Pose-independent efficient gauge equivariant network for 3D mesh aneurysm segmentation

Accurate detection and segmentation of intracranial aneurysms (IAs) in three-dimensional medical imaging are crucial for effective diagnosis and therapeutic planning, given the complex nature of cerebral vascular structures. These aneurysms present significant challenges due to their variable sizes, unpredictable locations, diverse poses, and morphological heterogeneity, making consistent and reliable segmentation a critical yet demanding task in medical imaging. To effectively tackle these challenges, this study leverages the principles of anisotropic gauge equivariant convolutions (GEC) to propose a comprehensive framework that encompasses three key innovations: a Pose-Independent feature Representation (PIR) module, an Intra-layer Recurrent Convolutional (IRC) module and a boundary enhanced Laplacian loss. We introduce a novel PIR module, that utilizes anisotropic GEC to handle the inherent geometric complexities that independently of their poses. Our network, featuring a IRC module, strategically reuses convolutional weights to extend the global receptive field without additional parameters, thereby maintaining efficient high-resolution feature learning across mesh surfaces. Additionally, we incorporate a novel Laplacian loss that enforces boundary sharpness, greatly enhancing the delineation of aneurysm boundaries. The proposed method achieves superior segmentation accuracy, clearly delineating aneurysm necks without extensive data augmentation. Experiments on two datasets (IntrA and IntrANeurIST) verify the validity of the proposed method by outperforming the state of the art method together with ablation study. The method can be easily extended in the similar aneurysm segmentation such as abdominal aortic aneurysm and ophthalmic aneurysms.