# Pavement Distress Detection Using Three-Dimension Ground Penetrating Radar and Deep Learning
## 2 Proposed Approaches
### Proposed Localization Model
#### 2.2.2 Structure of CP-YOLOX  
In order to localize anomalous waveforms, a CSP PAN YOLOX (CP-YOLOX) model has been proposed, which is modified from the original YOLOX [32]. The proposed model can be divided into three parts: CSPDarkNet-SPP as Backbone, Path Aggregation Network (PAN) as Neck, and Decoupled Head as Prediction [33; 34; 35]. The architecture of the model is shown in Figure 6.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**Layers**} & \multicolumn{2}{c}{\ \begin{tabular}{c} **Kernel Size and** \\ **Number** \\ \end{tabular}  } & \multicolumn{2}{c}{**Input Size**} & \multicolumn{2}{c}{ \begin{tabular}{c} **Output** \\ **Size** \\ \end{tabular}  } & \multicolumn{2}{c}{**Stride**} \\ \hline Focus & & \(3\times 4=12\) & \(416\times 416\) & \(208\times 208\) & - \\ CBS3 & & \(3\times 3\), \(48\) & \(208\times 208\) & \(208\times 208\) & 1 \\ \hline \multirow{4}{*}{CSPLayer 2} & CBS3 & \(3\times 3\), \(96\) & \(208\times 208\) & \(104\times 104\) & 2 \\  & CBS1 & \(1\times 1\), \(48\) & \(1\times 1\), \(48\) & \(104\times 104\) & \(104\times 104  
A CSP layer divides its input into two parts by performing a \(1\times 1\) convolution operation in which one part passes through multiple residual modules to extract features, and then the features are concatenated with another part. The residual module consists of two CBS and one residual edge. The first CBS was used for channel adjustment to reduce the computation cost, while the second one was used for feature extraction. The CSP layer reduces the calculation of the network as well as the redundancy of the network information while ensuring efficient feature extraction. Based on the proposed model, the number of CSP layers represents the number of residual module cycles, and the cycle numbers of the four residual modules were 2, 6, 6, and 2. The CBS consists of a convolutional layer, a batch normalization (BN) layer, and a SiLU activation function [36]. There were two sizes of convolutional kernels in the convolutional layer. The \(1\times 1\) convolutional kernels were used for channel adjustment to increase the nonlinear fitting ability, while the \(3\times 3\) convolutional kernels were used for feature extraction. The BN layer normalized the outputs of a convolutional layer to accelerate network convergence and alleviate overfitting. The SiLU activation function was a comprehensive version of the Sigmoid and ReLU functions and is defined as follows. \[\text{f(x)}=\text{x}\cdot\text{sigmoid(x)}, \tag{1}\]  
\[\text{sigmoid(x)}=\frac{1}{1+\text{e}^{-x}}. \tag{2}\]  
Its smooth and non-monotonic characteristics work well on deep neural networks. The function is shown in Figure 8.  
Prediction  
A decoupled head was proposed as the prediction architecture, using neck architecture features as inputs. The decoupled head decoupled the classification and regression tasks, as shown in Figure 10. The regression task aimed to predict the bounding box of each anomalous waveform area, while the classification task classified each anomalous waveform area into one of the distress classes. The decoupled head network used a CBS layer to generate two feature vectors based on the input features. The first vector was then passed through two CBS layers to produce a classification prediction vector, and the second  
Figure 8: Activation function of SiLU. vector was also passed through two CBS layers to produce a regression prediction vector. After concatenating the two vectors, the dimension of the concatenated vector was adjusted by using a \(1\times 1\) convolution layer. The final output of the model was a feature vector with the size of \(1\times 6\), where \(6\) can be divided into \(1+1+4\), corresponding to anomalous waveform or not, confidence, and location of the prediction boxes. The proposed model adopted the anchor-free strategy, which did not require pre-defining anchor sizes.