Dual-branch geometric algebra graph network with pyramid fusion for deformable medical image registration

Deformable medical image registration (DMIR) is a fundamental component in contemporary medical image analysis. Graph Neural Networks (GNNs) offer strong spatial modeling, but deeper, multi-stage GNNs often lead to over-smoothed features across different anatomical areas. This reduces sensitivity to fine structural details, limiting registration accuracy. Efficiently handling large volumetric deformations remains a significant challenge. We introduce the Geometric Algebra-based Graph Neural Networks (GAGNN) and Pyramid Network mechanism to address these challenges. GAGNN leverages geometric algebra to restructure spatial representations in non-Euclidean domains, enabling effective capture and integration of image features through enhanced global context modeling. Pyramid Network adopts a progressive strategy, leveraging high-level features to predict the deformation field accurately. Additionally, a dilated residual fusion block is used to combine multi-scale features by expanding the receptive field through dilated convolutions, while residual connections help preserve spatial details. Extensive qualitative and quantitative experiments were conducted on two publicly available 3D datasets to validate the proposed approach. The proposed method surpasses PIViT by achieving Dice score improvements of 0.9% and 0.6% on the two evaluated 3D datasets, respectively, while maintaining a comparable level of voxel folding. Moreover, it demonstrates reduced computational time, highlighting its efficiency in achieving accurate and smooth registration with lower time complexity.