Vector-Aware Anisotropic Gauge Equivariant Mesh Convolution Network for 3D Aneurysm Detection

Automatic detecting intracranial aneurysms (IAs) poses significant challenges due to their diversity, varying locations, and complex classifications by size, shape, and phenotype. Current shape-based IAs detection methods, while promising, often neglect the topological connectivity of IAs vertices and the variable traits of the aneurysm’s neck, leading to fragmented detections. To address these issues, we present a mesh convolutional neural network based on gauge equivariant convolution to leverage the topological and geometric features of 3D mesh models. Our network comprises four key components: anisotropic message passing (AMP) on mesh surfaces, gauge equivariant convolution (GEC), vector-aware feature reconstruction (VFR), and a pooling-free convolutional architecture. AMP ensures accurate detection of IAs from surrounding vessels by utilizing topological connectivity and anisotropic relationships between mesh vertices. GEC offers rotational equivariance for consistently learning geometric features, improving feature learning stability and efficiency. VFR preserves the geometric and directional integrity of the vector features, enriching the representational capacity of the network. The pooling-free convolutional architecture captures local and global geometric nuances of 3D meshes, achieving precise IAs detection and producing sharper IAs boundaries. Tests on the IntrA dataset show our method outperforms the current best by 1.83% and 1.02% in mIoU and mDSC, respectively.