## 4 Experimental Setup  
In previous studies on crack detection, we found that lightweight models were often used for subsequent deployment on edge devices [17; 60]. It is generally agreed that deeper models have better feature extraction capabilities, but this also means more parameters and a longer training time. Therefore, after a comprehensive consideration, 13 currently prevailing object detection models were used for experiments on the dataset we developed in this study. According to the number of parameters in the models, they were divided into four groups, so that the number of parameters in each group was similar, as shown in Table 2. All these models are open-source. YOLOv5s was the model used in this study to generate pseudo-labels, and we used it as a benchmark in the experiments. In our experiments, all these models were based on the PyTorch framework. We used a cloud server as the training platform, and the GPU used was an NVIDIA RTX A5000 with 24 GB memory. We adjusted the batch size to the scale of each model to maximize GPU utilization. All these models were pre-trained on COCO [31] or ImageNet [28], but instead of using the pre-trained weights, we trained them from scratch on our dataset. Precision (Equation 1), recall (Equation 2), F-score (Equation 3), and mAP are common metrics used to evaluate the performance of object detection models. Precision is the proportion of relevant instances in the retrieved instances, while recall is the proportion of relevant instances retrieved, and they are both based on relevance. In Equations (1) and (2), true positive (TP) indicates the correct detection of ground truth, false negative (FN) indicates objects that were not detected, and false positive (FP) indicates incorrect detection. In the post-processing stage, the detection of an object was evaluated by the intersection \begin{table}
\begin{tabular}{c c c} \hline \hline
**Group** & **Model** & **Parameters** \\ \hline \multirow{3}{*}{Group 1} & SSDlite320 MobileNetV3-Large & 3.4 M \\  & YOLOv5n & 1.9 M \\  & YOLOv5s & 7.2 M \\ \hline \multirow{3}{*}{Group 2} & Faster R-CNN MobileNetV3-Large-FPN & 19.4 M \\  & Faster R-CNN MobileNetV3-Large-320-FPN & 19.4 M \\  & YOLOv5m & 21.2 M \\ \hline \multirow{3}{*}{Group 3} & FCOS ResNet50-FPN & 32.3 M \\  & RetinaNet ResNet50-FPN & 34.0 M \\ \cline{1-1}  & RetinaNet ResNet50-FPN v2 & 38.2 M \\ \cline{1-1}  & SSD300 VGG16 & 35.6 M \\ \hline \multirow{3}{*}{Group 4} & Faster R-CNN ResNet50-FPN & 41.8 M \\ \cline{1-1}  & Faster R-CNN ResNet50-FPN v2 & 43.7 M \\ \cline{1-1}  & YOLOv5l & 46.5 M \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The 13 models divided into four groups. Figure 6: Comparison of manual annotation and semi-automatic annotation: (**a**) our dense and redundant manual annotation; (**b**) semi-automatic annotation, which was denser and more redundant. over union (IoU), which indicates the degree of overlap between the predicted result and the true annotation. In this study, we considered IoU \(>\) 0.5 to validate the detected instances. The confidence score is also a free parameter and indicates a model's certainty about the detection results. In this study, all detected instances with confidence scores less than 0.25 were filtered out. The F-score (Equation 3) is a method of combining the precision and recall of the model, and it is defined as the harmonic mean of these. We can adjust \(\beta\) (Equation 3) to give more importance to precision over recall, or vice versa. Common adjusted F-scores include the F0.5-score and the F2-score, as well as the standard F1-score. In this study, only the F1-score was considered, which effectively reflects the model's overall capability. Among the metrics defined for the Pascal VOC challenge [30], mAP was calculated over a single IoU value, 0.5, while COCO [31] was different and more rigorous, in that 10 different IoU thresholds were considered. Both evaluation criteria were considered in the study.