  When developing tools for automated cortical segmentation, the ability to
produce topologically correct segmentations is important in order to compute
geometrically valid morphometry measures. In practice, accurate cortical
segmentation is challenged by image artifacts and the highly convoluted anatomy
of the cortex itself. To address this, we propose a novel deep learning-based
cortical segmentation method in which prior knowledge about the geometry of the
cortex is incorporated into the network during the training process. We design
a loss function which uses the theory of Laplace's equation applied to the
cortex to locally penalize unresolved boundaries between tightly folded sulci.
Using an ex vivo MRI dataset of human medial temporal lobe specimens, we
demonstrate that our approach outperforms baseline segmentation networks, both
quantitatively and qualitatively.
