## 3 Methodology
### Graph Fusion Module  
While CNNs and transformers effectively extract local and global features, they face challenges in capturing structured spatial relationships--particularly in complex remote sensing scenes. Pixels in remote sensing images exhibit not only local attributes but also long-range, structured dependencies tied to object boundaries, textures, shapes, and inter-object interactions. To better model such spatial structures, we introduce a _Graph Fusion Module_ based on GCNs. This module enhances the semantic coherence and boundary accuracy of the segmentation results by learning topological relations across multi-source features. As shown in Figure 5, the multi-source graph convolution fusion network constructs dynamic graphs and learns adaptive weights to model the topological relationships between local and global features. The specific design process is as follows:  
(1) Graph Construction: The module constructs a multi-adjacency graph structure, converting local features, global features, and fused features into graph nodes, and performs graph convolution operations to enhance the expression of target boundaries, structural relationships, and spatial consistency. First, the local, global, and fused features are uniformly upsampled to generate feature maps:  
\[\text{feature\_map}=\text{UpSample}(\text{local\_features},\text{global\_ features},\text{fused\_features}). \tag{15}\]  
These feature maps are flattened to form the node feature matrix \(H\) and the adjacency matrix \(A\).  
(2) Graph Convolution Operation: The graph convolution operation updates the node features \(H\) as follows:  
\[H^{\prime}=\sigma(D^{-1/2}AD^{-1/2}HW), \tag{16}\]  
where \(D\) is the degree matrix, \(A\) is the adjacency matrix, \(W\) is the learnable weight matrix, and \(\sigma\) is the activation function. Here, the adjacency matrix \(A\in\mathbb{R}^{N\times N}\) is constructed using dot-product attention between each pair of nodes to capture the semantic similarity among spatial regions. The degree matrix \(D\) is a diagonal matrix where each element \(D_{ii}\) represents the sum of the \(i\)-th row of \(A\), i.e., \(D_{ii}=\sum_{j}A_{ij}\). The graph convolution operation is performed separately on local features, global features, and fused features. This formulation allows information to propagate across semantically related but spatially distant regions, which is especially beneficial in high-resolution remote sensing imagery.  
Figure 4: The main structure of the pyramid self-learning fusion module.  
(3) Weighted Fusion: A learnable vector \(\gamma=[\gamma_{1},\gamma_{2},\gamma_{3}]\) is used to perform weighted fusion on the graph convolution outputs of local, global, and fused features:  
\[\text{fused\_output}=\gamma_{1}H^{\prime}_{\text{local}}+\gamma_{2}H^{\prime}_ {\text{global}}+\gamma_{3}H^{\prime}_{\text{fused}}. \tag{17}\]  
The weights \(\gamma_{1}\), \(\gamma_{2}\), and \(\gamma_{3}\) are initialized equally and normalized using a softmax function during training to ensure numerical stability and interpretability. This adaptive fusion mechanism enables the model to dynamically emphasize the most informative source according to different scene contexts or object categories.  
(4) Category Mapping and Feature Recovery: Finally, the network maps the fused output to the category space using a \(1\times 1\) convolution and recovers the features to the input size using bilinear interpolation, thus obtaining the final semantic prediction map:  
\[\text{pred\_map}=\text{BilinearInterpolation}(\text{Conv}_{1\times 1}(\text{fused\_output})). \tag{18}\]  
This process is simple and efficient, supports end-to-end training, and is particularly suitable for segmentation tasks in remote sensing images with complex structures and diverse scales.