## 3 Proposed Method
### Preliminary Object Tracking Module  
In the preliminary object tracking module, the base structure of OSTrack-384 [19] with powerful SOT performance-speed balance perfectly fits our goal, which is selected as the main component of the module. The post-processor NeighborTrack [30] is used to optimize the preliminary tracking results. It is a method that uses the confidence score output from the backbone of an object tracking model to automatically derive the information of neighbor regions that are not obscured.  
The bipartite matching model in TRTrack maintains both the candidate pool \(P^{c}\) and the neighbor pool \(P^{n}\). The former is used to select the most suitable prediction tracking object, and the latter is used to verify the selected prediction tracking object. It converts the association problem between the template and search region in SOT into the bipartite matching problem between the candidate tracklets \(S^{c}=P^{c}\) and the neighbor tracklets \(S^{n}=P^{n}\cup\{\eta\}\), where \(\eta=\{b_{t-1},\ldots,b_{t-\tau}\}\) represents the real prediction tracking boxes, \(t\) is the sequence number of frames at any time, and \(\tau\) is the number of frames to be traced. The weight \(w_{ij}\) on the edge between two nodes, \(\xi_{i}^{t}\in S^{c}\) and \(\zeta_{j}^{t}\in S^{n}\), represents the average Jaccard overlap calculation between the two tracklets. This means that if \(\xi_{i}^{t}=\left(b_{t-1}^{c},\ldots,b_{t-\tau}^{c}\right)\) and \(\zeta_{j}^{t}=\left(b_{t-1}^{n},\ldots,b_{t-\tau}^{n}\right)\), the formula of the weight is denoted as  
\[w_{ij}=\frac{1}{\tau}\sum_{k=t-\tau}^{t-1}IoU(b_{k}^{c},b_{k}^{n}) \tag{1}\]  
where \(IoU\) represents the Jaccard overlap calculation between the two prediction bounding boxes, which reflects the similarity between the candidate tracklets \(S^{c}\) and the neighbor tracklets \(S^{n}\).  
It is worth noting that the Hopcroft-Karp algorithm, which can achieve the maximum matching of the bipartite graph and has high computation efficiency, is introduced to implement bipartite matching. The time complexity of it is \(O=\left(|E|\sqrt{|V|}\right)\), where \(|E|\) is the number of edges of the bipartite graph and \(|V|\) is the number of vertices in the bipartite graph. The specific formula of the improved bipartite matching result is as follows  
\[mat_{t}=HK(S^{c},S^{n}) \tag{2}\]  
where \(mat_{t}\) indicates the bipartite matching result of the \(I_{t}\) frame. If \(S^{c}\) does not match \(S^{n}\), which means the candidate tracklet \(\zeta_{m}^{t}\) does not match the target tracklet \(\eta\), it indicates that the target object is obscured or disappears. A function \(at\_bdy\) is added to judge whether the prediction bounding box \(b_{t}\) of the current frame \(I_{t}\) is at the shot boundary. The equation is as follows  
\[\begin{array}{c}at\_bdy(b_{t})=\left(x\in\left(0,\frac{W}{13}\right)\right) \ \cap\ \left(y\in\left(0,\frac{H}{13}\right)\right)\ \cap\ \left(x+w\in\left(\frac{12W}{13},W\right)\right)\\ \cap\left(y+h\in\left(\frac{12H}{13},H\right)\right)\end{array} \tag{3}\]where \(b_{t}=(x,y,w,h)\) are the bounding box containing abscissas and ordinates of the upper left corner and the size, \(W\) is the width of the video, and \(H\) is the length of the video. The final judgment of whether the target leaves the shot is shown as  
\[out_{t}=\widetilde{mat_{t}}\ \cap\ at\_bdy(b_{t}) \tag{4}\]  
where \(\widetilde{mat_{t}}\) represents the inverse value of \(mat_{t}\), and \(out_{t}\in\{0,1\}\) is the judgment variable of whether the target leaves the shot in the frame \(I_{t}\). If the value is 1, the target has left the shot. Conversely, a value of 0 means that the target is still in the shot.  
Figure 4 shows the feature maps obtained in the tracking network of the preliminary tracking module in TRTrack. The color in the feature maps reflects the similarity estimation between each position of the search region image and the target, and the greener the color indicates that the position of the current image is more likely to be the target.