An Adaptive Non-Reference Approach for Characterizing and Assessing Image Quality in Multichannel GPR for Automatic Hyperbola Detection

Abstract

The automation of the detection infrastructure in GPR imagery is a key issue, particularly in the context of the non-invasive acquisition of radargrams with a multi-antenna ground-penetrating radar. Due to the fact that the dataset acquired with a multi-antenna GPR is very large, in the context of automating the process of detecting hyperbolas, the authors have proposed an adaptive approach to the selection of GPR images. The aim of this project was to develop a method for the selection of GPR images by means of applying the appropriate quality indicators. The authors propose a new, adaptive approach to the selection of radargrams that were recorded during the route of a GPR in a single profile, where several radargrams were recorded. Depending on the obtained initial values of the standard indicators for the assessment of the quality and quality maps of the radargrams, those images from selected channels that will ensure the highest possible quality and efficiency of hyperbola detection were selected. The stage of image quality assessment is essential in the context of improving the effectiveness of the automated detection of underground infrastructure. The quality assessment was performed based on the entropy indicator, PIQE, and Laplacian variance. The selected quality indicators allowed the authors to assess the degree of blurring, noise, and the number of details representing the underground structures that are present in GPR images. An additional product of the quality assessment were the generated maps that present the distribution of entropy in the analyzed images. The image selection was verified based on the results of the parameters that assess the effectiveness of the detection of hyperbolas that represent underground networks. The proposed innovative adaptive approach to the selection of images acquired by GPR enabled a significant improvement in the efficiency of the detection of hyperbolas representing underground utility networks, by 15–40%, shortening data processing and infrastructure detection times.

1. Introduction

The modern management of underground infrastructure requires an accurate and reliable determination of the location, type, and technical condition of elements of utility networks. As far as the safety of the conducted modernization works of the existing infrastructure is concerned, non-invasive detection is crucial for the implementation of BIM technology and 3D cadastre [1,2,3]. One of the non-invasive geophysical methods for the detection of various underground media and the assessment of their technical condition is the ground-penetrating radar (GPR) method. The operating principle of GPR is based on the emission of electromagnetic waves from the transmitting antenna of the radar. The emitted sinusoidal signal penetrates the borders between media and materials that have different electric properties (i.e., electric permittivity and conductivity). Part of the signal penetrates into the medium, while the remaining part is dispersed or reflected, which is recorded by the receiving antenna of the ground-penetrating radar [4,5,6,7,8]. The dielectric constant, also referred to as electric permittivity, is a value that is specific for any given material. Its value is mainly determined by the presence of water in the given sub-surface medium [9,10,11,12,13,14].

The differences in the values of the electric permittivity of soil media and underground infrastructure allow for the detection of both metal and non-metal pipelines. Another factor that influences the ability to penetrate geological media is the attenuation of electromagnetic waves, whose value (the medium attenuation coefficient) increases in the vicinity of, for example, silty materials or salty water, as mentioned by Maślakowski, M. et al. [15].

An important aspect of the analysis of GPR (ground-penetrating radar) data is the number of radargrams acquired [16,17]. A high level of noise leads to the deterioration of image quality. Commonly used image quality factors are PSNR, contrast, brightness, focus, sharpness, and illumination [18,19]. There are also a few studies on the quality for target detection, target tracking, and event detection for reconnaissance applications. In the work by Irvine, J.M. and Nelson, E. [20], the applicability of the National Imagery Interpretability Ratings Scale (NIIRS) to an automated target detection algorithm was examined, and it was found that NIIRS is not a good predictor of target detection performance. This is why objective quality inspection methods are highly desirable. Their main aim is to obtain good-quality images. High image quality helps image detection methods extract certain features and objects. Unfortunately, there are few studies that propose a comprehensive evaluation index to evaluate image quality, which was discussed by the authors Lin, H.-I. and Lin, P.-Y. in [21].

The problems of the analysis and reduction in noise and interference that occur in GPR images has been the subject of research presented in many publications, such as by Iftimie, N. et al. in [22], and continues to pose a challenge in terms of the consequences and influence of these factors on the process of the detection and classification of underground objects. In multiple studies, the preliminary work begins with modeling noise, blur, and compression artifacts in order to address the blurriness, blockiness, graininess, and ringing in images [23,24,25,26]. The noise and low quality of the acquired images are determined by multiple factors, whose sources may be roughly divided into environmental ones (dielectric heterogeneity, moisture, presence of other objects, e.g., rocks, roots, or hollow spaces), instrumental ones (equipment limitations or electromagnetic interference), and methodological ones (settings of the measurement parameters and calibration of the ground-penetrating radar). So far, the authors of published research works have not analyzed the direct influence of the quality of radargrams (that are characterized by a clear presence of usable signals) on the effectiveness of the detection or classification of underground objects. The application of automated algorithms increases the number of falsely detected objects, thus eliminating the detection of the signatures of underground objects, i.e., the characteristic hyperbolas.

The key element in acquiring multiple images of the same area of interest is the assessment of their quality (in terms of the clear presence of usable signals). There are three types of image quality assessment (IQA) methods: full reference (FR) techniques that carry out assessment utilizing reference images, reduced reference (RR) techniques related to comparing extracted features, and non-reference (NR) techniques that do not use any reference images [27,28]. Full reference techniques enable the assessment of image quality in reference to a reference, i.e., the original image. These methods allow for the detection of areas that indicate distortions of the image. Reduced reference techniques consist in comparing selected properties of the image that were previously extracted from the reference image. Instead of the whole image, only important information is used in the analysis, which reduces the amount of data necessary to perform quality assessment. Finally, non-reference techniques do not require the use of reference images and are based on the identification of noisy areas and artifacts that prove the degradation of image quality. The traditional NR-IQA metrics are BLIINDS [29], NIQE [30], SSEQ [31], BRISQUE [32], and OG-IQA [33]. The significance of the use of blind-quality assessment was particularly emphasized in [34] by Chang, S. et al. However, the review of the existing literature does not reveal any studies on the analysis of images acquired with a ground-penetrating radar (both single- and multichannel) and on the selection of images of the highest quality.

