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

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper proposes an adaptive approach to GPR image quality assessment and hyperbola detection, showing promising efficiency gains. However, addressing the technical gaps (e.g., metric validation, threshold analysis)  would strengthen its contribution to automated subsurface utility detection.

1：The paper uses entropy, PIQE, and Laplacian variance as quality metrics. However, GPR images often contain impulse noise and dielectric heterogeneity -induced artifacts (Section 2.3.1). Are these metrics validated against GPR-specific noise types (e.g., salt-and-pepper noise, multipath interference)? 
2：The introduction mentions NIQE, BRISQUE, and other non-reference IQA methods (Section 1.1). However, no quantitative comparison is provided between the proposed metrics (entropy, PIQE, Laplacian variance) and these established methods . Including a baseline comparison (e.g., PSNR, SSIM) or a brief analysis of why PIQE is chosen over NIQE would improve the method’s credibility.
3：The adaptive selection uses a statistical significance threshold (α=0.1) to select the top/bottom 10% and 90% of images (Section 2.4). Is this threshold justified theoretically or empirically? The authors state it is "assumed" (Section 2.4), but sensitivity analysis (e.g., varying α to α=0.05 or 0.2) is missing. How does this threshold affect the final detection efficiency?
4：The paper emphasizes the need for "objective quality metrics for automatic analysis" (Section 1.1). To contextualize this challenge, the authors should cite “An advanced scheme for range ambiguity suppression of spaceborne SAR based on blind source separation” in the introduction. This would highlight the cross-domain relevance of blind quality assessment and strengthen the motivation for their GPR-specific approach.

 

 

 

 

Author Response

Comments 1: The paper uses entropy, PIQE, and Laplacian variance as quality metrics. However, GPR images often contain impulse noise and dielectric heterogeneity -induced artifacts (Section 2.3.1). Are these metrics validated against GPR-specific noise types (e.g., salt-and-pepper noise, multipath interference)?

Response 1: Thank you for the proper remark. We added better explanation of this subject.

The acquired radargrams were pre-processed. As part of this process, bandpass filtering, background filtering, and signal gain filtering were performed. Standard radargrams processing, therefore, includes time-zero correction, removing the background, frequency, and gain filters. As part of radargrams preprocessing, multipatch interference and salt-and-pepper noise were eliminated.

Background removal: This command applies the Clear-X filtering algorithm used to remove continuous components along the X axis (horizontal direction). Background  removal  filter  is  an  arithmetic process  that  sums  all  the  amplitudes  of  reflection  recorded  at  the same  time  along  a  profile  and  divides  it  by  the  number  of  traces. This value is then subtracted from the data set. Care must be taken in this process not to remove real linear events in profile.

Smoothed gain: The Smoothed gain filtering algorithm is used to equalize the power along a sweep for a moving window.

Move start time: This command is used to calculate the zero point, the transition air/ground. This algorithm must always be applied when you want to align the current radar map depth scale with the position of the surface of the investigated area. From the Settings command you can deactivate the Automatic function, defining the vertical scale zero point as a function of the height of the radar antennas from the scanning surface. This operation is mainly used when scans are performed with antennas not in contact with the surface.

Bandpass: This command applies the Filter X algorithm (FIR type filtering in the X direction).

FIR Y: Vertical bandpass filter in time domain is a way of removing unwanted low or high frequency from the band in order to produce a more interpretable GPR maps.

FIR X: Horizontal bandpass filter is applied along radar scan direction. It is applied to remove pseudo-horizontal noises.

