## 3 Methodology
### Multi-Scale CNN Feature Extractor  
To address the challenges of scale diversity and background noise in remote sensing change detection, the proposed EMF targets effective extraction of ground objects and complex textures across multiple scales. Inspired by ECA [46] and Inception [47], we designed a Multi-Scale Feature Extraction Module (EMF) to achieve efficient extraction of multi-scale features and noise suppression. The module first constructs a cross-channel information interaction network through a lightweight channel attention mechanism, adaptively enhancing the spectral-textural feature responses related to the change detection task, while suppressing redundant channel information to improve the pertinence of feature expression. Then, based on the feature pyramid structure, hierarchical deformable convolution processing is performed on the input feature maps to simultaneously obtain multi-resolution features. The shallow network of the EMF captures fine-grained position information such as edges and contours, while the deep network extracts coarse-grained contextual information such as semantic categories. As shown in Figure 2a, the specific implementation of the EMF is as follows: The input features first enter the ECA Channel Attention Module, and the aggregated feature \(f_{a}\) is obtained through global average pooling. Subsequently, a one-dimensional convolution is used to generate the channel attention weight \(f_{b}\), with a convolution kernel size of \(k=5\). Then, the \(f_{b}\) is normalized by the sigmoid activation function to obtain the final channel attention weight \(f_{c}\). Element-wise multiplication of \(f_{c}\) and the input features is performed to achieve adaptive optimization of channel features, obtaining \(f_{d}\). Then, \(f_{d}\) enters the deformable convolution part with a feature pyramid structure. Before being input into the deformable convolution, the number of channels is reduced to \(1/4\) of the input feature channels via \(1\times 1\) convolution. The sizes of the deformable convolution kernels are \(1\), \(3\), \(5\), and \(7\), respectively, and the strides of all convolutions are set to \(1\). Through this process, multi-resolution features are simultaneously obtained. Finally, the multi-scale features are concatenated in the channel dimension to obtain the output feature map of the EMF. In the EMF, deformable convolution conducts a new type of convolution calculation within an \(n\times n\) grid. Offset values are set at each position in the \(n\times n\) grid to perform the convolution operation. Its workflow is shown in Figure 2b. The calculation process is described by Equations (1)-(3). In Equation (1), the original image feature \(f\) undergoes a traditional convolution operation within the regular grid \(R^{\prime}\) to obtain the output image feature \(z_{1}\). \[z_{1}(p_{0}^{*})=\sum_{p_{n}^{*}\in R^{\prime}}w(p_{n}^{*})f(p_{0}^{*}+p_{n}^ {*}) \tag{1}\]  
where \(w\) represents the weight to be updated, \(p_{0}^{*}\) represents each position within the regular grid \(R^{\prime}\), and \(p_{n}^{*}\) represents the position during the traversal of \(R^{\prime}\). Figure 2: (**a**) The details of the EMF. (**b**) The implementation of deformable convolution. Information Flow: Input features are processed by global pooling and 1D convolution to enhance task-related spectral and texture features, then feature extraction is performed via multi-branch deformable convolutions (\(1\times 1\), \(3\times 3\), \(5\times 5\), \(7\times 7\)), and finally multi-scale features are output after concatenation. In Equation (2), within the regular grid \(R^{\prime}\), an offset \(\Delta p_{n}^{*}\) is added to the position, and the original image feature \(f\) is convolved to obtain the output feature \(z_{2}\). \[z_{2}(p_{0}^{*})=\sum_{p_{n}^{*}\in R^{\prime}}w(p_{n}^{*})f(p_{0}^{*}+p_{n}^{*}+ \Delta p_{n}^{*}) \tag{2}\]  
In Equation (3), bi-linear interpolation \(G()\) is used to calculate \(p^{*}\) and \(q^{*}\).