## 2 Materials and Methods
### Processing of Images  
The acquired radargrams were subjected to standard pre-processing. This process consists of the stages of noise reduction and signal enhancement. Standard radargram processing, therefore, includes time-zero correction, removing the background, frequency,  
Figure 1: Diagram of the placement of channels in the Stream C ground\(-\)penetrating radar.  
Figure 2: Location of the acquired GPR data.  
and gain filters. The aim of time-zero correction is to adjust the zero time to the time on the surface of the Earth. The difference in time may result from electronic instability, thermal drift, or variations in the antenna airgap. The background removal stage was conducted in order to eliminate random noise and to improve the signal-to-noise ratio. One of the applied filtration processes was gain processing, which refers to the enhancement of the amplitude and energy of electromagnetic waves, whose power diminishes after dispersion, diffraction, and absorption by the underground medium [6; 51]. As part of the radargram pre-processing, multipatch interference and salt-and-pepper noise were eliminated.  
The method of hyperbola detection proposed previously by the authors [PERSON] and [PERSON] in [52], based on the radiometric and geometric properties of the detected objects, consists of the automated detection of hyperbolas that represent elements of the underground infrastructure based on the Sauvola binarization method and the extraction of hyperbolas that meet three geometrical criteria: size (C\({}_{S}\)), curvature (C\({}_{C}\)), and the depth of the object (C\({}_{D}\)). The scheme of the detection method is presented in Figure 3.  
Both the manual and automated detection of underground utility networks was carried out on the acquired radargrams. The first stage of the process of the automated detection of hyperbolas representing the underground infrastructure was binarization with the Sauvola method that enables the determination of the automated binarization threshold (\(T\)--Formula (1)) based on a specified degree of noise in the image (\(k\)) [53; 54].  
\[T=m\cdot\left[1+k\cdot\left(\frac{s}{R}-1\right)\right] \tag{1}\]  
where  
\(k\)--parameter defining the degree of noise in the image, \(k\in<\)0;1\(>\);  
\(m\)--average standard deviation;  
\(s\)--local standard deviation in the neighborhood of the given pixel (x,y);  
\(R\)--range of the standard deviation.  
The size of the window that defines the neighborhood of the pixel (x,y) and the value of the \(k\) parameter are selected heuristically based on the analysis of a set of radargrams. The obtained results of the GPR measurements were verified against the reference data obtained from the National Geodetic and Cartographic Resource (NGCiR). At the subsequent stages, hyperbolas that met the predefined geometric conditions were extracted. These conditions were size (C\({}_{S}\)), curvature (C\({}_{C}\)), and the depth of the object (C\({}_{D}\)). Based on the research conducted by [PERSON] and [PERSON] in [52], predefined geometric conditions were determined that are met by the hyperboles representing underground infrastructure: (1 st condition) the size of the object (C\({}_{S}\)) is larger than 45 px, (2 nd condition)  
Figure 3: The scheme of hyperbolas detection method.  
the curvature of the object (C\({}_{\text{C}}\)) falls within the range of <0.016; 0.160>, (3 rd condition) the depth of the object (C\({}_{\text{D}}\)) is larger than 13 px [52]. The curvature of hyperbolas was determined based on the fitting of the parabola into a set of pixels with the use of the non-linear least squares method.