  Cortical surface reconstruction (CSR) from MRI is key to investigating brain
structure and function. While recent deep learning approaches have
significantly improved the speed of CSR, a substantial amount of runtime is
still needed to map the cortex to a topologically-correct spherical manifold to
facilitate downstream geometric analyses. Moreover, this mapping is possible
only if the topology of the surface mesh is homotopic to a sphere. Here, we
present a method for simultaneous CSR and spherical mapping efficiently within
seconds. Our approach seamlessly connects two sub-networks for white and pial
surface generation. Residual diffeomorphic deformations are learned iteratively
to gradually warp a spherical template mesh to the white and pial surfaces
while preserving mesh topology and uniformity. The one-to-one vertex
correspondence between the template sphere and the cortical surfaces allows
easy and direct mapping of geometric features like convexity and curvature to
the sphere for visualization and downstream processing. We demonstrate the
efficacy of our approach on infant brain MRI, which poses significant
challenges to CSR due to tissue contrast changes associated with rapid brain
development during the first postnatal year. Performance evaluation based on a
dataset of infants from 0 to 12 months demonstrates that our method
substantially enhances mesh regularity and reduces geometric errors,
outperforming state-of-the-art deep learning approaches, all while maintaining
high computational efficiency.
