## 2 Proposed MOT Method
### Trajectory Confidence  
Trajectory confidence is an important basis to distinguish whether a trajectory is reasonable or not and whether it can continue to match the new detection. The higher the trajectory confidence, the more likely it is to be the correct trajectory, and vice versa. Generally, there are many factors that determine the trajectory confidence, such as its total length, its length in the Vanished state, the confidence of its historical relevant detections, and its historical similarity distance. Based on the above factors, we define the trajectory confidence as follows:  
\[conf(K^{i})=conf_{aff}(K^{i})conf_{iou}(K^{i})conf_{\text{det}}(K^{i}) \tag{1}\]  
\(K^{i}\) represents the i-th trajectory in the whole trajectory set,\(K^{i}=\left\{k^{i}_{t},\dots,k^{i}_{t},\dots,k^{i}_{t_{e}}\right\}\), where \(t_{s}\) represents the number of initial frame of the trajectory and \(t_{e}\) represents the number of terminal frame. \(k^{i}_{t}\) represents the trajectory state in frame t. \(conf_{aff}\) represents the similarity distance between the trajectory and its corresponding historical relevant detections. \(conf_{iou}\) represents the Intersection over Union (IoU) score between the trajectory and its corresponding historical relevant detections.  
Figure 2: An example of an object state transition. (a–e) are from MOT17-02-SDP in the MOT17 benchmark dataset. Bounding boxes of different colors represent different objects.  
represents the weighted confidence of the detection which has been associated with the trajectory. Each score is derived from the following equation:  
\[\begin{array}{l}conf_{aff}(K^{i})=\frac{1}{h}\sum_{t\in[t_{s},t_{t}]}\Phi(k^{i}_ {t})A(k^{i}_{t},d^{j}_{t})\\ conf_{iou}(K^{i})=\frac{1}{h}\sum_{t\in[t_{s},t_{s}]}\Phi(k^{i}_{t})IoU(k^{i}_{t },d^{j}_{t})\\ conf_{\text{det}}(K^{i})=\frac{1}{h}\sum_{t\in[t_{s},t_{s}]}\Phi(k^{i}_{t})c^{ j}_{t}\end{array} \tag{2}\]  
where \(h\) represents the number of frames that the trajectory successfully matches to the detection, and \(h<=t_{e}-t_{s}+1\). \(\Phi(k^{i}_{t})\) indicates that if \(k^{i}_{t}\) successfully matches with detection in current frame, it equals to 1, otherwise 0. \(d^{j}_{t}\) represents the j-th detection in frame t. \(A(k^{i}_{t},d^{j}_{t})\) represents the similarity distance between \(k^{i}_{t}\) and \(d^{j}_{t}\) in frame t, which is described in Section 2.4. \(IoU(k^{i}_{t},d^{j}_{t})\) represents the IoU score between \(k^{i}_{t}\) and \(d^{j}_{t}\) in frames t. \(c^{j}_{t}\) represents the confidence of the j-th detection in frame t, which is given by the detector in advance.  
Figure 3 is part of the qualitative tracking results of our algorithm on the MOT15 benchmark dataset. Generally speaking, low confidence trajectories are often caused by overlapping occlusion, dynamic ambiguity, drastic changes in appearance, and other factors. These trajectories are prone to track segmentation, IDS, and other phenomena in subsequent frames. Therefore, we prefer to associate high confidence trajectories with detection targets first, and then deal with low confidence trajectories. The experimental results in Section 3 prove the feasibility of our algorithm.  
In order to cooperate on our matching strategy, we set the trajectory confidence threshold and the detection confidence threshold according to practical experience, which will be discussed in Section 3.4. Trajectories and detections that exceed the threshold will be classified as high confidence sets, while those below the threshold will be classified as low confidence sets.  
Figure 3: _Cont._