Object detection is the first and most fundamental step for the automatic analysis of visual information. The manual interpretation, detection, and analysis of underground objects in GPR images is a time-consuming process. There are many publications on the automated detection of hyperbolas that represent underground objects [11,35] and on the detection and reconstruction of sub-surface hollow spaces [35,36]. These methods usually employ deep learning [36,37,38]. The effectiveness of detection as explained by Zahir, N.H.M. et al. in [36] was 90%. Although the detection results are promising, a disadvantage of deep learning algorithms is the fact that they require obtaining large sets of data that will be used in the equally time-consuming training process of the network. Tam, N.H. et al. in [39] used edge filters for the detection of hyperbolas.

The issue of the automation of the detection and classification of underground objects has been the subject of research presented in multiple other studies [40,41,42,43,44,45,46,47,48]. Gu, K. in [49] noted, however, that a “universal” quality metric appears to be impossible: one application may use information of an image that is not useful to another application. There are only a few studies on the problem of the real objective quality evaluation for automatic analysis algorithms. The performance of automatic analysis methods relies on the quality of images that are processed. It is therefore essential to introduce objective metrics for predicting the quality of images evaluated by automatic analysis algorithms.

Research Aim

Works related to the detection of infrastructure are often carried out with the use of a single-antenna GPR. The operator acquires a single radargram from each measurement route, so that, in consequence, this specific single radargram may be used or not. On the other hand, if data are acquired with a multi-antenna GPR, the operator obtains over 30 radargrams from each profile. Such a high number of radargrams in the context of the automation of the hyperbola detection process has inspired the authors to develop an approach with the aim of selecting one or more radargrams based specifically on their quality indicators. This enables to select the radargrams of the highest quality, which will provide the basis for further processing.

Our research works addressed the challenge of developing a more general quality analysis method for radargrams depicting the features of hyperbolas. Another important issue in this area is the diversity of the background characteristics of such images that depends not only on the penetrated medium but also on the types of objects represented by such hyperbolas. In this paper, the authors have attempted to design an efficient quality assessment method with less computation complexity in comparison to ML methods.

The scientific novelty of the proposed method is the use of an adaptive approach, i.e., sequential image quality assessment. This approach uses various metrics for quality assessment and the correlation between the obtained results. In addition, the method was verified on the original parameters developed by the authors for evaluating the effectiveness of hyperbola detection. The authors propose a new, adaptive approach to the selection of radargrams that were recorded during the path of a multichannel ground-penetrating radar in a single profile. The proposed approach may be particularly justified if the same terrain is measured with different measurement equipment. The approach is based on non-reference blind-quality assessment. Then, in order to verify the correctness of the assumptions, the method uses the comparison of the number of detected hyperbolas that represent the objects of interest (at the stage of binarization) and the assumed actual values (full reference technique).

Based on the conducted preliminary research, it was noted that the type of the channel and the quality of the acquired image have a direct influence on the effectiveness of hyperbola detection, in general, as image features, and, in consequence, the detection of underground structures and infrastructure. The authors have proven that the application of the proposed adaptive approach to the selection of GPR images allows for the improvement of the quality of the detection of hyperbolas representing the underground infrastructure by 15–40%.

2. Materials and Methods

2.1. Study Area and Measurements

This research was conducted with the use of a multichannel GPR Stream C. The frequency of the acquired data is 600 MHz. The use of more than ten antennas with the same frequency shortens the duration of data acquisition or enables to increase the resolution of measurements by using smaller spacing between the antennas. The application of multi-antenna systems offers a possibility to obtain full 3D migration by recording a broadband signal, as outlined by authors Gabryś, M. and Ortyl, Ł. in [50]. Data are acquired on 32 channels, in a band of 1 m. Most of the images (23 images) are obtained from VV polarization (transverse to the direction of measurement), and nine are obtained from HH polarization (along the direction of measurement). For VV polarization, images are captured at the intervals of 4.5 cm, while for HH polarization, the interval is 10 cm. The placement of channels and the type of antennas (transmitter, receiver) together with information about polarization (VV, HH) for the Stream C ground-penetrating radar are presented in Figure 1.

The samples recorded in a temporal window (during a specific interval) create a single ground-penetrating radar track, the so-called A-scan (Figure 1). It is a record of the changes in the amplitude of the returning electronic signal in time. Further tracks recorded along the line form the radargram referred to as the B-scan, which is the vertical cross-section of the ground medium. The process of the interpolation of several B-scan profiles enables to generate so-called C-scans that provide data about the correlations between the phenomena recorded in the B-scans. GPR data were obtained on the campus of the AGH University in Krakow, Poland.

Figure 2 shows the location of the area where the GPR data were acquired. The orthophoto shows a horizontal cross-section (so-called C-scan) of the ground and the acquired underground utilities. In Figure 2, above the visible location of GPR data acquisition, three example C-scans generated at three different depths, i.e., 0.72 m, 0.94 m, and 1.50 m, are shown. The information contained in the C-scans is presented in the amplitude of A (V). In addition to the C-scan maps, vertical cross-sections of the ground known as B-scans are also shown.

