## 3 Results and Discussions
### Performance Comparisons of Mask R-CNN at Different Learning Rates  
Section 3.1 confirmed that the overall performance of the Mask R-CNN in pavement defect detection was superior to that of the Faster R-CNN. Therefore, the following study of the hyper-parameter LR of the Mask R-CNN was carried out. The model performance of the Mask R-CNN at three LRs of 0.01, 0.001, and 0.0001 was compared to obtain relatively optimal model in pavement defect detection, respectively. Figure 11(a) showed the AP trend of M-R50-C4 at three LRs, with an overall upward trend during iteration. The AP of M-R50-C4 that were highest at the LR was 0.0001, with the AP reaching 87.3 at the end of the iterations. Figure 11(b) shows the trend of the testing time of M-R50-C4 at the three LRs, and the average testing time of the image was between 0.525-0.575 SPF, and the testing time was shortest when the LR was 0.001.  
Figure 11(c) shows the trend of the AP of M-R101-FPN at the three LRs, and the overall trend rose with the number of iterations. The AP reached 92.1 when the LR was 0.0001. Figure 11(d) was the trend of the testing time corresponding to Figure 11(c); the three trends of the testing time were close and stable at about 0.245 SPF, and the testing time was as low as 0.242 SPF when the LR was 0.001. Meanwhile, the fastest testing speed in Figure 11(d) was 56% faster than that in Figure 11(b). Table 5 shows the performance data of different backbone structures of the Mask R-CNN when the LR was 0.0001. The corresponding result (Table A1) of when the LR was 0.01 is shown in the Appendix A.  
Figure 11: The testing time under different iterations: (**a**) F-R50-FPN and M-R50-FPN, (**b**) F-R101-FPN and M-R101-FPN.  
Figure 10: The AP under different iterations: (**a**) F-R50-FPN and M-R50-FPN, (**b**) F-R101-FPN and M-R101-FPN.  
The testing images of M-R50-C4 under different LRs are shown in Figure 13. Figure 13a shows the original image, which contained an N_crack and a P_groove. Figure 13b shows the testing results of the M-R50-C4 model when the LR was 0.01, which detected a large number of defects with large errors. Figure 13c showed that four defects were detected when the LR was 0.001. Figure 13d shows the detection effect of the model at the LR of 0.0001, and the model output six defects. The results showed that the M-R50-C4 model could detect the defects in the image but that the detection effect was quite different at different LRs, and the number of defects in the image could not be predicted correctly. The testing effect of the M-R101-FPN at three LRs is shown in Figure 14. Figure 14b shows the testing results of the model at the LR of 0.01, and the model detected three defects, and the error defect was a P_crack. The defects in the image could be accurately detected when the LR was 0.001 (Figure 14c), and the LR was 0.0001 (Figure 14d).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**Backbone Structures**} & \multicolumn{2}{c}{**Precision (\%)**} & \multicolumn{2}{c}{**Recall (\%)**} & \multicolumn{2}{c}{**F1 (\%)**} & \multicolumn{2}{c}{**AP (\%)**} & \multicolumn{2}{c}{**Time (SPF)**} \\ \hline \multirow{4}{*}{Mask R-CNN} & \multirow{2}{*}{ResNet50} & FPN & 91.3 & 93.6 & 92.4 & 88.4 & 0.210 \\  & & C4 & 88.5 & 92.1 & 90.3 & 86.2 & 0.568 \\  & & DC5 & 85.7 & 90.4 & 90.0 & 85.8 & 0.391 \\ \cline{2-6}  & \multirow{2}{*}{ResNet101} & FPN & 94.8 & 95.3 & 95.0 & 92.1 & 0.247 \\  & & C4 & 92.3 & 93.5 & 92.9 & 88.5 & 0.595 \\  & & DC5 & 90.6 & 91.2 & 90.9 & 89.7 & 0.426 \\ \hline \hline \end{tabular}
\end{table}
Table 5: The performance data of different models of the Mask R-CNN under LR = 0.0001.  
Figure 12: The AP and testing time of different models under different iterations and learning rates. (**a**) The AP of M-R50-C4, (**b**) The testing time of M-R50-C4, (**c**) The AP of M-R101-FPN, (**d**) The testing time of M-R101-FPN.