## 5 Results and Discussions
### Evaluation of Accuracy and Reliability of the Present Algorithm  
To quantify the performance of the proposed crack identification method, the accuracy rate, regression rate, and F-score were calculated throughout the training process. The accuracy rate is defined as the percentage of correctly classified pixels in all detected pixels in 3D shadow maps; the regression rate is defined as the percentage of correctly classified cracked pixels out of all actual cracked pixels; and F-score is defined as a measure of the training accuracy [45; 46]. To verify the effectiveness and accuracy of the resultant CNN in pipeline corrosion crack identification, 200 testing images were employed and 81 selected crack samples are utilized for computing the accuracy and regression rate. Figure 15 and Table 3 show the crack identification results for the 81 crack samples. The testing samples are divided into 10 groups of 3D shadow maps, denoted as \(G_{1}\), \(G_{2}\), \(\ldots\), and \(G_{10}\). Four indexes that include the true-positive rate (TPR), true-negative rate (TNR), false-positive rate (FPR), and false-negative rate (FNR) are computed. The definitions of these four indexes are:  
**True-positive rate (TPR):** The element originally belongs to the target class but it is also correctly identified and marked as the target class;  
**True-Negative rate (TNR):** The element does not belong to the target class but it also correctly identified and marked as a non-target class; \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Layer** & **Kernel Size** & \
\begin{tabular}{c} **Number of** \\ **Parameter** \\ \end{tabular} &
\begin{tabular}{c} **Number of** \\ **Connection** \\ \end{tabular} \\ \hline C1 & \(12\times 12\) & 580 & 16,369,920 \\ S2 & \(6\times 12\) & 4 & 383,616 \\ C3 & \(12\times 12\) & / & / \\ S4 & \(6\times 6\) & / & / \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Detailed settings of the CNN for crack identification. Figure 14: Identification results for pipeline corrosion cracks. **False-positive rate (FPR):** The element does not belong to the target class but it is incorrectly identified and marked as the target class;  
**False-negative rate (FNR):** The element originally belonged to the target class but was incorrectly identified and marked as a non-target class. Figure 15: Cont. Based on the definitions of TPR, TNR, FPR, and FPR, the accuracy rate (\(P\)), regression rate (\(R\)) and F-score (\(F\)) can be determined:  
\[P=\frac{N_{TP}}{N_{TP}+N_{FP}} \tag{22}\]  
\[R=\frac{N_{TP}}{N_{TP}+N_{FN}} \tag{23}\]  
\[F=\frac{2N_{TP}}{2N_{TP}+N_{FN}+N_{FP}} \tag{24}\]  
where \(N_{TP}\) is \(N_{FP}\) and \(N_{FN}\) are the number of true-positive, false-positive, and false-negative elements, respectively. Figure 15 shows the resultant accuracy, regression rate and F-score versus the number of epochs (an epoch refers to one cycle through the full training dataset). The results of the ten groups of 3D shadow maps (i.e., \(G_{1}\), \(G_{2}\),..., and \(G_{10}\)) are indicated with solid  
Figure 15: The training proceed comparison based on the crack detection test data for the 10 groups of 3D shadow maps. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Group No.** & **Image Number Range** & **Accuracy (\%)** & **Regression Rate (\%)** & **F-Score (\%)** \\ \hline
1 & 0 \(\sim\) 7 & 94.17 & 96.53 & 85.4 \\
2 & 8 \(\sim\) 15 & 93.97 & 91.61 & 85.27 \\
3 & 16 \(\sim\) 23 & 95.19 & 96.05 & 90.28 \\
4 & 24 \(\sim\) 31 & 89.71 & 86.02 & 90.18 \\
5 & 32 \(\sim\) 39 & 87.35 & 85.93 & 91.92 \\
6 & 40 \(\sim\) 47 & 93.86 & 94.61 & 94.47 \\
7 & 48 \(\sim\) 55 & 95.12 & 91.69 & 92.96 \\
8 & 56 \(\sim\) 63 & 96.18 & 94.76 & 93.85 \\
9 & 64 \(\sim\) 71 & 93.56 & 94.73 & 94.39 \\
10 & 72 \(\sim\) 80 & 96.14 & 88.49 & 93.06 \\
**Summary** & **0 \(\sim\) 80** & **93.53** & **92.04** & **91.18** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comprehensive evaluation results for automatic crack detection algorithm.