The GPR measurement was integrated with the GNSS-RTK receiver to ensure the accurate positioning and mapping of underground objects.

2.2. 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, 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 Pasternak, K. and Fryskowska-Skibniewska, A. 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].

$$T=m·\left[1+k·\left({\displaystyle \frac{s}{R}}-1\right)\right]$$

(1)

where

• k—parameter defining the degree of noise in the image, k ϵ <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 Pasternak, K. and Fryskowska-Skibniewska, A. in [52], predefined geometric conditions were determined that are met by the hyperboles representing underground infrastructure: (1st condition) the size of the object (C_S) is larger than 45 px, (2nd condition) the curvature of the object (C_C) falls within the range of <0.016; 0.160>, (3rd condition) the depth of the object (C_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.

2.3. Non-Reference Quality Assessment Metrics

2.3.1. Quality Metrics

This sub-section provides a description of the functioning and application of all the indicators used, i.e., entropy, PIQE, and Laplacian variance. These indicators were selected based on the criterion of their functioning in images with a very high degree of noise that, at the same time, contain a large number of artifacts (being both objects of interest and unidentified objects that cannot be classified as elements of utility networks). Based on the theoretical analyses and the conducted experiments, it was noted that the selected indicators also cooperate well with binary images, so they will be appropriate for the whole process of data processing and the process of characterizing and selecting specific radargrams.

Entropy

The entropy of an image is determined based on the distribution of probability of the intensity of pixels in the analyzed image. Assuming that p_i represents the probability of the occurrence of intensity i in the image, the value of entropy may be calculated from Equation (2):

$$H_N={\displaystyle \frac{1}{L}}{\sum }_{i=0}^{2^L-1}{p}_i{log}_2{\displaystyle \frac{1}{p_i}},$$

(2)

where

• L—number of intensity values;
• p_i—probability of occurrence of the given intensity i in the image.

Images with high entropy are characterized by a large number of details and a diversity of the structures represented in the image. In such images, the distribution of pixel intensity is wide. Low-entropy images are characterized by the homogeneity and low diversity of structures. In such cases, the values of pixel intensity fall into a narrow range. Low entropy indicates a small amount of information and a low level of image complexity as described by Kim, W. et al. in [55].

PIQE (Perception-Based Image Quality Evaluator)

The operating principle of the PIQE algorithm consists in dividing the image into smaller regions, where the level of noise and artifacts is analyzed locally. Areas characterized by large artifacts are identified as low-quality areas. The PIQE algorithm consists in dividing the image into blocks (e.g., of the size of 8 × 8, 16 × 16, 32 × 32). The first stage is the calculation of the MSCN (mean subtracted contrast normalized) index, which allows to highlight local contrasts in the image by deducting the local average and normalization in reference to local variance [56,57]. The value of the MSCN coefficient is expressed by Equation (3):

$$MSCN\left(x,y\right)={\displaystyle \frac{I\left(x,y\right)-\mu (x,y)}{\sigma \left(x,y\right)+C}},$$

(3)

where

• $I\left(x,y\right)$—value of the pixel (x,y);
• $\mu (x,y)$—value of the local average within the pixel (x,y);
• $\sigma \left(x,y\right)$—value of the local standard deviation within the pixel (x,y);
• C—value of the constant that prevents division by 0.

Then, based on the determined values of MSCN, the algorithm identifies the blocks that are characterized by high and low local variance. In areas characterized by a low value of local variance, the algorithm analyses the standard deviation of pixel intensity from the average value—Equation (4):

$$\sigma ={\displaystyle \frac{1}{N}}{\sum }_{i=1}^N{\sum }_{j=1}^N\left|p\left(i,j\right)-\mu \right|,$$

(4)

where

• $\mu$—value of average intensity within the block;
• $N$—number of pixels in the given block.

Higher values of standard deviation point to the presence of noise in the image. The algorithm also analyses the distinguished blocks of images in terms of the presence of Gaussian noise. The value of the PIQE index is calculated based on the number of degraded blocks and all blocks within the image. Lower values of PIQE indicate a higher quality of the image. The PIQE index calculates the non-reference quality score for an image based on the following steps presented in

Table 1. Scheme of the functioning of image quality assessment with the PIQE index.

Input: Radargram after standard pre-processing

Compute MSCN coefficient for each pixel in the image:      MSCN = ComputeMSCN(I) Divide the input radargram into non-overlapping blocks of size 32-by-32:      Blocks = DivideIntoBlocks(I, BlockSize = 32 × 32) Identify high spatially active blocks based on the variance of the MSCN coefficients. For each block in Blocks:      Calculate variance of MSCN coefficients      If Variance of MSCN > Threshold           Mark block as high spatially active Generate activityMask using the identified high spatially active blocks:      activityMask = GenerateActivityMask(Blocks, HighSpatialActivity) Evaluate distortion due to blocking artifacts and noise using the MSCN coefficients. For each block in Blocks:      Evaluate distortion using MSCN coefficients      Assess blocking artifacts and Gaussian noise Classify the blocks using Threshold criteria as distorted and undistorted blocks:      ClassifyBlocks(Blocks, ThresholdCriteria) Generate noticeableArtifactsMask from the distorted blocks Compute the PIQE score for input image      PIQE_score = MeanScore(DistortedBlocks)

Output: PIQE value, Quality of image

.