A detailed description of the filters used in preprocessing the radargrams was described by the authors in their previously published paper: „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 results from thermal drift, electronic instability, or variations in antenna airgap. In order to improve image quality and the signal to noise ratio, both time filters (i.e., simple mean, simple median, low pass, high pass, and band pass) and space filters (i.e., simple running average, average subtraction, and background removal) may be implemented [4]. One of the applied filtration processes consisted in conducting the 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. If the signal of the return electromagnetic wave is weak, it may be enhanced with the function of exponential enhancement. At the next stage, background removal was conducted in order to eliminate random noise and to improve the signal to noise ratio. One of the final stages of processing of a radargram involves conducting migration and the correction of height and depth, whose value may be determined based on the velocity of propagation of the electromagnetic wave.” - Onyszko, K.; Fryśkowska-Skibniewska, A. A New Methodology for the Detection and Extraction of Hyperbolas in GPR Images. Remote Sens. 2021, 13, 4892. https://doi.org/10.3390/rs13234892

References:

• GRED HD 01.06, GPR Data Post Processing, IDS Georadar, 2016.

Onyszko, K.; Fryśkowska-Skibniewska, A. A New Methodology for the Detection and Extraction of Hyperbolas in GPR Images. Remote Sens. 2021, 13, 4892. https://doi.org/10.3390/rs13234892 

Comments 2: The introduction mentions NIQE, BRISQUE, and other non-reference IQA methods (Section 1.1). However, no quantitative comparison is provided between the proposed metrics (entropy, PIQE, Laplacian variance) and these established methods. Including a baseline comparison (e.g., PSNR, SSIM) or a brief analysis of why PIQE is chosen over NIQE would improve the method’s credibility.

Response 2: Thank you for the proper remark. We added better explanation of this subject.

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 the article, we did not add the results obtained from all coefficients to the article. The table A1 (Appendix A) adds the values of the aforementioned coefficients determined for the images from the three measurement routes (routes 1-3).

Appendix A1

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 route 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

Based on Table A1 (Appendix 1), it can be noted that there is no correlation between the values of the coefficients obtained from NIQE, 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, 3 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.

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.

• NIQE indicator is based on the construction of a quality aware collection statistical features depends on 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 artefacts is analysed locally. Areas characterized by large artefacts are identified as low-quality areas. The PIQE algorithm consists in dividing the image into blocks (e.g. of the size of 8x8, 16x16, 32x32). 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.

We agree with the reviewer's comment that frequently used coefficients in image quality studies are: Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM). However, it is worth noting that these coefficients assess the similarity between the processed image and the reference image. In the case of the present study, the authors do not have the reference images necessary to determine the values of the aforementioned coefficients. PSNR, which is the peak signal-to-noise ratio, contains information on the maximum power of a signal to the power of noise interfering with that signal. SSIM, which evaluates structural similarity, takes into account contrast, structure and luminance distortion. Accordingly, the authors in this paper used non-reference methods to assess image quality.

Comments 3: The adaptive selection uses a statistical significance threshold (α=0.1) to select the top/bottom 10% and 90% of images (Section 2.4). Is this threshold justified theoretically or empirically? The authors state it is "assumed" (Section 2.4), but sensitivity analysis (e.g., varying α to α=0.05 or 0.2) is missing. How does this threshold affect the final detection efficiency?

Response 3: The threshold selection of the confidence level (often expressed by the significance level α) is important in the context of statistical hypothesis testing, as it determines how rigorously one can approach the evaluation of the results of the analyses performed. Confidence levels of 0.02 and 0.05 are fairly stringent yet common thresholds in social and natural science fields. Our research, however, is preliminary (preliminary and quite exploratory), where the aim was to identify potential solutions and point in further directions rather than definitive conclusions. This allowed us to define and discover important characteristics of qualitative images.

In addition, our data resource is specific and limited in quantity. Consequently, tightening the confidence level threshold would likely fail to detect specific correlations.

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 following table shows the results of image selection obtained from the three measurement routes for a threshold value of 0.02 and 0.05. These results are compared with those obtained, based on a threshold value of 0.10.

