Isotropic spherical region enlargement and background contraction for sulcal labeling

The cortical sulci of the posterior medial cortex play a crucial role in cognitive and behavioral functions. However, automatic labeling of these sulci is challenging due to severe class imbalance (i.e., only a small portion of the cortex is labeled) and high neuroanatomical variability. To tackle these challenges, we propose an effective spherical deformation-based sulcal labeling method that automatically enlarges the sulcal regions of interest (ROIs) while contracting unlabeled regions. This allows the proposed method to capture detailed sulcal patterns more effectively and suppress confounding analogous patterns. Specifically, we introduce a generic expansion function with a generalized condition for homeomorphic isotropic deformation. Based on this, we propose a parameterizable exponential expansion design which provides flexibility to fully accommodate non-uniform spatial densities of sulcal ROIs. We also propose an end-to-end SO(3)-equivariant model to enhance its expressive power while improving generalization capability under data scarcity. Furthermore, we offer an explicit regularization on the extent of deformation to provide the stable enlargement of ROIs while preventing the unintended contraction. In the experiments, we show that the proposed method outperforms baseline methods on both adult and pediatric cohorts, particularly in small and variable ROIs. The most notable improvement of 11.16% in Dice score was observed in the smallest sulcus, which is hominoid-specific and implicated in cognition and different neurodevelopmental and clinical disorders. Strong negative correlations between performance gains and ROI size confirm its suitability for labeling small sulci.