Laplacian Variance

The value of the Laplacjan operator variance is a measure of the scattering of Laplacian results in the whole image. For blurred images, the value of the variance will be low, as a result of slight changes in pixel intensity and less marked edges. On the other hand, in sharpened images, the values of the Laplacjan variance are higher, as major changes in pixel intensity in the areas of edges lead to more differentiated results. The value of variance may be calculated from Equation (5):

$$\sigma ={\displaystyle \frac{1}{N}}{\sum }_{i=1}^N{\sum }_{j=1}^N\left|p\left(i,j\right)-\mu \right|,$$

(5)

where

• L_i—Laplacian value in the ith pixel of the image;
• ${\mu }_{\mathrm{L}}$—average Laplacian value in the image;
• N—number of pixels in the image.

A high value of Laplacian operator variance is characteristic for highly sharp images, where clear edges are visible. On the other hand, a low value of variance indicates an image that is blurred, which may be caused by the presence of noise or artifacts resulting from the compression process.

2.4. Adaptive Method of Radargram Quality Assessment

The image quality assessment took into account the influence of the degree of blurring, noise, and the structures and details that were present in the analyzed images. The assessment also took into consideration the indicators that operate on whole radargrams (Laplacian variance, entropy) and on specific blocks of the image of a predefined size, e.g., 8 × 8, 16 × 16, or 32 × 32 (perception-based image quality evaluator—PIQE). The flow chart of the proposed method for image quality assessment is provided in Figure 4.

The first stage after the pre-processing of radargrams is the assessment of the quality of all acquired images with the entropy indicator. Quality assessment maps were generated for the analyzed images. Then, the maps were superimposed on the pre-processed image, which enabled the visualization of the quality distribution within the whole radargram. The first, general verification of the quality indicators in the later process of the automated detection of features (hyperbolas) used the total number of features detected (M₂—the number of objects detected in the output image (i.e., after pre-processing)—Step 1 in Figure 3). At this stage, the initial assumption/thesis stating that the overall quality of the image has a direct influence on the number of detected features was confirmed. Due to the aim being the detection of underground infrastructure in radargrams, the authors have proposed the adaptive approach and a further detailed assessment of image quality. This is why in the second step, the images acquired from channels characterized by the highest and lowest image quality were designated based on the selected criteria that define the threshold for the selection of images that are characterized by only the boundary values of GPR data quality. This process enabled the elimination of data of the lowest quality.

For the purposes of this analysis of the boundary conditions, a threshold of statistical significance at the level of α = 0.1 was assumed. Based on this criterion (α = 10% and, respectively, 1−α = 90%), images of the lowest quality (10%) and of the highest quality (90%) were designated. The final selection of a threshold of 0.10 was dictated by the limited dataset. With a threshold of 0.02 or 0.05, it would have been impossible to extract significant qualitative features from the images. In addition to theoretical considerations, the threshold value was chosen experimentally. The authors tested a variant with a threshold of 0.02 and 0.05, but the results indicated that this was too strict an approach that would make it impossible to capture and analyze the qualitative changes occurring in the GPR images. The aim of the proposed criterion (α = 0.1) for image selection is to eliminate overly similar images. At the second stage, in the group of images selected based on entropy, image quality was assessed (in terms of blur and noise) with Laplacian variance and the PIQE indicator. The obtained values of the Laplacian variance and PIQE indicator were the basis for selecting the channels of the highest quality. Based on the images selected with the use of these indicators, a set of common elements, being one or several images, was defined. Due to the introduced selection criterion, there is no specific number of the resultant number of channels from which the images were acquired. In some cases, the user may obtain 1, 2, 3, or more images. If only one or two channels are obtained, the analysis should be expanded to include a selection of at least three channels. This process will ensure the possibility of verifying the detected underground objects in a minimum of three images. This stage will provide additional verification of the detected objects that are not elements of underground utility networks. In the event of no common set of channels being selected for further analysis, one should take into account the images that have been selected based on the Laplacian variance. The images obtained from the selected channels will be implemented with the detection algorithm. The reliability of the quality assessment and of its influence on the effectiveness of the detection of hyperbolas was determined based on the M and L parameters (Equations (6) and (7)). The effectiveness of detection assessed with the M parameter is based on the number of detected objects after binarization and in the target image. The M parameter is calculated with Equation (6):

$$M={\displaystyle \frac{M_2-M_1}{M_2}}·100\%,$$

(6)

where

• M₁—the number of objects detected in the target image (i.e., after the pre-processing stage, filtration, and the application of conditions C_S, C_C, and C_D)—Step 4 in Figure 3;
• M₂—the number of objects detected in the output image (i.e., after pre-processing)—Step 1 in Figure 3.

The effectiveness of the detection of hyperbolas was also assessed based on the L parameter, which takes into account both the number of detected objects not being underground utility networks and the number of undetected objects that are such networks. The L parameter is calculated with Equation (7):

$$L={\displaystyle \frac{N_L-(n_{L_1}+n_{L_2})}{N_L}}·100\%,$$

(7)

where

• N_L—number of all objects detected in the image (the number is determined automatically);
• n_L1—number of detected objects not being underground utility networks (the number is calculated manually);
• n_L2—number of undetected objects being underground utility networks (the number is calculated manually).

3. Results and Discussion

3.1. Image Quality Assessment

In this section, we present the results obtained from the overall quality assessment of raw GPR images (Section 3.1.1) and the assessment of the quality of GPR images for the detection of hyperbolas representing underground utilities (Section 3.1.2).

3.1.1. Overall Quality Assessment of Raw GPR Images

In the first, rough assessment of GPR image quality, the total number of features detected in the analyzed radargrams was presented (M₂—the number of objects detected in the output image (i.e., after pre-processing))—Step 1 in Figure 3. The number of objects (M₂) was determined based on the image obtained from the binarization process. Figure 5 presents the number of objects detected in images acquired from three measurement routes.

