## 3 Results
### Testing Process
\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 & 636 & 0.9732 & 0.0121 & 95.41\% & 98.28\% & 94.21\% & 96.20\% & 0.0528 \\ \hline
2 & 661 & 0.9992 & 0.0052 & 95.41\% & 99.12\% & 93.39\% & 96.17\% & 0.0558 \\ \hline
3 & 647 & 0.9912 & 0.0018 & 94.90\% & 95.87\% & 95.87\% & 95.87\% & 0.0547 \\ \hline
4 & 663 & 0.9940 & 0.0072 & 93.37\% & 95.76\% & 93.39\% & 94.56\% & 0.0584 \\ \hline
5 & 664 & 0.9952 & 0.0026 & 94.90\% & 100.00\% & 91.74\% & 95.69\% & 0.0580 \\ \hline
6 & 658 & 0.9296 & 0.0019 & 95.41\% & 100.00\% & 92.56\% & 96.14\% & 0.0579 \\ \hline
7 & 642 & 0.9896 & 0.0019 & 94.90\% & 95.87\% & 95.87\% & 95.87\% & 0.0564 \\ \hline
8 & 664 & 0.9880 & 0.0016 & 94.90\% & 95.12\% & 96.69\% & 95.90\% & 0.0606 \\ \hline
9 & 665 & 0.9903 & 0.0233 & 92.86\% & 98.20\% & 90.08\% & 93.97\% & 0.0583 \\ \hline
10 & 662 & 0.9900 & 0.0064 & 94.39\% & 100.00\% & 90.91\% & 95.24\% & 0.0582 \\ \hline Mean & 656 & 0.9840 & 0.0064 & 94.65\% & 97.82\% & 93.47\% & 95.56\% & 0.0571 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Experimental results of wall control group image classification. Figure 8: Confusion matrix of wall testing set images: (**a**) testing group; (**b**) control group. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Original Image** & **Heatmap** \\ \hline TP & & 8.9854 (T) & 9.7063 (T) \\ \hline TN & & 0.0008 (T) & 0.0013 (T) \\ \hline FP & & 0.0481 (C) & 0.0125 (C) \\ \hline FN & & 0.0043 (C) & 0.0039 (C) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Original images and Heatmap results of the wall testing set. It can be seen from Figure 11a and Table 8 that the trained network model tends to be stable with about 50 epochs and 1767 s. The model is used to detect the calibration set. The prediction results are shown in Figure 11b. Generally, the crack detection prediction results are satisfactory. For non-crack images, the average thermal scores are roughly around 0; for crack images, some blurry or tiny-crack crack images tend to be 0-1, whereas clear or wide crack images are greater than 1. This further shows that the average thermal scores obtained by the proposed method can be approximately considered as the differences from the central threshold obtained with the network model, i.e., as the average thermal scores of the image become larger, the difference between cracks and non-crack images becomes greater, and the possibility of defects becomes higher. In the ROC curve, the AUC value can reach 0.9730, and finally, the thermal threshold reaches 0.0513. Figure 11: The results of the bridge 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. The trained model is then applied to the testing set. The prediction results are shown in Table 8. The bridge crack image classifier of the confusion matrix is shown in Figure 12. The main indicators, Accuracy and F1-Score, reach 92.31% and 93.21%, respectively, and the testing speed reaches 0.0531 s/img. Some non-crack concrete images containing continuous grooves have relatively high average thermal scores, resulting in them being misclassified as cracks. Nevertheless, some small hairy cracks are very close to the background and have low average thermal scores, resulting in being misclassified as non-crack images.