## 3 Proposed Method
### Multi-Granularity Embedding Module
#### 3.1.1 Spatial Multi-Granularity Embedding Module  
The spatial multi-granularity embedding module employs a three-branch architecture designed to extract multi-scale and multi-level semantic features from spatial information. Each branch comprises two convolutional layers. The first layer implements dilated convolution with a kernel size of \(3\times 3\) across varying dilation rates, while the second layer utilizes a \(1\times 1\) convolution. This architecture is strategically designed to capture semantic features from diverse local receptive fields and to integrate contextual information effectively. The three branches utilize a trapezoidal input strategy that progressively amalgamates the outputs from different branches, thereby providing a more comprehensive representation of the spatial features. The specific algorithmic flow is delineated as follows.  
For an input feature map \(X\in\mathbb{R}^{B\times h\times w\times c}\), where \(B\) denotes the batch size, \(h\) and \(w\) represent the spatial dimensions of the feature map, and \(c\) indicates the number of channels.  
First Branch: The operation \(Conv_{1,1}\) is performed, which involves applying a \(3\times 3\) dilated convolution with a dilation rate of 1, followed by batch normalization (BN) and a ReLU activation function. Subsequently, the operation \(Conv_{1,2}\) is executed, which applies a \(1\times 1\) convolution with BN and ReLU, resulting in \(X_{1,2}\). The expression can be formally represented as:  
\[X_{1,2}=\delta(Conv_{1,2}(\delta(Conv_{1,1}(X)))) \tag{3}\]  
Second Branch: Starting with the input \(X+X_{1,2}\), the operation \(Conv_{2,1}\) is performed, utilizing a \(3\times 3\) dilated convolution with a dilation rate of 2, followed by BN and ReLU.  
Next, \(Conv_{2,2}\) is executed with a \(1\times 1\) convolution, yielding \(X_{2,2}\). This can be expressed mathematically as follows:  
\[X_{2,2}=\delta(Conv_{2,2}(\delta(Conv_{2,1}(X+X_{1,2})))) \tag{4}\]  
Third Branch: With \(X+X_{1,2}+X_{2,2}\) as input, the operation \(Conv_{3,1}\) is initiated using a \(3\times 3\) dilated convolution with a dilation rate of 3, followed by BN and ReLU. Finally, \(Conv_{3,2}\) is performed utilizing a \(1\times 1\) convolution, resulting in \(X_{3,2}\). This expression is represented as follows:  
\[X_{3,2}=\delta(Conv_{3,2}(\delta(Conv_{3,1}(X+X_{1,2}+X_{2,2})))) \tag{5}\]  
Fusion and Transformation: The results \(X_{1,2}\), \(X_{2,2}\), and \(X_{3,2}\) are concatenated, followed by a \(1\times 1\) convolution with BN and ReLU, producing \(\bar{X}\):  
\[\bar{X}=\delta(Conv(Concat(X_{1,2},X_{2,2},X_{3,2}))) \tag{6}\]  
A rearrangement operation is executed to modify the dimensions of the feature map, resulting in the spatial embedded Token \(X_{spa\_Token}\). Consequently, the output \(X_{spa\_Token}\in R^{\mathbb{R}\times(w\times h)\times c}\) consists of \((w\times h)\) spatially embedded tokens corresponding to both the elements in the feature image, and \(C\) representing the channels of the convolution output feature map, depicted in the upper part of Figure 2.  
\[X_{spa\_Token}=Rearrange(\bar{X}) \tag{7}\]