Looking closely at Figure 5, one may notice that in this case, images characterized by a higher number of detected features were obtained for the selected channels. Due to the ultimate goal being the detection of underground infrastructure in radargrams, the authors have proposed the adaptive approach and a further detailed assessment of image quality (Section 3.1.2). Figure A1 in Appendix A presents the number of objects detected in images acquired from routes 1–3, with the specification of channels selected from the quality assessment in Section 3.1.2.

3.1.2. Assessment of the Quality of GPR Images for the Detection of Hyperbolas Representing Underground Utilities

In the process of our research work, we tested the following coefficients: NIQE, BRISQUE, PIQE, entropy, and Laplacian variance. Due to the quantitative limitations of this article, we did not include the results obtained from all coefficients.

Table A1. Results of the quality assessment indicators (entropy, Laplacian variance, PIQE, NIQE, and BRISQUE) and the effectiveness of the detection of hyperbolas (M, L) obtained for routes 1–3.

Route No.	Image No.	Entropy	Laplacian Variance	PIQE	NIQE	BRISQUE	M	L
3	1	0.903	0.281	0.424	0.814	0.505	0.659	0.818
3	2	1.000	0.369	0.260	0.438	0.173	0.634	0.750
3	3	0.907	0.134	0.000	0.513	0.000	0.605	0.636
3	4	0.976	0.445	0.273	0.672	0.438	0.600	0.750
3	5	0.598	0.145	0.304	0.608	0.766	0.690	0.636
3	6	0.822	0.420	0.473	0.673	0.985	0.575	0.750
3	7	0.291	0.073	0.348	0.473	0.819	0.605	0.714
3	8	0.757	0.424	0.459	0.442	0.692	0.700	0.692
3	9	0.592	0.172	0.550	0.404	0.601	0.514	0.727
3	10	0.753	0.363	0.440	0.850	0.919	0.606	0.650
3	11	0.000	0.000	0.062	0.466	0.848	0.676	0.636
3	12	0.771	0.362	0.460	0.624	1.000	0.526	0.750
3	13	0.528	0.108	0.340	0.521	0.450	0.690	0.636
3	14	0.710	0.322	0.373	0.795	0.798	0.619	0.818
3	15	0.084	0.014	0.207	0.731	0.999	0.525	0.750
3	16	0.679	0.351	0.505	0.808	0.908	0.745	0.636
3	17	0.535	0.128	0.372	0.679	0.830	0.630	0.750
3	18	0.647	0.310	0.418	0.801	0.788	0.672	0.714
3	19	0.216	0.077	0.246	0.807	0.823	0.725	0.692
3	20	0.662	0.282	0.492	1.000	0.913	0.662	0.727
3	21	0.487	0.083	0.350	0.910	0.620	0.576	0.650
3	22	0.486	0.143	0.296	0.387	0.651	0.597	0.600
3	23	0.486	0.143	0.296	0.387	0.651	0.597	0.636
3	24	0.652	0.767	1.000	0.408	0.732	0.507	0.636
3	25	0.798	0.901	0.853	0.476	0.848	0.637	0.750
3	26	0.122	0.629	0.656	0.312	0.883	0.537	0.636
3	27	0.869	0.875	0.823	0.306	0.901	0.646	0.750
3	28	0.830	0.973	0.963	0.000	0.761	0.620	0.800
3	29	0.894	1.000	0.810	0.146	0.898	0.534	0.773
3	30	0.394	0.853	0.825	0.051	0.987	0.513	0.850
3	31	0.871	0.988	0.847	0.386	0.889	0.628	0.810
3	32	0.852	0.951	0.863	0.039	0.529	0.700	0.733
1	1	0.795	0.162	0.382	0.927	0.846	0.364	0.786
1	2	0.918	0.289	0.468	0.493	0.527	0.269	0.789
1	3	0.378	0.018	0.188	0.299	0.927	0.350	0.769
1	4	0.893	0.341	0.403	0.527	0.527	0.615	0.600
1	5	0.703	0.153	0.474	0.639	0.680	0.476	0.636
1	6	0.846	0.373	0.436	0.397	0.601	0.526	0.778
1	7	0.264	0.063	0.235	0.797	0.990	0.522	0.727
1	8	0.905	0.406	0.722	0.515	0.626	0.444	0.800
1	9	0.696	0.169	0.654	0.545	0.518	0.429	0.667
1	10	0.878	0.346	0.521	0.990	0.892	0.167	0.733
1	11	0.000	0.000	0.000	0.544	0.807	0.273	0.688
1	12	0.862	0.361	0.710	0.538	0.313	0.400	0.667
1	13	0.715	0.132	0.416	0.549	0.549	0.391	0.714
1	14	0.905	0.375	0.667	0.735	0.732	0.421	0.818
1	15	0.209	0.048	0.368	1.000	1.000	0.278	0.846
1	16	0.896	0.379	0.556	0.709	0.927	0.333	0.700
1	17	0.678	0.130	0.508	0.473	0.333	0.267	0.636
1	18	0.878	0.366	0.595	0.569	0.490	0.345	0.684
1	19	0.352	0.089	0.194	0.358	0.891	0.478	0.750
1	20	0.905	0.404	0.572	0.511	0.658	0.391	0.714
1	21	0.706	0.164	0.353	0.234	0.296	0.368	0.667
1	22	0.930	0.454	0.733	0.410	0.502	0.690	0.778
1	23	0.773	0.250	0.563	0.747	0.634	0.571	0.778
1	24	0.940	1.000	1.000	0.131	0.463	0.409	0.692
1	25	0.983	0.865	0.967	0.161	0.126	0.436	0.727
1	26	0.207	0.552	0.519	0.363	0.857	0.412	0.650
1	27	0.990	0.815	0.844	0.248	0.154	0.595	0.600
1	28	0.907	0.937	0.960	0.000	0.250	0.438	0.667
1	29	0.965	0.813	0.658	0.335	0.159	0.258	0.696
1	30	0.423	0.696	0.666	0.461	0.952	0.478	0.750
1	31	1.000	0.750	0.807	0.255	0.426	0.367	0.789
1	32	0.960	0.820	0.956	0.105	0.000	0.342	0.800
2	1	0.666	0.354	0.503	0.270	0.650	0.500	0.818
2	2	0.824	0.465	0.650	0.381	0.458	0.429	0.750
2	3	0.307	0.152	0.407	0.598	0.667	0.353	0.636
2	4	0.785	0.528	0.567	0.524	0.488	0.526	0.556
2	5	0.576	0.324	0.611	0.513	0.548	0.381	0.769
2	6	0.746	0.532	0.740	0.621	0.638	0.391	0.714
2	7	0.277	0.200	0.407	0.575	0.760	0.294	0.750
2	8	0.779	0.563	0.722	0.446	0.574	0.519	0.769
2	9	0.600	0.322	0.600	0.579	0.468	0.357	0.667
2	10	0.784	0.541	0.706	0.993	0.794	0.478	0.833
2	11	0.011	0.156	0.300	0.544	0.968	0.375	0.800
2	12	0.793	0.593	0.961	1.000	0.715	0.364	0.786
2	13	0.623	0.341	0.705	0.586	0.591	0.381	0.786
2	14	0.769	0.509	0.768	0.941	0.786	0.481	0.750
2	15	0.176	0.160	0.442	0.608	0.776	0.300	0.714
2	16	0.709	0.521	0.817	0.660	0.795	0.400	0.833
2	17	0.544	0.270	0.673	0.716	0.616	0.385	0.688
2	18	0.724	0.487	0.782	0.580	0.555	0.261	0.765
2	19	0.318	0.193	0.480	0.634	0.917	0.364	0.643
2	20	0.758	0.440	0.601	0.552	0.718	0.333	0.682
2	21	0.590	0.188	0.537	0.404	0.382	0.455	0.667
2	22	0.535	0.228	0.514	0.271	0.186	0.323	0.714
2	23	0.000	0.000	0.000	0.000	0.000	0.696	0.429
2	24	0.918	0.961	0.921	0.278	0.701	0.500	0.833
2	25	0.966	0.973	0.652	0.274	0.626	0.429	0.750
2	26	0.217	0.617	0.568	0.242	1.000	0.424	0.789
2	27	0.994	0.913	1.000	0.469	0.704	0.349	0.750
2	28	0.965	1.000	0.938	0.360	0.546	0.302	0.800
2	29	1.000	0.939	0.983	0.336	0.267	0.463	0.773
2	30	0.520	0.783	0.605	0.342	0.696	0.444	0.850
2	31	0.968	0.875	0.675	0.468	0.817	0.400	0.810
2	32	0.970	0.890	0.957	0.250	0.258	0.367	0.000

