
MRI scan. To this end, we present a geometric neural network that models the
deformation-describing ordinary differential equation in a continuous manner.
The network architecture comprises convolutional and graph-convolutional
layers, which allows it to work with images and meshes at the same time.
V2C-Flow is not only very fast, requiring less than two seconds to infer all
four cortical surfaces, but also establishes vertex-wise correspondences to the
template during reconstruction. In addition, V2C-Flow is the first approach for
cortex reconstruction that models white matter and pial surfaces jointly,
therefore avoiding intersections between them. Our comprehensive experiments on
internal and external test data demonstrate that V2C-Flow results in cortical
surfaces that are state-of-the-art in terms of accuracy. Moreover, we show that
the established correspondences are more consistent than in FreeSurfer and that
they can directly be utilized for cortex parcellation and group analyses of
cortical thickness.
