## 3 Methods
### Mamba Fusion Block
#### 3.2.1. Recombine Attention Module  
Inspired by convolutional attention mechanisms such as Squeeze-and-Excitation Attention [37] and Coordinate Attention Blocks [39], we propose a Recombine Attention Module (RAM) to address the issues of information conflict and inconsistency that arise during the fusion of feature maps with high-resolution differences. This module enables each pixel to focus on more specific contextual information from multi-level features during the aggregation phase, as illustrated in Figure 2. To explain in detail, given two input feature maps with different resolutions, corresponding to Figure 2b,d, let us assume \(Y\) is the feature map from a deeper level. In our network, this can be specifically represented as:  
* Cross-branch connection scenario: \(X\) is the detail feature map output from stage 5 of the high-resolution branch, and \(Y\) is the context feature map output from stage 5 of the low-resolution branch. * Cross-stage connection scenario: \(X\) is the output feature map from the cross-branch connection, and \(Y\) is the deep feature map output from stage 6 of the low-resolution branch. To enhance the RAM's overall grasp of spatial and texture information, as well as its sensitivity to the spatial location of information, the input features \(X\) and \(Y\) are first fused to obtain feature (a), which is then input into a carefully designed attention calculation unit to acquire attention weights, as shown in the dashed box in Figure 2. Specifically, the fused feature map (a) of \(X+Y\) is input into global average pooling and global max pooling layers in parallel, obtaining a pair of location-aware feature encodings along the \(H\) and \(W\) dimensions. At this stage, the transformation output of the global average pooling at height \(H\) in channel \(c\) can be represented as:  
\[z_{c}^{h}(h)=\frac{1}{W}\sum_{0\leq i\leq W}f_{c}^{X+Y}(h,i). \tag{2}\]  
Figure 2: Schematic diagram of the Recombine Attention Module (RAM) structure. In the diagram, the spatial dimensions of the feature maps at each stage are indicated. The images within the dashed boxes represent intermediate process feature maps, which are connected to the corresponding positions in the RAM with dashed lines. The two input branches on the left represent the input feature maps with high-resolution differences, corresponding to feature maps (**b**,**d**). After processing, the feature maps of each branch can be compared with (**b**) and (**d**) by (**c**) and (**e**), respectively. The feature maps after passing through the RAM can be compared with (**a**,**f**). where \(z_{c}^{h}\in\mathbb{R}^{c\times H\times 1}\) and \(f_{c}^{X+Y}\) represent the fused feature map of \(X+Y\) in channel \(c\). Similarly, if we let \(Max(\cdot)\) denote the global max pooling transformation function, then the transformation output of the global max pooling at width \(W\) in channel \(c\) can be represented as:  
\[z_{c}^{w}(w)=Max(f_{c}^{X+Y}(h,w)). \tag{3}\]  
Next, the feature sequences obtained from the aforementioned transformations are projected into the same spatial dimension for concatenation. The concatenated feature map is then processed by a combined transformation function \(F\), which consists of \"\(1\times 1\) convolution + BN + ReLU\", to encode the spatial information of the feature map in both the horizontal and vertical directions, resulting in:  
\[f=F([z^{h},z^{w}]) \tag{4}\]  
where \(f\in\mathbb{R}^{c/r\times(H+W)\times 1}\) represents the intermediate feature map generated and \(r\) denotes the channel reduction ratio, which is used to control the number of parameters in the computation process. The notation \([\cdot,\cdot]\) represents the concatenation operation. Finally, the \(f\) is split into two tensors, and each is processed through a \(1\times 1\) convolution transformation. The width and height of the two convolutions are restored to match those of \(z^{w}\) and \(z^{h}\), respectively.