# Deep Learning for Traffic Sign Recognition Based on Spatial Pyramid Pooling with Scale Analysis
## 3 Results
### Training Results
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & **Loss** & **ID** & **AP** & **FP** & **Precision** & **Recall** & **F1-score** & **IoU** & _[EMAIL_ADDRESS] \\  & **Value** & **(\%)** & **TP** & **FP** & **Precision** & **Recall** & **F1-score** & **(\%)** & **(\%)** \\ \hline \multirow{4}{*}{Yolo V3 1} & \multirow{4}{*}{0.0141} & P1 & 97.5 & 77 & 0 & & & & & \\  & P2 & 98.8 & 83 & 0 & & & & & & \\  & P3 & 99.9 & 62 & 1 & 0.99 & 0.99 & 0.99 & 82.19 & 98.73 \\  & & P4 & 98.74 & 76 & 2 & & & & & \\ \hline \multirow{4}{*}{Yolo V3 2} & \multirow{4}{*}{0.015} & P1 & 97.5 & 78 & 0 & & & & & \\  & P2 & 100 & 83 & 0 & & & & & & \\  & P3 & 99.85 & 61 & 3 & 0.98 & 0.99 & 0.98 & 83.09 & 98.84 \\  & & P4 & 98.01 & 75 & 3 & & & & & \\ \hline \multirow{4}{*}{Yolo V3 3} & \multirow{4}{*}{0.0129} & P1 & 97.5 & 77 & 0 & & & & & \\  & P2 & 98.8 & 83 & 0 & & & & & & \\  & P3 & 99.92 & 59 & 0 & & & & & & \\  & P4 & 97.75 & 72 & 5 & & & & & & \\ \hline \multirow{4}{*}{Average} & \multirow{4}{*}{0.014} & \multirow{4}{*}{0.0125} & P1 & 97.5 & 78 & 0 & & & & & \\  & P2 & 98.8 & 83 & 0 & & & & & & \\  & P3 & 99.9 & 62 & 1 & 0.99 & 0.99 & 90.09 & 98.88 \\  & & P4 & 98.94 & 79 & 3 & & & & & \\ \hline \multirow{4}{*}{Yolo V3  SPP 1} & \multirow{4}{*}{0.0144} & P1 & 97.43 & 78 & 0 & & & & & \\  & P2 & 100 & 83 & 0 & & & & & \\  & P3 & 100 & 62 & 1 & 0.99 & 0.99 & 0.99 & 89.4 & 99.12 \\  & & P4 & 99.05 & 76 & 2 & & & & & \\ \hline \multirow{4}{*}{Yolo V3  SPP 2} & \multirow{4}{*}{0.0133} & P1 & 97.5 & 78 & 0 & & & & & \\  & P2 & 100 & 83 & 0 & & & & & & \\  & P3 & 100 & 62 & 0 & & & & & \\ \cline{1-1}  & & P4 & 98.23 & 76 & 2 & & & & & \\ \hline \multirow{4}{*}{Average} & \multirow{4}{*}{0.0134} & \multirow{4}{*}{0.0134} & \multirow{4}{*}{0.099} & 0.99 & 0.99 & 89.34 & 98.97 \\ \cline{1-1}  & & P4 & 98.23 & 76 & 2 & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Training loss value, _mAP_, and _AP_ performance for all classes. Figure 4: Training performance for all classes using (**a**) Yolo V3 1 and (**b**) Yolo V3 SPP 1. Table 2 displays the loss value of training, \(mAP\), and \(AP\) results for all classes after 8000 cycles of training. The average training validity failure is about 0.013 for both levels. Therefore, the training model has extremely reliably identified objects. After 7200 iterations, the training model converges and stays consistent for the rest of the training. The validation loss for Yolo V3 1 is 0.0141, Yolo V3 2 is 0.015, Yolo V3 3 is 0.0129, Yolo V3 SPP 1 is 0.0125, for Yolo V3 SPP 2, 0.0144, and Yolo V3 SPP 3, 0.0133. The mean average accuracy (\(mAP\)) is averaged over the \(p(o)\) accuracy by Equation (10) [52,53]. \[mAP=\int_{0}^{1}p(0)do \tag{10}\]  
Furthermore, \(p(o)\) is the precision of the Taiwan prohibitory sign detection. Precision and Recall are illustrated by Equations (12) and (13), [40,54]:  
\[\textit{Precision}\ (P)=\frac{\textit{True Positive}\ (\textit{TP})}{\textit{True Positive}\ (\textit{TP})+\textit{False Positive}\ (\textit{FP})} \tag{11}\]  
\[\textit{Recall}\ (R)=\frac{\textit{True Positive}\ (\textit{TP})}{\textit{True Positive}\ (\textit{TP})+\textit{False Negative}\ (\textit{FN})} \tag{12}\]  
Moreover, TP represents True positives. FP is a positive sample of the misclassified. FN stands for a negative sample of the misclassified. The value of \(IoU\) is the relationship between the result of the detection, the reality of the ground truth, and its relation [55]. \(IoU\) measures the projection ratio and shown in Equation (13) [1,56,57]. \[IoU=\frac{\textit{Area}_{pred}\ \cap\ \textit{Area}_{gt}}{\textit{Area}_{pred} \ \cup\ \textit{Area}_{gt}} \tag{13}\]  
In Table 2, Yolo V3 SPP (98.88%, 99.12%, 98.93%) obtains a maximum \(mAP\) better than that of Yolo V3 (98.73%, 98.84%, 98.49%). Furthermore, Yolo V3 loaded 107 layers during the \(mAP\) calculation with BFLOPS rates of 65,312, and Yolo V3 SPP loaded 114 layers with BFLOPS rates of 65,69. SPP can enhance the overall BFLOFS 0.378, making Yolo V3 SPP more stable and precise.