(Appendix A) adds the values of the aforementioned coefficients determined for the images from the three measurement routes (routes 1–3). Based on Table A1 (Appendix A), it can be noted that there is no correlation between the values of the coefficients obtained from NIQE and BRISQUE and the coefficients determining the effectiveness of hyperbola detection (M, L). After analyzing the values of the obtained coefficients and the correlation between the image quality assessment coefficients and the effectiveness of hyperbola detection, three image quality assessment coefficients were selected for further analysis and image selection: entropy, Laplacian variance, and PIQE. However, the use of NIQE and BRISQUE coefficients in the adaptive radargram selection method was rejected.

The results of the quality assessment indicators (entropy, PIQE, and Laplacian variance) and of the effectiveness of hyperbola detection (M and L) for a sample measurement route (route 2) are presented in Figure 6. The results of these indicators for the two remaining measurement routes (routes 1 and 3) are presented in Appendix A, Figure A2 (route 1), and Figure A3 (route 3).

The images acquired on route 2 (Figure 6) show the lowest values of entropy in comparison to routes 3 (Appendix A—Figure A3) and 1 (Appendix A—Figure A2), which may prove that the image contains a larger amount of information. The lowest values of entropy were obtained for images acquired from channels 3, 7, 11, 15, 19, and 23. Higher values obtained for routes 1 and 2 point to a higher degree of noise and heterogeneity of data. The highest values of PIQE were obtained for images acquired from channels 1, 6, 8–10, 12, 16, 19–21, and 24–32. The highest value of Laplacian variance was obtained for the image acquired from channel 24. Images acquired on route 3 are characterized by a lower degree of blurring than those acquired on routes 1 and 2.

Table 2. Results of entropy and parameters M and L for selected images of high and low quality from route 1.

Channel	25	27	31	20	8	14	28	2	22	24	32	29	11	26	15
Entropy	0.983	0.990	1.000	0.905	0.905	0.905	0.907	0.918	0.930	0.940	0.960	0.965	0.000	0.207	0.209
Quality	highest	highest	highest	highest	highest	highest	highest	highest	highest	highest	highest	highest	lowest	lowest	lowest
M	0.436	0.595	0.367	0.391	0.444	0.421	0.438	0.269	0.690	0.409	0.342	0.258	0.273	0.412	0.278
L	0.727	0.600	0.789	0.714	0.800	0.818	0.667	0.789	0.778	0.692	0.800	0.696	0.688	0.650	0.846

,

Table 3. Results of entropy and parameters M and L for selected images of high and low quality from route 2.

