## 4 Experiments and Discussion
### Crack Region Detecting Accuracy  
In this subsection, the crack region detecting accuracies of the proposed method and of the other compared crack detectors are discussed. First of all, six kinds of divided image patches from the 100 test concrete images were calculated: \(P\) (positive) is the number of image patches containing cracks; \(N\) (negative) denotes the number of image patches excluding cracks; \(FN\) (False Negative) denotes the number of crack regions which were identified as non-cracks; \(FP\) (false positive) denotes the number of non-crack regions which were identified as cracks; \(TP\) (true positive) represents the number of correctly detected to be crack regions; and \(TN\) (true negative) denotes the number of correctly detected non-crack regions. The crack region detecting accuracy of a crack detector was computed with the \(FNR\) (false negative rate) and \(FPR\) (false positive rate) criteria, as follows:  
\[\left\{ \begin{array}{l}FNR=\frac{FN}{P}\times 100\%\\ FPR=\frac{FP}{TP+FP}\times 100\%.\end{array} \right. \tag{20}\]  
It should be noted that the two criteria, mentioned above, require the accurate number of cropped image patches. In this case, the Otsu and Canny crack detections can not be valued. Using the three testing Datasets (i.e., DS1, DS2, and DS3) containing cracks, the experimental results of the local analysis-based crack detectors (i.e., DL, SVM, and the presented MECD model) are shown in Table 1.  
Mathematically, the \(FNR\) value represents the ratio between the mistakenly identified crack patches and the manually labeled crack patches. It is obvious that a crack detection model with a small \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Challenges** & **DataSets (Number)** & **Method** & \(P\) & \(N\) & **TP** & **TN** & **FN** & **FP** & **FNR (\%)** & **FP (\%)** \\ \hline \multirow{3}{*}{Background disturbances} & \multirow{3}{*}{DS1 (59)} & SVM & & 23,797 & 138,271 & 983 & 2503 & 3.97\% & 9.52\% \\  & & DL & 24,780 & 140,774 & 23,107 & 140,049 & 1673 & 725 & 6.75\% & 3.04\% \\  & & MECD & & & 24,328 & 140,262 & 452 & 512 & **1.83\%** & **2.06\%** \\  & & SVM & & 13,637 & 70,710 & 623 & 2016 & 4.37\% & 12.88\% \\ \multirow{3}{*}{Illumination changes} & \multirow{3}{*}{DS2 (31)} & DL & 14,260 & 72,726 & 13,348 & 72,268 & 912 & 458 & 6.40\% & 3.32\% \\  & & MECD & & & 13,962 & 72,411 & 298 & 315 & **2.09\%** & **2.21\%** \\  & & SVM & & & 2584 & 24,871 & 216 & 389 & 7.71\% & 13.08\% \\ \multirow{3}{*}{Image blurring} & \multirow{3}{*}{DS3 (10)} & DL & 2800 & 25,260 & 2444 & 25,164 & 356 & 96 & 12.71\% & 3.78\% \\  & & MECD & & & 2718 & 25,204 & 82 & 56 & **2.93\%** & **2.02\%** \\  & & SVM & & & 40,018 & 233,852 & 1822 & 4908 & 4.35\% & 10.92\% \\ \multirow{3}{*}{Average testing accuracy} & \multirow{3}{*}{DS1,DS2,DS3 (100)} & DL & 41,840 & 238,760 & 38,899 & 237,481 & 2941 & 1279 & 7.03\% & 3.18\% \\  & & MECD & & & 41,008 & 237,877 & 832 & 883 & **1.99\%** & **2.11\%** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparisons of crack region testing accuracy. SVM; Support Vector Machine. Figure 8: Representative crack damage detecting results of the field experiment: (**a**) The field environmental scene; (**b**) and (**c**) two sides of concrete beam; (**d**) the concrete bridge deck; (**e**–**i**) stress concentration areas. All the detected crack regions are marked with a blue X symbol. \(FNR\) value would have a high crack damage detecting performance. As shown in Table 1, one can see that the presented MECD model achieved the best detecting results (with a \(FNR\) value lower than 0.03) among all the compared crack detectors. Similarly, the \(FPR\) value denotes the ratio between the falsely recognized non-crack patches and the total number of detected crack regions, which depicts the incorrect detection rate of crack regions. Generally, a favorable crack detector should have a small \(FPR\) value.