# Application of Augmented Reality in Waterway Traffic Management Using Sparse Spatiotemporal Data
## 5 Experiments
### Evaluation Metrics  
To validate the effectiveness of the proposed method, we randomly selected five congested segments from the Wuhu waterway dataset for comparative experiments on vessel detection, tracking, and data fusion. The detailed information of the test set is shown in Table 2, where NOV and NOA represent the number of detected vessels and the number of vessels with AIS data, respectively: \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**MMSI** & **Name** & **Speed** & **Course** & **Lon** & **Lat** & **Type** \\ \hline
413847933 & TENGEFI0516 & 4.7 & 237.0 & 118.240973 & 31.28031 & Cargo \\
413790501 & WANXUANCHENGHO8598 & 0.0 & 48.9 & 118.223678 & 31.27985 & Cargo \\
413818093 & YUANYANG166 & 5.1 & 235.2 & 118.19577 & 31.29483 & Cargo \\
413868128 & WUHULIANSHUN79 & 5.4 & 229.3 & 118.17557 & 31.28103 & Unknown \\
413826319 & MINGSHENG0088 & 4.0 & 66.7 & 118.21308 & 31.29341 & Cargo \\
413868128 & HUALING967 & 4.6 & 55.0 & 118.186505 & 31.27687 & Tanker \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Partial AIS data display. Figure 4: Range of video and AIS reception devices. The Evaluation of the Object Detection Model  
This study divides the two small subregions within the waterway vessel detection area into key and regular detection zones to enhance the accuracy of vessel identification within the visual range. The regular detection zones are denoted as V\({}_{1}\) and V\({}_{2}\), while the key detection zones are represented by V\({}_{3}\), V\({}_{4}\), V\({}_{5}\), and V\({}_{6}\). Computational resources are primarily focused on the key detection zones, and if no vessels are detected in these zones, resources are reallocated to the remaining detection areas. The allocation of regions is depicted in Figure 5.  
The experiment evaluated the model's performance based on precision, recall, and mean average precision (mAP). Precision represents the false detection rate when the model detects targets, while recall indicates the missed detection rate. [EMAIL_ADDRESS] is the sum of the average precision (AP) for all labels divided by the total number of categories. A higher [EMAIL_ADDRESS] value indicates better detection accuracy for the model. The calculation formulas for precision (P), recall (R), and mAP are shown below:  
\[\mathrm{P=}\frac{\mathrm{TP}}{\mathrm{TP+FP}} \tag{37}\]  
\[\mathrm{R}\ =\frac{\mathrm{TP}}{\mathrm{TP+FN}} \tag{38}\]  
\[\mathrm{AP=}\int_{0}^{1}\mathrm{PRdr} \tag{39}\] \begin{table}
\begin{tabular}{c c c c} \hline
**Video** & **Video Length** & **NOV** & **NOA** \\ \hline
1 & 01 m 20 s & 2 & 2 \\
2 & 01 m 20 s & 3 & 3 \\
3 & 02 m 24 s & 4 & 4 \\
4 & 02 m 46s & 3 & 3 \\
5 & 02 m 38 s & 4 & 4 \\ \hline \end{tabular}
\end{table} 
Table 2: Test video segment information. Figure 5: Division of target detection range for waterway vessels. \[\text{mAP}= \frac{1}{n}\sum_{i=0}^{n}\text{AP}_{i} \tag{40}\]  
Here, P represents precision, R represents recall, TP is the number of true positives, FN is the number of false negatives, FP is the number of false positives, and \(n\) is the total number of categories. To evaluate the performance of ship consistency labeling in the waterway, we use Multi-Object Tracking Accuracy (MOTA) and modified Multi-Object Detection Accuracy (MOCA) as evaluation metrics. These metrics assess the detection results for each frame in the five test videos by comparing them with the actual ground truth. Additionally, we employ identification precision (IDP), identification recall (IDR), and the IDF\({}_{1}\) score as evaluation criteria for maintaining consistent ship identities.