## 4 Experiments and Results
### Quantitative Performance Evaluation of the Framework
#### 4.1.1 Trajectory Generation  
Evaluation Metrics  
To assess the performance of the detectors and trackers, we employ the CLEAR multiple object tracking (MOT) metrics, a commonly used collection of metrics for evaluating tracking algorithms [44]. Among the list of CLEAR metrics, we report several key metrics that can be measured for a dataset with only point-wise trajectory annotation (rather than bounding box annotations). Specifically, multiple object detection accuracy (MODA) is used as the primary metric to evaluate the detector, and multiple object tracking accuracy (MOTA) as the primary metric to evaluate the tracker. Additionally, to provide more detailed information about where errors occur (whether errors are due to missed tracks or inaccurate tracks), recall and precision on the detections are also reported following common MOT challenge practices in crowded scenes [33]. The four metrics are computed as follows:  
\[\mathrm{MODA}=1-\frac{\sum_{t}(\mathrm{FN}_{t}+\mathrm{FP}_{t})}{\sum_{t} \mathrm{GT}_{t}} \tag{9}\]  
\[\mathrm{MOTA}\ =1-\frac{\sum_{t}(\mathrm{FN}_{t}+\mathrm{FP}_{t}+\mathrm{IDSW}_{t})}{ \sum_{t}\mathrm{GT}_{t}} \tag{10}\]  
\[\mathrm{Recall}=\frac{\mathrm{TP}_{t}}{\mathrm{TP}_{t}+\mathrm{FN}_{t}} \tag{11}\]  
\[\mathrm{Precision}=\frac{\mathrm{TP}_{t}}{\mathrm{TP}_{t}+\mathrm{FP}_{t}} \tag{12}\]  
where \(\mathrm{FN}_{t}\), \(\mathrm{FP}_{t}\), \(\mathrm{TP}_{t}\), \(\mathrm{GT}_{t}\) and \(\mathrm{IDSW}_{t}\) are the number of false negatives, false positives, true positives, ground truths, and of identity mismatches at time \(t\), respectively. Implementation Details  
The YOLOv7 network and the Faster-RCNN network are compared as the pedestrian detector module, followed by the SORT algorithm as the tracker module. For faster inference speed, we employ the YOLOv7-tiny configuration, which slightly affects performance but can conduct inference in real time due to smaller parameter sizes. Both detectors are pre-trained using the ImageNet dataset [45]. The experiments were conducted on a computer equipped with an Intel Core i7-7820X processor and an NVIDIA GeForce GTX 1080 Ti graphics processing unit (GPU). The code repository is publicly available at [46]. Experimental Results  
The results are detailed in Table 1. The YOLOv7-tiny network outperforms the Faster-RCNN in MOTA, as seen in Table 1. The recall and precision are also increased. Nonetheless, both YOLO and Faster-RCNN detectors have a high precision and a low recall, indicating a high number of false negatives (missed targets), FN. A high FN indicates the presence of a large number of untracked pedestrians. This is possibly owing to the fact that the GCS video has a low frame rate, and as a result, pedestrians move at a very quick speed, frequently without overlap between successive bounding boxes. The DeepSORT algorithm with the Re-ID model is employed as the pedestrian tracker to improve the outcomes. As shown in Table 2, we notice a significant improvement in MOTA, MODA, and recall when the detector is either YOLOv7-tiny or Faster-RCNN, albeit at the cost of a slight reduction in precision. This is perhaps due to the fact that incorporating the Re-ID model allows bounding boxes to be associated with the same \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Detector** & **Tracker** & **MOTA** & **MODA** & **Recall** & **Precision** \\ \hline YOLOv7-tiny & SORT & **62.8** & **70.8** & **72.2** & **98.2** \\ Faster R-CNN & SORT & 58.8 & 66.5 & 71.0 & 94.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: CLEAR MOT metrics of YOLOv7-tiny and Faster-RCNN detectors with the SORT tracker. person even when there is no overlap, as the pedestrian would have similar visual features between frames. The Re-ID model, extracting deep appearance features, allows tracks to be more accurately associated by considering the cosine distance between detection and predicted bounding boxes during the matching cascade process.