Vertex Correspondence and Self-Intersection Reduction in Cortical Surface Reconstruction

Mesh-based cortical surface reconstruction is essential for neuroimaging, enabling precise measurements of brain morphology such as cortical thickness. Establishing vertex correspondence between individual cortical meshes and group templates allows vertex-level comparisons, but traditional methods require time-consuming post-processing steps to achieve vertex correspondence. While deep learning has improved accuracy in cortical surface reconstruction, optimizing vertex correspondence has not been the focus of prior work. We introduce Vox2Cortex with Correspondence (V2CC), an extension of Vox2Cortex, which replaces the commonly used Chamfer loss with L1 loss on registered surfaces. This approach improves inter- and intra-subject correspondence, which makes it suitable for direct group comparisons and atlas-based parcellation. Additionally, we analyze mesh self-intersections, categorizing them into minor (neighboring faces) and major (non-neighboring faces) types.To address major self-intersections, which are not effectively handled by standard regularization losses, we propose a novel Self-Proximity loss, designed to adjust non-neighboring vertices within a defined proximity threshold. Comprehensive evaluations demonstrate that recent deep learning methods inadequately address vertex correspondence, often causing inaccuracies in parcellation. In contrast, our method achieves accurate correspondence and reduces self-intersections to below 1% for both pial and white matter surfaces.