STF: A spherical transformer for versatile cortical surfaces applications.

Inspired by the remarkable success of attention mechanisms in various applications, there is a growing need to adapt the Transformer architecture from conventional Euclidean domains to non-Euclidean spaces commonly encountered in medical imaging. Structures such as brain cortical surfaces, represented by triangular meshes, exhibit spherical topology and present unique challenges. To address this, we propose the Spherical Transformer (STF), a versatile backbone that leverages self-attention for analyzing cortical surface data. Our approach involves mapping cortical surfaces onto a sphere, dividing them into overlapping patches, and tokenizing both patches and vertices. By performing self-attention at patch and vertex levels, the model simultaneously captures global dependencies and preserves fine-grained contextual information within each patch. Overlapping regions between neighboring patches naturally enable efficient cross-patch information sharing. To handle longitudinal cortical surface data, we introduce the spatiotemporal self-attention mechanism, which jointly captures spatial context and temporal developmental patterns within a single layer. This innovation enhances the representational power of the model, making it well-suited for dynamic surface data. We evaluate the Spherical Transformer on key tasks, including cognition prediction at the surface level and two vertex-level tasks: cortical surface parcellation and cortical property map prediction. Across these applications, our model consistently outperforms state-of-the-art methods, demonstrating its ability to effectively model global dependencies and preserve detailed spatial information. The results highlight its potential as a general-purpose framework for cortical surface analysis.