## 3 Proposed Superpixel-Based MSGATN
### Graph Construction  
To acquire credible prior information for GATN, a preliminary but representative graph construction is indispensable. In the proposed graph construction method, difference intensity and bitemporal remote sensing images are integrated to obtain comprehensive non-local change information, which advances the changed region detection in GATN. The overall graph construction can be further illustrated by the following steps. Initially, the pixel-wise difference intensity \(DI\in\mathbb{R}^{H\times W}\) can be represented as  
\[distance=\sqrt[2]{(T1-T2)^{2}} \tag{1}\]  
\[DI=\frac{distance-min(distance)}{max(distance)-min(distance)} \tag{2}\]  
After the difference intensity is acquired, the multi-scale superpixel segmentation over \(DI\) can be given as  
\[S^{DI}=\left\{p_{1},p_{2},\cdots,p_{N\_seg}\right\}=\text{SLIC}_{N\_seg}(DI) \tag{3}\]  
where \(\text{SLIC}_{N\_seg}(\cdot)\) denotes the simple linear iterative clustering with different numbers of segmented superpixels, and \(N\_seg\) represents the number of superpixels. Generally, the more superpixels, the smaller they are. In this case, we can obtain multi-scale superpixels for the multi-scale feature recognition of the proposed MSGATN. Then, the region adjacency co-relations \(\mathcal{G}_{sp}\) of \(S^{DI}\) can be modeled as  
\[\mathcal{G}_{sp}\big{(}\mathcal{V},\mathcal{E}_{sp}\big{)}=RAG\Big{(}S^{DI} \Big{)} \tag{4}\]  
in which \(RAG(\cdot)\) represents the region adjacency graph construction operation. The edges \(\mathcal{E}_{sp}\) are exploited to model the local and non-local relations inside bitemporal superpixels. To achieve this, the bitemporal superpixels need to be firstly acquired as \(S^{T1}=\left\{p_{1}^{1},p_{2}^{1},\cdots,p_{N\_seg}^{1}\right\}\) and \(S^{T2}=\left\{p_{1}^{2},p_{2}^{2},\cdots,p_{N\_seg}^{2}\right\}\). Then, the bitemporal features of these superpixels can be denoted as  
\[F^{1}=concat\Big{[}min\Big{(}S^{T1}\Big{)},max\Big{(}S^{T1}\Big{)},mean\Big{(} S^{T1}\Big{)},std\Big{(}S^{T1}\Big{)},skew\Big{(}S^{T1}\Big{)},kur\Big{(}S^{T1} \Big{)}\Big{]} \tag{5}\]  
\[F^{2}=concat\Big{[}min\Big{(}S^{T2}\Big{)},max\Big{(}S^{T2}\Big{)},mean\Big{(} S^{T2}\Big{)},std\Big{(}S^{T2}\Big{)},skew\Big{(}S^{T2}\Big{)},kur\Big{(}S^{T2} \Big{)}\Big{]} \tag{6}\]  
where \(concat(\cdot)\) indicates a feature-level integration, and \(min(\cdot)\), \(max(\cdot)\), \(mean(\cdot)\), \(std(\cdot)\), \(skew(\cdot)\), and \(kur(\cdot)\) represent the superpixel-wise minimum, maximum, mean, standard deviation, skewness, and kurtosis, respectively. Given these dependable and discriminative features of bitemporal superpixels, the nodes can be obtained as follows:  
\[\mathcal{V}_{f}=concat\Big{(}F^{1},F^{2}\Big{)} \tag{7}\]  
at which \(concat(\cdot)\) denotes a feature-wise concatenation. With the nodes and edges obtained, the input multi-scale graphs for MSGATN can be constructed as  
\[\mathcal{G}_{input}^{N\_seg}=\Big{(}\mathcal{V}_{f},\mathcal{E}_{sp}\Big{)} \tag{8}\]With different \(N\_seg\), input graphs of varied scales can be provided for the proposed MSGATN; thus, the multi-scale change objects obtain a finer cognition.