# Detection Based on Crack Key Point and Deep Convolutional Neural Network
## 2 Crack Characterization
### Reference Anchor Point Method
#### 2.2.2 Set Reference Anchor Point  
Although the sparsity of crack key points can be controlled through set-distance scattering, which reduces the error caused by the density of crack key points to an extent, the number of crack key points is still a problem in real-life detection. If the number of crack key points is too low, it may result in an inability to identify all cracks accurately; if the number is too large, it is very computationally intensive. Therefore, this research proposes a reference anchor point method for crack identification.  
The reference anchor point method is derived from the anchor mechanism of the prediction box in the faster R-CNN model [37]; in this research, the anchors were considered the prediction points for crack detection. We laid out the anchor points on the image in advance and detected whether each anchor point was near a crack key point to keep only the nearest anchor points as the final detection results. This method can effectively solve the latter two problems mentioned above.  
We set the reference anchor point as in Equation (5):  
\[p^{\text{anchor}}=\{(x_{1},y_{1}),(x_{1},y_{1}),\cdots,(x_{N^{\text{anchor}}}, y_{N^{\text{anchor}}})\}, \tag{5}\]  
where \(N^{\text{anchor}}\) is the number of the anchor point of a single image, and \(N^{\text{anchor}}\) is related to the anchor point layout. The distance between the adjacent two anchor points \(S\) is the only parameter for determining the anchor point location, i.e., the anchor point stride. The reference anchor point method is used to set anchor points in an image based on a certain pixel distance in advance, as the red dots show in Figure 4. Thus, crack detection has turned into a matter of calculating the probability value of reference anchor points as crack key points, and when the probability value is higher than a certain threshold, the anchor point will be regarded as a detected crack key point.  
The number of anchor points varies according to the actual situation, enabling the reference anchor point method to accurately detect cracks based on anchor points in different densities. For example, the crack area is first determined using anchor points with large step lengths, and then the local crack area obtained is refined to make a more accurate prediction of the cracks using dense anchor points, thus establishing a multiscale crack identification method.  
The interval between the anchor step and the crack key determines the crack identification accuracy. If the anchor step is in pixel units, this crack-critical point method  
Figure 3: The process and result of set-distance scattering.  
is almost equivalent to the pixel-based image crack identification method (conventional image segmentation method). They differ only in terms of the labeling error in crack labeling and whether the pixel width of the crack is considered. On the other hand, if the entire cracked image has only one crack key, the method is equivalent to the image classification task, which divides the whole image into areas with or without cracks. Thus, the image segmentation and image classification methods are special cases of the crack key point method.