## 3 Results
### Pavement Images  
Secondly, 1157 RGB images with a resolution of 256 \(\times\) 256 pixels in the pavement dataset are used as the experimental samples, including 308 crack images and 849 non-crack images. The specific division results are listed in Table 9. The dataset contains images of uneven illumination, black stains and various cracks, as shown in Figure 13. The partial results of image augmentation are shown in Figure 14.  
Figure 12: Confusion matrix of bridge testing set images.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Situation**} & \multicolumn{2}{c}{**Training Set**} & \multicolumn{2}{c}{**Calibration set**} & \multicolumn{4}{c}{**Testing Set**} \\ \cline{2-9}  & \begin{tabular}{c} **Training** \\ **Time (s)** \\ \end{tabular} & **AUC** & \
\begin{tabular}{c} **Thermal** \\ **Threshold** \\ \end{tabular} & **Accuracy** & **Precision** & **Recall** & **F1-Score** &
\begin{tabular}{c} **Testing Speeds** \\ **(s/img)** \\ \end{tabular} \\ \hline
1 & 1767 & 0.9730 & 0.0513 & 92.31\% & 96.31\% & 90.31\% & 93.21\% & 0.0531 \\ \hline
2 & 1759 & 0.9683 & 0.0556 & 90.28\% & 93.19\%  
As shown in Figure 15a and Table 10, the trained network model tends to be stable with about 50 epochs and 2178 s. The model is used to detect the calibration set. The prediction results are shown in Figure 15b. Generally, the crack detection prediction results are satisfactory. For the non-crack images, the average thermal scores are roughly around 0, and for the crack images, most of the data are far away from 0. For the ROC curve, the value of AUC is 0.9726, and the thermal threshold is 0.2133.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Situation**} & \multicolumn{2}{c}{**Training Set**} & \multicolumn{2}{c}{**Calibration Set**} & \multicolumn{2}{c}{**Testing Set**} \\ \cline{2-9}  & \multicolumn{1}{c}{**Training**} & \multirow{2}{*}{**AUC**} & \multicolumn{1}{c}{**Thermal**} & \multirow{2}{*}{**Accuracy**} & \multirow{2}{*}{**Precision**} & \multirow{2}{*}{**Recall**} & \multirow{2}{*}{**F1-Score**} & \multicolumn{2}{c}{**Testing Speeds**} \\  & \multicolumn{1}{c}{**Time(s)**} & & & & & & & **(s/img)** \\ \hline
1 & 2185 & 0.9916 & 0.0835 & 96.22\% & 94.74\% & 93.10\% & 93.91\% & 0.0505 \\ \hline
2 & 2263  
The obtained trained network model is applied to the testing set. The prediction results are shown in Table 10. The pavement crack image classifier of the confusion matrix is shown in Figure 16. The main indicators, Accuracy and F1-Score, reach 97.57% and 96.00%, respectively. Moreover, the testing speeds reach 0.0510 s/img. Some non-crack images containing tree leaves have relatively high average thermal scores, resulting in them being misclassified as cracks. Some small hairy cracks have low average thermal scores, resulting in being misclassified as non-crack images. The effectiveness of the proposed method is validated again.  
Figure 15: The results of the pavement image classification training and calibration process: (**a**) training process; (**b**) calibration set prediction results; (**c**) ROC curve; (**d**) overall diagram of scores-positive rate; (**e**) detailed diagram of a scores-positive rate. The red star represents the thermal threshold.