# Single-Task Joint Learning Model for an Online Multi-Object Tracking Framework
## 2 STJL Model Applied to Online Multi-Object Tracking
### Tracker Initialization and Terminate  
After matching, unmatched boxes might indicate new objects or false positives. Traditionally, they start as trial trackers, becoming official if they persist. This \"continuous tracking determination\" filters single-frame errors but may still track consecutive errors. A stringent initialization confidence threshold is recommended to prevent this. To enhance tracking accuracy, detection boxes in frame \(t\), denoted as \(D^{t}\), are filtered based on \"detection confidence\", which is calculated using the likelihood score provided by the detector. Detection confidence serves as a preliminary criterion for tracker initialization and error reduction. Specifically, detection boxes are separated into two subsets according to a confidence threshold \(th1\): strong detection boxes \(D_{strong}^{t}\), which meet or exceed the confidence threshold, and weak detection boxes \(D_{weak}^{t}\), which fall below this threshold. High-confidence detections, \(D_{strong}^{t}\) are preferred for initializing trackers, providing a robust foundation for accurate tracking. In contrast, weak detection boxes \(D_{weak}^{t}\) are more prone to errors and are therefore cautiously considered or excluded from the initialization process. This two-tier confidence-based filtering approach, as represented by Equation (2), helps to reduce false positives and enhance the reliability of tracker initialization, contributing to overall tracking stability:  
\[D_{i}^{t}=\left\{ \begin{array}{ll}D_{strong}^{t},&if\;D_{i}^{t}\text{.}\; confidence>th1\\ D_{weak}^{t},&otherwise\end{array} \right., \tag{2}\]  
Strong detection boxes with high confidence are suitable for target linking and initialization, while weak detection boxes with lower confidence are prone to errors but can still be used for linking. Depending solely on the detection box, confidence can be misleading, as high-confidence errors might resemble human features. To address this, trajectory confidence is proposed via assessing the detection boxes from a tracking perspective. Reliable trajectories indicate genuine objects, whereas errors can lead to fragmented paths. Unmatched boxes start as trial trackers, and they are promoted to official trackers with unique IDs only when their trajectory confidence consistently exceeds a threshold. The trajectory confidence, as shown in Equation (3), is based on two factors: the similarity between the linked detection boxes and the trajectory length. A consistent tracker will have similar boxes, and longer trajectories indicate higher reliability. \[Conf(T_{i})=\left(\frac{1}{L}{\sum_{h\in[t_{i}^{i},t_{e}^{i}]}{\Lambda\left(T_{i},z_{h}^{i}\right)}}\right)\times(1-exp^{-\beta-\sqrt{L}}), \tag{3}\]  
where \(T_{i}\) is the trajectory of object \(i\). The first term represents the average similarity of detection boxes between frames, where \(L\) is the length of the trajectory and \(h\) refers to the index of the frames considered in the calculation of the trajectory similarity. The interval of \(h\) typically ranges from the starting frame of the detection to the current frame, i.e., \(h\in[t_{s},t_{e}]\), where \(t_{s}\) is the frame when the detection first appears and \(t_{e}\) is the current frame being analyzed. The similarity between detection boxes, \(\Lambda\left(T_{i},z_{h}^{i}\right)\), is calculated using cosine similarity between the feature vectors extracted from the deep learning model. \(z_{h}^{i}\) is the detection box of object \(I\) in frame \(h\). Specifically, for two feature vectors \(r_{i1}\) and \(r_{i2}\), the similarity is computed as \(\Lambda\left(T_{i},z_{h}^{i}\right)=\frac{r_{i1}r_{i2}}{\left|r_{i1}\right| \left|r_{i2}\right|}\). This similarity helps measure how closely related the detection boxes are in terms of appearance, contributing to the overall trajectory confidence. The first term sums the detection boxes' similarities from time \(t_{s}\) to \(t_{e}\) and divides by the trajectory length \(L\), yielding the average similarity of the detection boxes.