## 3 Model Structure
### Construct Graph Structure  
#### 3.2.1 Construct Intra-Frame Graph Structure  
Research shows that models based on planar convolutions, such as CNN, RNN, and LSTM, could be applied to target detection tasks. However, directly processing images as primary data when extracting spatial and temporal features increased the overall computational load of the model. Moreover, the large number of parameters posed significant challenges to the storage space of some terminal devices. Therefore, when the input data volume was large or when the system had strong real-time requirements, the computational time overhead was significantly increased. As a result, we adopted the lower computational cost approach of graph convolution to build the target tracking model. We used  
Figure 4: The results of different scale superpixel segmentation: **(a)** Raw image; **(b)** The result of superpixel segmentation scale 100; **(c)** The result of superpixel segmentation scale 196; **(d)** The result of superpixel segmentation scale 256; **(e)** The result of superpixel segmentation scale 324; **(f)** The result of superpixel segmentation scale 1024.  
the superpixel segmentation results to construct the graph structure for the tracked target, with the superpixel seeds serving as the nodes of the graph. We constructed the graph structure for each frame in the target tracking video in the same manner. The process could be expressed as follows:  
\[G_{m}=\tau(S_{m}),m=1,\ldots,M \tag{4}\]  
where \(G_{m}\) was the graph structure computed for the mth frame of video \(I\), \(S_{m}\) represented the superpixel segmentation result of the \(m\)th frame of the target tracking video, \(\tau()\) was the graph structure construction function, and \(M\) was the total number of frames in the target tracking video.The graph structure consisted of the adjacency matrix, degree matrix, and feature matrix, and could be expressed in the following form:  
\[G_{m}=\{A,D,F_{m}\},m=1,\ldots,M \tag{5}\]  
where \(A\) represented the adjacency matrix between the intra-frame nodes, and its calculation process could be expressed as follows:  
\[A_{t-1,t}= \begin{bmatrix}\alpha_{11}&\cdots&\alpha_{1N}\\ \vdots&\ddots&\vdots\\ \alpha_{N1}&\cdots&\alpha_{NN}\end{bmatrix}  \tag{6}\]  
\[a_{ij}= \begin{cases}1,&\text{if }s_{i}\leftrightarrow s_{j},\\ 0,&\text{if }s_{i}\leftrightarrow s_{j},\end{cases} \quad i=1,\ldots,N,\quad j =1,\ldots,N \tag{7}\]  
Here, \(s_{i}\leftrightarrow s_{j}\) indicated that superpixel block \(s_{i}\) was spatially adjacent to superpixel block \(s_{j}\), and, correspondingly, \(s_{i}\leftrightarrows_{j}\) indicated that the two superpixel blocks were not spatially adjacent. \(D\) was the degree matrix of the nodes, and its calculation process could be expressed as follows:  
\[D= \begin{bmatrix}\sum_{j=1}^{N}a_{1j}&\cdots&0\\ \vdots&\ddots&\vdots\\ 0&\cdots&\sum_{j=1}^{N}a_{Nj}\end{bmatrix}  \tag{8}\]  
\(F_{m}\) was the feature matrix of the graph nodes in the \(m\)th frame. We used the average brightness \(L_{t}\) of all superpixel blocks in the \(m\)th frame as the threshold, and constructed the feature matrix using the binarized segmentation result. Its calculation process could be expressed as follows:  
\[F_{m}= \begin{bmatrix}y_{m1}\\ \vdots\\ y_{mN}\end{bmatrix}  \tag{9}\]  
\[y_{mm}= \begin{cases}1,&L_{mm}>L_{t},\\ 0,&L_{mm}\leq L_{t}.\end{cases}  \tag{10}\]  
\[L_{t}=\frac{1}{n}\sum_{l=1}^{n}L_{n} \tag{11}\]  
\(L_{n}\) was obtained using Equation (3), while \(L_{t}\) was independently calculated for each frame and remained fixed within that frame. This statistical approach ensured that the inter-frame adjacency criteria were consistent, data-dependent, and repeatable across the entire dataset. At this point, we had completed the construction of the intra-frame graph structure. In the first layer of the proposed model, we used a graph convolutional network in combination with the intra-frame graph structure to calculate the regions of the target within the frame. The specific computation process of the model was detailed in Section 3.3.