  The automated segmentation of cortical areas has been a long-standing
challenge in medical image analysis. The complex geometry of the cortex is
commonly represented as a polygon mesh, whose segmentation can be addressed by
graph-based learning methods. When cortical meshes are misaligned across
subjects, current methods produce significantly worse segmentation results,
limiting their ability to handle multi-domain data. In this paper, we
investigate the utility of E(n)-equivariant graph neural networks (EGNNs),
comparing their performance against plain graph neural networks (GNNs). Our
evaluation shows that GNNs outperform EGNNs on aligned meshes, due to their
ability to leverage the presence of a global coordinate system. On misaligned
meshes, the performance of plain GNNs drop considerably, while E(n)-equivariant
message passing maintains the same segmentation results. The best results can
also be obtained by using plain GNNs on realigned data (co-registered meshes in
a global coordinate system).