Channel	32	27	29	24	28	25	31	23	11	15
Entropy	0.970	0.994	1.000	0.918	0.965	0.966	0.968	0.000	0.011	0.176
Quality	highest	highest	highest	highest	highest	highest	highest	lowest	lowest	lowest
M	0.367	0.349	0.463	0.500	0.302	0.429	0.400	0.696	0.375	0.300
L	0.733	0.750	0.773	0.833	0.800	0.750	0.810	0.429	0.800	0.714

and

Table 4. Results of entropy and parameters M and L for selected images of high and low quality from route 3.

Channel	3	4	2	11	15	26
Entropy	0.907	0.976	1.000	0.000	0.084	0.122
Quality	highest	highest	highest	lowest	lowest	lowest
M	0.605	0.600	0.634	0.676	0.525	0.537
L	0.636	0.750	0.750	0.636	0.750	0.636

present the values of entropy obtained for sample measurement routes (respectively, for routes 1, 2, and 3) for the images of the lowest and the highest quality, obtained based on the proposed selection criteria of 10% and 90%. The entropy results for a sample measurement route were juxtaposed with the values of the parameters for assessing the effectiveness of detection, M and L, obtained for the channels indicated in the quality assessment.

As for the entropy parameter for route 1, the selection of a higher number of channels in the 90% value criterion proves the existence of highly differentiated structures and details that are present in the analyzed images. Images with low entropy values (channels 11, 26, and 15) are characterized by the homogeneity and low diversity of structures.

The selected images (Table 2, Table 3 and Table 4) characterized by low and high quality were the basis for generating quality assessment maps. Figure 7 and Figure 8 present the quality assessment maps generated based on entropy for the selected images, for which extreme values of entropy were obtained, for three sample routes (routes 1 and 2—Figure 7, route 3—Figure 8).

The yellow areas mark high levels of entropy (larger amount of information), while blue ones indicate low levels of entropy (potentially areas with a smaller amount of information or non-correlated noise level). High values of entropy are also a measure of the quality of the GPR signal. Areas characterized by low levels of entropy may indicate either a homogeneous ground medium or noise and the loss of GPR signal caused by higher attenuation of the ground medium. Areas characterized by lower entropy values may indicate a lower quality of data resulting from a smaller amount of information contained in the image.

The quality of images selected with the entropy index was then assessed with the Laplacian variance and the PIQE indicator. Based on the obtained results (i.e., the images selected with two indicators: PIQE and the Laplacian variance), an intersection set of images was selected. The obtained selection results for three sample routes are presented in Figure 9, Figure 10 and Figure 11 in form of Venn diagrams, respectively, for routes 1–3.

The results presented in the Venn diagrams (Figure 9, Figure 10 and Figure 11) enable the identification of images characterized by various levels of quality. Images selected based on the 90% criterion (highest quality images) are marked in green, while images selected using the 10% criterion (lowest quality images) are marked in red, based on the indicators entropy, PIQE, and Laplacian variance. The analysis of the intersection of the sets represents the channels that ensure high quality based on all three indicators (e.g., Figure 10—channels 24 and 28). Images obtained based on two indicators point to channels that meet two criteria at the same time, e.g., entropy and Laplacian variance—channel 25 (Figure 11). The analysis of Figure 11 reveals that no channels were selected based on the criterion of 90% of value for the three indicators. In such events, one should select those channels that were determined based on entropy (i.e., channels 2–4)

As for the entropy parameter (Figure 9), a higher number of channels was selected in the 90% criterion than for the PIQE indicator or for Laplacian variance. This proves the existence of highly differentiated structures and details that are present in the analyzed images. Images that are characterized by low entropy values (channels 11, 26, and 15) are characterized by the homogeneity and low diversity of structures. The image acquired from channel 22 is characterized by a high value of entropy, which proves a large amount of information and the heterogeneity and complexity of the structures represented in the radargrams. Higher entropy values are also characterized by higher PIQE values. This points not only to the heterogeneity of the image, but also to the presence of noise, which translates into a larger number of degraded blocks into which the input image was divided. Figure 12 presents sample resultant images of detection for extreme values of the quality of these radargrams, along with the assessment of detection effectiveness.

One of the images is characterized by a high degree of blurring, which, in such a case, leads to a lower effectiveness of detection (M = 35%) than for the image acquired from channel 25 (M = 44%). Images with a lower degree of blurring are characterized by higher values of the PIQE indicator. Images with higher entropy values have a lower number of undetected objects being underground utility networks (n_L2). Higher values of the Laplacian variance of the image lead to a larger number of all objects detected in the input image (considering the number of objects that are utility networks and those that are not—n_L1, n_L2). The higher the value of the Laplacian variance, the more blurred the image. This indicates a larger number of undetected objects being underground utility networks in the input image (n_L2). Images with a lower degree of blurring are characterized by higher values of the PIQE indicator.

All non-reference coefficients (NIQE, BRISQUE, PIQE) were analyzed for their workings, capabilities, and limitations in the context of evaluating the quality of radargrams acquired from multichannel GPR.

