# A U-Shaped Architecture Based on Hybrid CNN and Mamba for Medical Image Segmentation
## 3 Method
### Hybrid Convolutional Mamba Block  
Effective medical image segmentation requires capturing both local details and global context. To achieve this, we design a lightweight and efficient feature extraction module. While CNN-based models are proficient at capturing local features, their ability to capture long-range dependencies remains inherently limited. In contrast, Mamba-based models excel at capturing global context through structured State Space mechanisms. However, they are often computationally intensive and may lack the inductive biases needed for learning precise local structures. To address the complementary limitations, we propose the Hybrid CNN-Mamba (HCM) block, a dual-branch module integrated into the HCMUNet framework. The HCM block is specifically designed to learn local and global representations simultaneously and efficiently. As illustrated in Figure 2, we adopt a channel-splitting strategy, which partitions the input feature map into two parallel branches for processing. One branch is processed by a convolutional branch to extract detailed local representations, while the other captures long-range dependencies via the Mamba branch, facilitating a balanced distribution of features across the branches. This design effectively reduces computational costs while maintaining high processing efficiency. The outputs of both branches are subsequently fused through channel concatenation to restore the original channel dimension. To address potential challenges such as information fragmentation and feature redundancy introduced by grouped processing, we incorporate a channel shuffle mechanism. This mechanism rearranges the channels of the output feature map, promoting effective information exchange between branches and ensuring more comprehensive utilization of features in each channel, thus enhancing feature diversity. In addition, activation functions are carefully selected to optimize feature expressiveness and training stability:  
Figure 1: The overall architecture of HCMUNet integrates the strengths of CNNs and the Mamba network through HCM blocks, which are designed to capture both local and global features effectively. To address spatial information loss induced by down-sampling, the SCDA module enhances cross-dimensional interactions by jointly leveraging channel and spatial attention. Furthermore, the resolution and dimensionality of feature maps are preserved within the bottleneck to maintain representational integrity.  
ReLU [34] is used in the convolutional branch, while SiLU [35] is employed in the Mamba branch to improve gradient flow and convergence. Due to its efficient balance of local and global feature extraction and a lower parameter count relative to ViT-based models, the HCM block presents a compelling solution for medical image segmentation.  
Given a feature input \(X\in\mathbb{R}^{H\times W\times C}\), the feature output after processing is \(Y\in\mathbb{R}^{H\times W\times C}\). \(X\) is divided equally into \(X_{1}\) and \(X_{2}\), followed by separate feature extraction in two branches. To ensure compatibility with convolution operations, the original feature map is rearranged for subsequent processing.