## 2 Materials and Methods
### ROI-Binarized Hyperbolic Region  
#### 2.2.1 The Residual Convolutional Neural Network  
The proposed deep Res-CNN architecture is illustrated in Figure 2. The Res-CNN is a kind of end-to-end learning network widely used in image segmentation that can integrate features of different scales to achieve better learning results. A convolutional neural network can extract low-level, intermediate, and high-level features. As the number of layers increases, features at different levels can be extracted. The deeper the network, the more abstract the features extracted. But simply adding depth can lead to gradient dispersion or a gradient explosion. Therefore, a novel Res-CNN has been proposed, which combines the characteristics of skip connections and residual structure to extract the ROI-binarized hyperbolic region in the GPR profile, facilitating the quick separation of reflected waves from the GPR background profile and simplifying the GPR profile. As shown in Figure 2, the proposed Res-CNN architecture consists of an encoding process, a decoding process, and an output process. The encoding process consists of five downsampling modules; each downsampling module consists of a convolutional layer, a LeakyReLU activation function layer, and a MaxPooling layer (the last downsampling module does not contain) to achieve dimensionality reduction in GPR input data. The downsampling module includes a convolution layer with small 4 \(\times\) 4 kernels, increasing feature maps from 16 to 256 by a factor of 2, and a LeakyReLU activation with a negative slope coefficient (\(\alpha\) = 0.2) and a max-pooling with 2 \(\times\) 2 filters and stride 2. The decoding process is made up of five upsampling modules; each upsampling module is made up of a transposed convolution layer, a Batch Normalization layer, and a ReLU activation function  
Figure 1: ROI-binarized hyperbolic region extraction algorithm flowchart in GPR raw data. layer to recover GPR data. Between the downsampling module and the upsampling module, a skip connection is used to overcome the problem of vanishing or exploding gradients when the number of convolutional layers increases and can use features learned from earlier layers in deeper layers. The skip connections involve skipping some of the layers in the neural network and feed the output of one layer as the input to the next layers. The layers in the encoder part are connected with skip connections and concatenated with layers in the decoder part. This enables the Res-CNN to use fine-grained details learned in the encoder part to construct an image in the decoder part. Finally, the output process contains a transposed convolution layer and a sigmoid activation function layer to obtain the extraction of ROI-binarized hyperbolic regions in the GPR profiles. In our network architecture, three activation functions are used, respectively. The leaky rectified linear unit, or Leaky ReLU, is a type of activation function based on a ReLU, but it has a small slope for negative values instead of a flat slope. It is adopted to prevent the degradation problem of losing neuron information caused by the negative value in the downsampling module and accelerate convergence. The rectified linear activation unit (ReLU) is used as a default activation function to recover data since the negative values are not involved in the upsampling module in CNNs. The sigmoid activation function takes input and maps the resulting values between 0 and 1 for binary classification in the output process. In addition, skip connections are introduced to cascade the layers in the downsampling module with the upsampling module. The design allows information to flow more freely and preserves the details and semantic information in the original input data. This makes it easier for information to spread to subsequent levels and avoids information loss. A batch normalization layer is added to the upsampling module to overcome the problem of slow convergence due to discontinuous data distribution.