Geometric deep learning with adaptive full-band spatial diffusion for accurate, efficient, and robust cortical parcellation

Cortical parcellation delineates the cerebral cortex into distinct regions according to their distinctiveness in anatomy and/or function, which is a fundamental preprocess in brain cortex analysis and can influence the accuracy and specificity of subsequent neuroscientific research and clinical diagnosis. Conventional methods for cortical parcellation involve spherical mapping and multiple morphological feature computation, which are time-consuming and prone to error due to the spherical mapping process. Recent geometric learning approaches have attempted to automate this process by replacing the registration-based parcellation with deep learning-based methods. However, they have not fully addressed spherical mapping and cortical features quantification, making them sensitive to variations in mesh structures. In this work, to directly parcellate original surfaces in individual space with minimal preprocessing, we present a full-band spectral-accelerated spatial diffusion strategy for stable information propagation on highly folded cortical surfaces, contributing to adaptive learning of fine-grained geometric representations and the construction of a compact deep network (termed Cortex-Diffusion) for fully automatic parcellation. Using only raw 3D vertex coordinates and having merely 0.49 MB of learnable parameters, it demonstrates state-of-the-art parcellation accuracy, efficiency, and superior robustness to mesh resolutions and discretization patterns in both the cases of infant and adult brain imaging datasets.