• The NIQE indicator is based on the construction of a quality-aware collection of statistical features that depend on a simple and successful space domain natural scene statistic (NSS) model. These features are derived from an entity of natural, undistorted images [58,59].
• The operating principle of the PIQE algorithm consists in dividing the image into smaller regions, where the level of noise and artifacts is analyzed locally. Areas characterized by large artifacts are identified as low-quality areas. The PIQE algorithm consists in dividing the image into blocks (e.g., of the size of 8 × 8, 16 × 16, 32 × 32). The value of the PIQE index is calculated based on the number of degraded blocks and all blocks within the image. Dividing the image into smaller blocks gives a better assessment of quality than the NIQE or BRISQUE index [58,59].
• The BRISQUE indicator compares the image with a default model generated from images of natural scenes with similar distortions. Radargrams do not represent natural scenes. Therefore, the BRISQUE indicator, based on the statistics of natural images, will not reliably assess the quality of GPR-acquired images.

3.2. Verification of Detection Efficiency

The table below presents a comparison of the values of the parameters for the assessment of hyperbola detection efficiency in reference to GPR images recorded from channels that are characterized by extreme values of the indicators (Laplacian variance, PIQE, and entropy) in the obtained quality assessment.

Table 5. Evaluation of the increase in the quality of hyperbola detection based on the analyzed image quality indicators.

Parameter	Laplacian Variance			Entropy			PIQE
Route No.	1	2	3	1	2	3	1	2	3
Mmax-min [%]	16.5	14.7	17.5	41.7	20.0	10.9	13.6	39.3	16.9
Mmax-average [%]	2.8	9.3	8.3	28.0	9.3	1.7	6.9	28.9	5.9
Lmax-min [%]	4.0	40.5	17.3	16.8	40.5	11.4	10.3	6.7	11.4
Lmax-average [%]	0.5	9.6	8.5	9.6	9.6	2.5	4.7	6.2	2.5

presents the differences in the values of the M and L parameters that may be obtained by the user for images of the lowest and highest quality from the selected three measurement routes.

The analysis of the data presented in Table 4 reveals that, in each case, the differences between the maximum and minimum values (M_max-min, L_max-min) of the M and L parameters are larger than the differences between the maximum and average values of the M and L parameters for the whole routes (M_max-average, L_max-average). As far as the Laplacian variance is concerned, the largest difference was obtained for routes 2 and 3 (M_max-min = 17.5%, L_max-min = 40.5%). Analyzing the entropy parameter, one may notice that the largest difference was obtained for routes 1 and 2 (M_max-min = 41.7%, L_max-min = 40.5%). As for the PIQE parameter, the largest differences were obtained for routes 2 and 3 (M_max-min = 39.3%, L_max-min = 11.4%). The efficiency of the detection of underground utility networks was also verified based on the generated quality assessment maps and the binary resultant images obtained in the process of the automated detection of hyperbolas (Figure 13 and Figure 14).

Areas characterized by lower entropy values may indicate a lower quality of data, including the blurring of specific areas in the image.

4. Conclusions

Research has demonstrated that the proposed innovative adaptive approach to the selection of images acquired by ground-penetrating radar enabled a significant improvement of the efficiency of the detection of hyperbolas representing underground utility networks, by 15–40% in comparison to the detection performed in the lowest-quality images and by 10–20% in comparison to the average values of efficiency. High values of entropy, presented on the map of image quality assessment, were noted in the locations where underground utility networks are present. The hyperbolas in the binary image clearly overlap with the areas with increased values of entropy that represent higher quality (characterized by a noticeable presence of useful signals) fragments of the radargrams. High values of entropy are also a measure of the quality of the GPR signal. Areas characterized by low levels of entropy may indicate either a homogeneous ground medium or noise and the loss of GPR signal caused by higher attenuation of the ground medium. Using entropy to superimpose quality maps on binary images not only improves the clarity but also enables the employment of machine learning algorithms for the identification and classification of the detected objects. Images characterized by high entropy may be automatically filtered as potential locations of underground infrastructure, which will allow to shorten the time required to perform manual analyses of the acquired GPR data. Areas characterized by lower entropy values may indicate a lower quality of data resulting from a smaller number of objects detected in the image.

The application of quality indicators (entropy, PIQE, and Laplacian variance) allows for a reliable assessment of the degree of blurring, noise, and the number of details that are present in the analyzed images. The proposed approach enables a quick evaluation of the quality of radargrams (that are characterized by a clear presence of usable signals), which supports the process of detecting underground objects. In most of the analyzed radargrams, all the existing utility infrastructure was detected. The number of undetected utility networks was higher in images characterized by a high degree of blurring (low values of Laplacian variance).

The proposed adaptive approach enables to shorten the time of processing GPR data, while it also indicates the radargrams with noticeable useful signals. The selection of these images improves the quality of the detection of hyperbolas in images. The approach based on non-reference image quality assessment methods enables the adaptive selection of images of the highest quality, even before the process of the automated detection of hyperbolas. In spite of their multiple advantages, the applied quality assessment methods also have certain limitations. One of them is the fact that a single value of the quality indicator (entropy, PIQE, or Laplacian variance) is determined for the whole image. The global image quality assessment does not take into account local distortions and artifacts that might have a significant influence on the process of detecting hyperbolas. Considering the above limitations, the authors are planning future research to develop a new approach to image quality assessment, based on sector-specific indicators. This will allow for the determination of the quality of radargrams within parts of the image, i.e., blocks. The sector-specific radargram quality assessment may significantly improve the efficiency of quality assessment, which will likely lead to an improvement in the quality of the detection of underground infrastructure. This approach will probably enable us to overcome the limitations of global quality assessment methods, constituting a basis for further research on the methods of the detection of hyperbolas in GPR images of diverse quality parameters.