## 4 Results
### Evaluation Metrics and Methodology  
To evaluate vehicle and license plate detection performance, COCO evaluation metrics such as Average Precision (AP), AP.5, AP.75, and Average Recall (AR) were used. AP represents the area under the precision-recall curve, indicating the mean precision at various Intersection over Union (IoU) thresholds (0.5:0.05:0.95). AP.5 and AP.75 represent the AP at IoU thresholds of 0.5 and 0.75, respectively. AR refers to the average recall at various detection confidence thresholds.  
These evaluation metrics are calculated based on precision and recall. Precision is the ratio of actual objects among detected objects, as shown in Equation (10). Recall is the ratio of detected objects among actual objects, as shown in Equation (11). Here, True Positive (_TP_) refers to correctly detected objects, False Positive (_FP_) refers to incorrectly detected objects, and False Negative (_FN_) refers to undetected objects.  
\[Precision=\frac{TP}{TP+FP} \tag{10}\]  
\[Recall=\frac{TP}{TP+FN} \tag{11}\]  
The performance of license plate corner detection was also evaluated using standard keypoint detection metrics: AP, AP.5, AP.75, and AR. In this case, Object Keypoint Similarity (_OKS_) is used instead of IoU to measure similarity based on the distance between predicted corners and actual corners. The Euclidean distance between predicted corners and actual corners is calculated as shown in Equation (12). Here, \(\left(x_{ij}^{pred},y_{ij}^{pred}\right)\) represents the coordinates of the predicted corner and \(\left(x_{ij}^{gt},y_{ij}^{gt}\right)\) represents the coordinates of the actual corner, while \(i\) indicates the image index and \(j\) indicates the corner index. Based on this Euclidean distance, _OKS_ is expressed as shown in Equation (13).  
\[d_{ij}=\sqrt{\left(x_{ij}^{pred}-x_{ij}^{gt}\right)^{2}+\left(y_{ij}^{pred}-y_{ ij}^{gt}\right)^{2}} \tag{12}\]  
\[OKS=\exp\left(-\frac{d_{ij}^{2}}{2s^{2}k^{2}}\right) \tag{13}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Corner Detection Dataset** & \multicolumn{2}{c}{**License Plate Detection Dataset**} & \multicolumn{2}{c}{**Vehicle Detection Dataset**} \\ \hline Number of Images & 3619 & 16,188 & 24,914 \\ Training Set & 3319 & 16,060 & 23,575 \\ Validation Set & 301 & 128 & 1339 \\ Resolution Range & 302 \(\times\) 192\(\sim\)600 \(\times\) 450 & 640 \(\times\) 640 & 640 \(\times\) 640 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Dataset overview.  
Here, \(d\) is the Euclidean distance calculated in Equation (12), \(s\) is the scale of the object (license plate) size (typically the square root of the object area), and \(k\) is a constant depending on the corner type. AP.5 is the AP calculated by considering only cases where the OKS value is 0.5 or higher as True Positive, and AP.75 is the AP calculated by considering only cases where the OKS value is 0.75 or higher as True Positive.  
To objectively evaluate the performance of the proposed method, it was compared with various existing methods. For corner detection models, CSPNext [30], RTMPose [31], Uniformer [32] were selected, and for vehicle and license plate detection models, YOLOv7 [33] and YOLOv8 were selected. Through these various comparison targets, the superiority of the proposed method was verified from multiple angles.