Geometric Algebra-based Dual-branch Graph Convolutional Network for Deformable Medical Image Registration with...

Deformable medical image registration (DMIR) plays a central role in modern medical image analysis. Recent studies involving Graph Neural Networks (GCNs) have demonstrated promising performance in medical image registration tasks due to their strong ability to aggregate and leverage spatial features. However, as GCN models become deeper and more complex, particularly with multi-stage deployments, the feature extraction mechanism often leads to increased feature similarity across different anatomical regions. This can reduce the ability of the model to capture fine-grained structural differences, thereby diminishing the accuracy and effectiveness of the registration process. Accurate and efficient deformable registration remains challenging, especially with large volumetric deformations. We introduce the Geometric Algebra-based MorphNet (GAMN) and Bi-Directional Flow (BDF) mechanism to address these challenges. GAMN utilizes geometric algebra to restructure geometric information in non-Euclidean space, enabling the effective capture and integration of image features through global contextual interactions. BDF adopts a progressive strategy, leveraging high-level features to predict the deformation field accurately. Additionally, we employ Specified Skip Propagation (SSP), which enhances the registration process by efficiently transferring essential features across different levels, ensuring accurate and consistent alignment through adaptive feature propagation at each stage. We evaluated the proposed method through both qualitative and quantitative analyses using two 3D datasets (OASIS and LPBA40). The results showed a significant improvement in Dice similarity scores of 0.7% and 1.4%, respectively, across both datasets compared with the PIViT baseline method. Comprehensive ablation experiments were conducted to assess the role of each module, demonstrating their positive impact on the proposed network performance.