# Automated Pixel-Level Deep Crack Segmentation on Historical Surfaces Using U-Net Models
## 4 Experimental Results
### Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Loss Function**} & \multicolumn{2}{c}{**Contrast Stretching**} & \multirow{2}{*}{**Accuracy \%**} & \multirow{2}{*}{**Precision\%**} & \multirow{2}{*}{**Recall\%**} & \multirow{2}{*}{**mIoU\%**} & \multirow{2}{*}{**Dice Score\%**} & \multirow{2}{*}{** Jaccard\%**} \\ \cline{2-2} \cline{6-6}  & No & 98.189 & 46.312 & 40.651 & 65.226 & 40.231 & 25.181 \\ \cline{2-6}  & Yes & 98.135 & 63.760 & 52.642 & 69.77 & 52.489 & 35.583 \\ \hline \multirow{2}{*}{**Binary Cross-Entropy**} & No & 98.256 & 58.618 & 41.761 & 67.069 & 40.712 & 25.559 \\ \cline{2-6}  & Yes & 98.279 & 79.968 & 61.607 & 74.959 & 57.923 & 40.769 \\ \hline \multirow{2}{*}{**Hybrid**} & No & 98.022 & 47.336 & 32.855 & 62.567 & 34.495 & 20.842 \\ \cline{2-6}  & Yes & 98.155 & 70.195 & 44.622 & 67.876 & 47.678 & 31.301 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Deep ResU-Net performance metrics. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**Individual Test Dataset**} & \multirow{2}{*}{**Accuracy \%**} & \multirow{2}{*}{**Precision\%**} & \multirow{2}{*}{**Recall\%**} & \multirow{2}{*}{**mIoU\%**} & \multirow{2}{*}{**Dice Score\%**} & \multirow{2}{*}{** Jaccard\%**} \\ \hline Dataset [7] & 98.67 & 78.10 & 81.81 & 82.01 & 77.80 & 63.67 \\ \hline Historical Dataset & 98.19 & 67.03 & 33.17 & 63.92 & 37.98 & 23.44 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results of ResU-Net++-based crack segmentation on individual datasets (no contrast stretching). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Individual Test Dataset**} & \multirow{2}{*}{**Accuracy \%**} & \multirow{2}{*}{**Precision\%**} & \multirow{2}{*}{**Recall\%**} & \multirow{2}{*}{**mIoU\%**} & \multirow{2}{*}{**Dice Score\%**} & \multirow{2}{*}{** Jaccard\%**} \\ \hline Dataset [7] & 98.34 & 73.92 & 87.94 & 82.05 & 79.58 & 66.09 \\ \hline Historical Dataset & 97.34 & 62.37 & 69.20 & 73.11 & 61.42 & 44.32 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results of ResU-Net++-based crack segmentation on individual datasets (with contrast stretching). It is concluded from Table 7 that the proposed crack segmentation approach based on the \(U^{2}\)-Net model outperforms the DeepCrack [7] approach without any preprocessing or post-processing by achieving an mIoU of 83.87%. Moreover, the proposed approach performs well on the primary dataset, although it is excluded from training. Figure 11 shows some result samples of \(U^{2}\)-Net on the primary dataset. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Individual** & **Accuracy \%** & **Precision\%** & **Recall\%** & **mIoU\%** & **Dice Score\%** & **Jaccard\%** \\ \hline Dataset [7] & 98.87 & 79.71 & 85.39 & 83.78 & 80.52 & 67.392 \\ \hline Historical Dataset & 98.32 & 67.73 & 83.03 & 78.38 & 71.09 & 55.147 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Results of \(U^{2}\)-Net-based crack segmentation on individual datasets. Figure 11: \(U^{2}\)-Net result samples. Figure 14: Results on several samples of the used crack detection dataset, with different patterns—group-3. In each column, we present the results based on: (**a**) Image with a short wide crack on the edge, (**b**) Wide crack on the edge, (**c**) Image with a crack and corrosion, (**d**) Blurred image with a crack, (**e**) Blurred image with a crack inside ornaments. Figure 15: Results on several samples of the used crack detection dataset, with different patterns—group-4. In each column, we present the results based on: (**a**) Image with a branched crack (a multi-depth view), (**b**) Image with a crack inside carvings, (**c**) Image with a crack and marker, (**d**) Image with a crack inside ornaments, (**e**) Image with a branched crack. As shown in Figures 12a, 13a,c,d and 14d,e, ResU-Net++ without contrast stretching has difficulty in dealing with blurred images, where it cannot detect all or most of the crack pixels.