## 4 Lightweight Crack Detection Model
### Crack-Amnotation Method Evaluation  
First, a small trial dataset containing 120 images is prepared to assess these three crack annotation methods, referred as the trial set, as seen in Figure 6.  
Using Mask RCNN for crack detection: The training tests were conducted using an Ubuntu 20.04 operating system, an Intel (R) Xeon (R) W-2133 CPU @ 3.60 GHz, Python as the programming language and 3.7 as the interpreter version. An NVIDIA GeForceRTX2080 Ti GPU was used as the accelerator for the model training tests. Model training and testing  
Figure 5: Overview of crack-detection model training and model evaluation.  
were accelerated using CUDA and Cudnn. The deep learning framework of choice was Pytorch.  
To evaluate the models' performance, precision and recall are basic indicators, which are calculated as True Positive (TP), False Positive (FP), False Negative (FN) and True Negative (TN), as seen in Equations (1) and (2).  
\[\text{Precision}=\frac{\text{TP}}{\text{TP}+\text{FP}} \tag{1}\]  
\[\text{Recall}=\frac{\text{TP}}{\text{TP}+\text{FN}} \tag{2}\]  
where TP indicates the number of detected objects that are correctly classified, while FP denotes the number of backgrounds in the image that are misidentified as detected objects. Additionally, FN denotes the number of detected objects in the image that are misclassified as backgrounds, and TN denotes the number of backgrounds in the image that are correctly classified as backgrounds.  
Average precision, termed AP, is a measure of how well an object detection algorithm performs. To assess the model's performance, mean average precision (mAP), which means the average precision of different categories, is also taken into consideration. Similarly, average recall, named AR, is a performance metric in object detection that measures the average ratio of correctly detected objects compared to the total number of objects across multiple recall thresholds. In general, the AR, AP and mAP are performance metrics that can be used to evaluate the accuracy of object detection algorithms.  
The results are summarized in Table 2. As can be seen, the results show that relative-breakpoint crack annotation suits the model best and performs best, as indicated by the highest AP or AR values. For instance, in addition to the indicator AP:0.5-0.95, Rel-break has the highest value of all other indicators. Overall, Rel-break has an AP value of 28.4,  
Figure 6: Part of the trial datasets, using different crack annotation methods.  
much higher than Cont's 12.5 and Abs-break's 18. In addition, Rel-break has a large advantage over AP and AR for large-scale targets, with a value of 55.8. On the other hand, the AP of the Cont method for large-scale targets is very low, only 19, which indicates that slender and large-scale labels are not suitable for model training. Additionally, Abs-break is slightly better than Rel-break in the index of small-scale objects. This might be due to the fact that, if there are intersection points in small-scale objects, boundary distinction is difficult to carry out because the scale is too small. Thus, Rel-break does not show an advantage in distinguishing different cracks at the intersection points.  
Therefore, the outperformance of the proposed relative breakpoint annotation can be demonstrated, as previously analyzed in Table 1. It was chosen to label more images in order to examine further its feasibilities.