## 3 Results
### Model Testing of Simple Pipe Simulation  
To test the effectiveness of the proposed method, a simple pipe model is designed as shown in Figure 5. The model size is 1.1 m \(\times\) 5.0 m, with an air layer set to 0.1 m. The relative permittivity of the background is 9, and some small pores with a relative permittivity of 1 are randomly distributed in the medium models. Seven empty pipes with different material walls are distributed in the model, and the pipe parameters are shown in Table 1. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Pipeline Number**} & \multirow{2}{*}{**Pipeline Material**} & **Pipeline** & **Pipeline** & **Pipeline** \\  & & **Outer-Diameter (m)** & **Inner-Diameter (m)** & **Pipeline Depth (m)** \\ \hline I & metal pipeline & 0.200 & 0.180 & 0.600 \\ \hline II & metal pipeline & 0.150 & 0.130 & 0.575 \\ \hline III & PVC & 0.200 & 0.180 & 0.350 \\ \hline IV & metal pipeline & 0.150 & 0.130 & 0.375 \\ \hline V & PVC & 0.150 & 0.130 & 0.375 \\ \hline VI & metal pipeline & 0.200 & 0.180 & 0.675 \\ \hline VII & metal pipeline & 0.150 & 0.130 & 0.450 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: FDTD models of different pipes parameters in a random medium. Figure 4: Loss function curves of the model. Figure 5: Simple underground pipe model distribution. The transmitting and receiving antennas move along the ground surface to collect data, as shown in the figure with the red stars. The forward simulation adopts the finite difference time domain algorithm, and the center frequency of the excitation source is 900 MHz. The special step of the forward model was set to 0.005 m in both the x and y directions. The time step was set to 0.01 ns, and the time window is 15 ns. The radargram obtained from the forward simulation result is shown in Figure 6a, and the GPR profile after preprocessing is shown in Figure 6b. In the forward simulation results, the energy of the airwave is much larger than the energy required to obtain reflected waves from the underground pipe targets, and the stronger airwave will seriously affect our ROI-binarized hyperbolic region extraction. To eliminate the effect of air waves, the moving average method is employed to eliminate the horizontal arrivals in our preprocessing results. As shown in Figure 6b, seven different types of pipe reflection hyperbolas are well visualized during the forward simulation, and the diffraction waves and multiple waves from between pipes can be distinguished, but the energy of the target reflection hyperbola is weakened or even submerged due to the inhomogeneity of the background random medium. In order to simplify the GPR profile and extract the hyperbolic reflected waves of interest in the GPR profiles more quickly and efficiently, and to provide a good guiding relevance for the interpretation of the subsurface medium, the current popular image segmentation methods, namely the Otsu thresholding method and the K-means clustering segmentation method, are compared with our proposed Res-CNN method, as illustrated in Figure 7.  
Figure 6: Radargram from FDTD simulation of a pipe model in random media and its preprocessing result. (**a**) the forward simulation results; (**b**) the preprocessing results. The profile of interest obtained from the forward modeling results in a homogeneous medium that serves as the ground truth, as shown in Figure 7a. In Figure 7b, due to the random interference of the background random medium, the Otsu threshold method makes it difficult to search for a suitable threshold that minimizes the intraclass variance to achieve the separation of the hyperbolic region and the background in the GPR image and extracts the binarized ROIs. In Figure 7c, the K-means clustering segmentation method performs better than the original one. The results of the proposed method are shown in Figure 7c. In Figure 7c, the K-means clustering segmentation method performs better than the original one. The results of the proposed method are shown in Figure 7d.