# Detection Based on Crack Key Point and Deep Convolutional Neural Network
## 3 Crack Detection Model KP-CraNet
### Feature Filtration Network  
The outputs of FPN feature fusion and reinforce network need another convolution operation for feature processing and finally output an anchor point prediction result the same size as the corresponding original feature layers. Different layers contain different numbers of local or global features, so the prediction results of each layer can be regarded as the prediction results for different features' extent, i.e., whether the corresponding area contains a crack. Predictions that consider global features will have higher prediction accuracy, while predictions considering local features will have higher localization accuracy. Thus, starting with global features, the feature points that do not have cracks are gradually filtered out based on the results of the current layer prediction. Finally, the identification results are obtained, and the prediction accuracy and crack location accuracy are guaranteed. The process of crack detection shown in Figure 9 exemplifies how a feature filtration network works. Firstly, we input the prediction results of the bottom feature layer that contains the most comprehensive global information, as shown in Figure 9, into the feature filtration network. Due to the relatively large distance between feature points, each feature point  
Figure 9: Feature filtration network. contains comprehensive global feature information. The prediction result of the current layer helps to distinguish between the crack area and noncrack area, as shown in Figure 9b. We removed the feature points in noncrack areas and kept those in the crack area, as shown in Figure 9c. Based on this filtering result, the feature points corresponding to the next feature layer were retained. As shown in Figure 9d, the features and anchor points of this layer were screened, and after the screening, only the anchor points of the current layer in the crack-containing area were retained again; this process was repeated continuously. According to the network structure, three times in sequence were filtered, and the points finally retained were the anchor points of the positive sample of the lowest local features at the maximum resolution set and the minimum step size. These were the key points of the identified cracks. It is important to note that the above method is completely different from directly deciding whether an area contains cracks. The method depends totally on convolution or pooling operations, whose weight is obtained via the model's automatic learning. ### Feature Filtration Network  
In model training, the input for each layer level is the anchor point prediction result of the previous layer of features and the eigenvalue of the current layer of features. The output is the anchor point prediction result of the current layer, which is used to determine whether each anchor point is a positive sample point of the current layer. Due to the different sizes of the input images at different layers, or the different sizes of the feature layers, the tolerance of the critical point determination for identifying cracks is also different. So, the thresholds \(\varepsilon_{\text{P}}\), \(\varepsilon_{\text{N}}\), and loss function are determined by the size of feature maps. For reticulated reference anchor points at equal intervals, if their anchor point stride is S pixels, then the maximum distance between a crack key point and its nearest anchor point is \(\sqrt{2}S/2\) pixels. As shown in Figure 10, the yellow and green points are fracture key points, and the furthest possible location from the nearest anchor point to that fracture key point is the four red points around it. \(\varepsilon_{\text{P}}=0.8S\) and \(\varepsilon_{\text{N}}=1.5S\) can be extracted to define positive and negative sample anchor points in every layer. When the possibility that the reference anchor point is a positive sample point is higher than the set threshold, the reference anchor points are regarded as positive sample points of the current layer.