## 4 Experiments
### Evaluation of DO-YOLOv4-IPTs for Crack Segmentation  
Once the cracks are detected by DO-YOLOv4 using multiple oriented bounding boxes, the IPTs are further employed in the regions enclosed by those boxes for crack segmentation, by which the crack sizes, e.g., the lengths, widths, and areas, etc., can be quantified on the pixel level. To evaluate the performance of DO-YOLOv4-IPTs for crack segmentation, several existing CNN-based crack segmentation methods, including FCN [9], Unet [10], CrackSegNet [64] and CrackPix [65], were selected for comparison study, and the results of different methods are depicted in Figure 12, in which the crack areas are denoted in terms of the numbers of pixels in the brackets. It can be seen from image (a) and image (b) of Figure 12 that, for the cases with fewer background interferences, CrackSegNet, CrackPix, and DO-YOLOv4-IPTs perform well with similar segmentation results, while certain discrepancies can be observed in the results of FCN and Unet. For the very tiny crack with background interferences shown in image (c) of Figure 12, all four CNN-based methods fail to identify the crack, while DO-YOLOv4-IPTs is still capable of segmenting the crack correctly. Furthermore, to investigate the influence of crack-like interferences, the crack images shown in image (d) and image (e) of Figure 12 were employed for crack segmentation. It can be observed that the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **Feature Extraction Network (Size)** & **Bounding Box** & **AP (\%)** \\ \hline Faster R-CNN & VGG16 (527.8 MB) & Single, horizontal & 58.89 \\ SSD & Resnet50 (89.67 MB) & Single, horizontal & 41.04 \\ YOLOv3 & Darknet53 (154.82 MB) & Single, horizontal & 45.16 \\ YOLOv4 & CSPDarknet53 (101.5 MB) & Single, horizontal & 53.10 \\ DO-YOLOv4 & Improved CSPDarknet53 (53.3 MB) & Multiple, oriented & 80.43 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of different object detection methods. Figure 11: The P-R curve for different object detection methods. CNN-based methods are very sensitive to crack-like interferences, and over-segmentation results were more or less obtained by the CNN-based methods. Whereas DO-YOLOv4-IPTs still exhibits ideal performance under crack-like interferences. To quantify the performance of different crack segmentation methods, the pixel-level IoU (PIoU) metric is defined herein as the ratio of intersection to union of the ground-truth crack area and the segmented crack area in terms of the pixel numbers. The PIoU metrics of different methods for crack segmentation of the images shown in Figure 12 are presented in Table 2, from which it can be seen that, in general, DO-YOLOv4-IPTs has higher PIoU metrics than CNN-based methods, in particular for the case of image (c). The mean PIoU metrics of different segmentation methods are also presented in Table 2, from which it can be found that DO-YOLOv4-IPTs has the highest mean PIoU metric, as expected. In summary, DO-YOLOv4-IPTs can maintain a good standard for crack segmentation even with the presence of complex background within the crack images, which is mainly due to the high accuracy of DO-YOLOv4 for crack detection, as discussed in Section 4.2. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{5}{c}{**PIoU (\%)**} & \multirow{2}{*}{**Mean PIoU (\%)**} \\ \cline{2-2} \cline{4-7}  & **Image (a)** & **Image (b)** & **Image (c)** & **Image (d)** & **Image (e)** \\ \hline FCN & 39.10 & 47.43 & 6.95 & 52.96 & 55.73 & 40.44 & 5 \\ Unet & 54.17 & 69.63 & 18.38 & 65.32 & 40.35 & 49.57 & 5 \\ CrackSegNet & 64.53 & 70.39 & 21.43 & 49.98 & 53.54 & 51.97 & 5 \\ CrackPix & 68.85 & 77.54 & 19.22 & 67.08 & 52.67 & 57.07 & 5 \\ DO-YOLOv4-IPTs & 72.49 & 75.14 & 61.42 & 78.24 & 70.93 & 71.64 & 0.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of CNN-based methods and DO-YOLOv4-IPTs for crack segmentation. Figure 12: Crack segmentation results of CNN-based methods and DO-YOLOv4-IPTs.