BFMMorph: a dual-stream brain image registration framework based on Bidirectional Fourier Mamba

Abstract

Abstract. Three-dimensional (3D) brain image registration is a vital branch of medical image processing, with broad applications in disease monitoring, preoperative planning, and multimodal fusion. The current registration models based on the U-Net framework are limited by the implicit feature learning paradigm between image pairs and direct prediction of deformation fields, resulting in poor ability to simulate large deformations and complex structural differences, thereby affecting registration performance. To address these issues, we propose an end-to-end dual-stream unsupervised registration framework based on U-Net, named BFMMorph. Specifically, BFMMorph adopts a dual-stream input, performs self-encoding using a Bidirectional Fourier Mamba (BFM), and leverages a Forward Match module (FMM) to enhance cross-volume structural difference modeling. Finally, a progressive Deformation Field Enhancement Estimator is used to complete the deformation field fitting. Unlike previous methods that rely solely on implicit learning, BFMMorph explicitly guides the deformation field estimation process. Extensive experiments conducted on three publicly available 3D brain image datasets, IXI, OASIS, and SR-Reg, demonstrate that BFMMorph achieves superior registration accuracy and computational efficiency compared to state-of-the-art methods, highlighting its excellent performance.