Visually Stabilized Mamba U-Shaped Network With Strong Inductive Bias for 3-D Brain Tumor Segmentation

Multimodal magnetic resonance imaging (MRI) plays a crucial role in the precise segmentation of brain tumors, which is essential for clinical quantitative assessment, diagnostic processes, and treatment strategy planning. As a state-space model (SSM), Mamba has shown remarkable results in handling long-range dependency modeling of sequence data. However, it still faces challenges in inductive bias capability and stability. Therefore, a visually stabilized Mamba U-shaped network (VSMU-Net) with strong inductive bias is proposed. Inherent inductive bias mamba (IB Mamba) is presented to exploit the inherent scale invariance and local correlation of convolutions. It embeds multiscale contextual information and local feature information into the input sequence, thereby achieving precise image segmentation. In addition, a Mamba stabilization module (MSM) is designed, which uses a spectral gating network (SGN) to ensure that the eigenvalues in the Mamba state-space converge to the left half of the complex plane, thereby achieving stability in the Lyapunov sense. Extensive experiments on two brain tumor datasets, BraTS2020 and BraTS2021, demonstrate that the proposed method outperforms state-of-the-art methods. The source codes of the proposed method are available at https://github.com/nice66/VSMU.