## 4 Results
### Tracking  
Keeping track of the workers is the main purpose of monitoring applications. Accordingly, the tracking should be preferably accurate to provide satisfying results. The detectors of such monitoring systems are the key components for a reliable tracking as their detections serve as initializations and updates for the tracks. In this experiment, we compared the performances of both detectors developed in this paper with respect to the aforementioned requirements. We applied Kalman filtering to their detections to implement a simple and easy to evaluate tracking system. Each generated tracker has the same dimension during evaluation. The selected size was set manually before, so that the rectangle completely encloses the construction worker in the center of the image. If the detector does not detect a construction worker who is already tracked, the Kalman filter determines its next position only using the prediction. This allows tracking a construction worker who is in motion but is covered, for example, by an object temporarily. Since the accuracy of the position determination decreases without correction of the motion model, these predictions are executed up to a maximum of one second. Otherwise, the track is erased and a new one is set up for the construction worker when the detector detects him again. The prediction is also used to mark the direction of the worker's movement in the image. For this, the next position in the current image is predicted. Construction workers who move towards a dangerous area can be better identified this way. The precision and continuity of the underlying detector primarily determines the accuracy and robustness of the tracks. We relied on the approach of [PERSON] and [PERSON] [36] to measure these metrics. They proposed the average sequence overlap score (AOS) and center location error ratio (CER) measures for accuracy and track length (TL) for robustness. Ambiguity errors caused by tracks crossing each other \begin{table}
\begin{tabular}{c c c} \hline \hline
**Image Size (px)** & **Detection Speed (ms)** & **mAP** \\ \hline
416 \(\times\) 416 & 46 & 72.9 \\
512 \(\times\) 512 & 56 & 75.2 \\
608 \(\times\) 608 & 67 & 78.5 \\
704 \(\times\) 704 & 83 & 80.3 \\
800 \(\times\) 800 & 97 & 82.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The results of detection accuracy and detection speed for different image sizes. are not taken into account since this is a feature of the tracker rather than of the detector. We adapt those metrics to fit to our experimental setup, as shown in Equations (2)-(4). \[\text{AOS} =\frac{1}{n}\sum_{t=1}^{n}\frac{A_{t}^{G}\cap A_{t}^{T}}{A_{t}^{G} \cup A_{t}^{T}}, \tag{2}\] \[\text{CER} =\frac{1}{n}\sum_{t=1}^{n}\frac{||C_{t}^{G}-C_{t}^{T}||_{2}}{ \text{size}(A_{t}^{G})},\] (3) \[\text{TL} =\frac{n}{N}, \tag{4}\]  
where \(t\) represents the current time step, \(n\) denotes the number of video frames in which a worker is tracked and \(N\) is the number of frames in which the worker is present. The worker's bounding box areas are indicated by \(A\) and their centers by \(C\) where the superscripts \(G\) and \(T\) mark ground truth and tracked bounding boxes, respectively. Finally, \(||\circ||_{2}\) denotes the two dimensional euclidean distance and \(\text{size}(\circ)\) represents the two dimensional size of an area. For an eligible comparison of their performances, we evaluated the tracking systems, emerging from each detector combined with Kalman filtering, to identical scenes of construction sites. These scenes are chosen as described in Section 2.1. None of them have been shown to any detector before, neither during training nor during calibration and validation. In the following, we refer to Scene 1 as the scene of four pedestrian workers from the video sequence which is well illuminated, while Scene 2 denotes its overexposed counterpart from the other sequence. The scene showing a car approaching a worker is referred to as Scene 3. The tracking results using the classical detection approach are given in Section 4.2.1.