## 3 Methodologies
### Trajectory Generation
#### 3.2.2 Pedestrian Tracker
Existing benchmarks for pedestrian tracking datasets are typically created with the objective of accurate algorithm development in nearly ideal conditions using high-quality videos. The most notable dataset benchmarks are the MOTChallenge benchmarks, including MOT17 [32] and MOT20 [33], which create leaderboards that spark much academia and industry efforts to develop new tracking algorithms that score higher in a range of accuracy metrics. However, surveillance videos in the real world differ from these selected quality benchmarks. Empirically, we observe at least two significant difficulties, namely frame rates, and annotations, from real-world datasets, including our experimental ones, that are rarely seen in high-quality benchmarks such as the MOTChallenge. The following describes how the tracking algorithms are adjusted to deal with the real-world datasets that are used in this study. (1) **Low frame rate**  
High-quality data often comes with a higher frame rate. For example, MOT20 [33] contains videos of 25 FPS. On the other hand, the Grand Central Station videos are only annotated every 20 frames, rendering the effective frame rate of 1.25 FPS. This is especially challenging for the tracker, as bounding box association works better when there is more overlap between bounding boxes of the same pedestrian in consecutive frames. Reduced performance at lower frame rates can be explained by the matching process used by SORT and DeepSORT. To cross-check detections and tracks, SORT first use IoUmatching followed by track decay. Before IoU matching, DeepSORT incorporates an additional stage known as the matching cascade. During the IoU matching stage, unassigned track and unassigned detection boxes with IoU higher than a certain threshold are matched using the Hungarian algorithm. However, because pedestrians have traveled a large distance between successive frames when the frame rate is low, a smaller IoU between the detections and tracks is more appropriate. We, therefore, lower the IoU threshold to 0.1 (instead of the conventional implementation of 0.7) in order to retain unmatched candidate tracks and detections that would be otherwise discarded due to the low frame rate. With a low IoU threshold, pedestrians can be tracked more effectively in videos with a low frame rate. (2) **Lack of associated bounding box annotation**  
Data annotation is expensive and time- and labor-intensive. The average time required to manually annotate a bounding box, according to research, is at least 88 s per bounding box [34]. For the tracking problem, additional time is necessary to assign each bounding box a unique person ID. Consequently, it is challenging to construct high-quality tracking annotations for surveillance videos featuring large crowds. Typically, high-quality benchmark datasets include these annotations so that detectors and trackers can be trained on the provided video data. The Grand Central Station dataset utilized in this research comprises just point annotations, whereas the stadium video is unannotated. We, therefore, rely on using detectors and trackers pre-trained on other datasets of completely different scenarios. In addition, since there is no bounding box ground truth to compare the Grand Central Station dataset to during the evaluation phase, we employ the Euclidean similarity measure instead of the IoU similarity measure to compare each track to the point-wise ground truth. The Euclidean similarity thresholds the Euclidean distance between two points. For numerical experiments in this paper, the threshold is set to be a 1 m-distance in the physical space.