Table. Selected images based on tested threshold a = 0.02 i 0.05

Measurement route no.	Selected image numbers based on entropy
	Threshold a = 0.02	Threshold a = 0.05	Threshold a = 0.10
1	25, 27, 31	32, 29, 25, 27, 31	2, 22, 29, 20, 27, 8, 14, 31
2	27, 29	28, 25, 31, 32, 27, 29	29, 27, 31, 24, 28
3	2	2, 4	2, 3, 4

The results obtained in the above table confirm that based on the threshold of 0.02 and 0.05, the qualitative features of the analyzed images cannot be extracted. Therefore, the authors decided to choose a threshold value of 0.10. The numbers of images, indicated in the table above, are images selected only on the basis of entropy values. In the case of further image selection with the indicated thresholds (0.02 and 0.05), a maximum of one image would be selected based on the value of PIQE index and Laplacian variance.

Comments 4: The paper emphasizes the need for "objective quality metrics for automatic analysis" (Section 1.1). To contextualize this challenge, the authors should cite “An advanced scheme for range ambiguity suppression of spaceborne SAR based on blind source separation” in the introduction. This would highlight the cross-domain relevance of blind quality assessment and strengthen the motivation for their GPR-specific approach.

Response 4: Thank you for proper remark. We added citation in the Introduction.

The significance of the use of blind-quality assessment was particularly emphasized in the article [34] by the authors Chang, S. et al.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

A very interesting article that addresses an important applied scientific problem of high-quality interpretation of radargrams from ground-penetrating radar (GPR) surveys. The method for automatic hyperbola detection proposed by the authors will significantly facilitate the work of engineers and reduce the time required to process radargrams. However, several comments and clarifications should be noted:

1. When citing individual literature sources, it is necessary to mention the authors' surnames before the reference. For example: In the work by Irvine, J.M.; Nelson, E [20] the authors... (Lines 64, 70, 116).

2. What is the scientific novelty of the proposed method?

3. Is this methodology universal for the investigation of any objects, or is it limited to a specific list of soil types?

4. Have the authors tested this methodology on objects with varying soil moisture and different dielectric permittivity?

5. The presentation of the results shown in Figure 2 should be better explained in the text.

6. The article does not clearly specify the range of hyperbola curvature to which the method can be applied. If the hyperbola that localizes the subsurface object is only slightly curved, will the algorithm still detect it?

7. Did the authors conduct experiments to determine the maximum depth at which the proposed method remains effective for hyperbola localization?

Author Response

Comments 1: When citing individual literature sources, it is necessary to mention the authors' surnames before the reference. For example: In the work by Irvine, J.M.; Nelson, E [20] the authors... (Lines 64, 70, 116).

Response 1: Thank you for the proper remark. We have completed references in the text to the authors of publications when citing individual articles as follows:

• 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 authors Maślakowski, M. et al. [15].
• In the work by Irvine, J.M., 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.
• Unfortunately, there are few studies that propose a comprehensive evaluation index to evaluate the image quality, which was discussed by the authors Lin, H.-I.; Lin, P.-Y. in publication [21].
• The problems of the analysis and reduction of noise and interferences that occur in GPR images has been the subject of research presented in many publications such as by authors Iftimie, N. et al. in publication [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.
• The significance of the use of blind-quality assessment was particularly emphasized in the article [34] by the authors Chang, S. et al.
• The effectiveness of detection is explained by the authors Zahir, N.H.M. et al. in the article [36] was 90%.
• The authors Tam, N.H. et al. in publication [39] used edge filters for the detection of hyperbolas.
• The authors Gu, K. of the article [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.
• 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., Ortyl, Ł. in the paper [50].
• The method of hyperbola detection proposed previously by the authors Pasternak, K. Fryskowska-Skibniewska, A. in the paper [52], based on the radiometric and geometric properties of the detected objects consists of: automated detection of hyperbolas that represent elements of underground infrastructure based on the Sauvola binarization method and the extraction of hyperbolas that meet 3 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 Fig. 3.
• Low entropy indicates a small amount of information and a low level of image complexity as described by the authors of Kim, W. et al. in the article [55].

Comments 2: What is the scientific novelty of the proposed method?

Response 2: Thank you for this question. Our explanation is below. We add this explanation in the text of our paper.

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.

Comments 3 and 4: Is this methodology universal for the investigation of any objects, or is it limited to a specific list of soil types? Have the authors tested this methodology on objects with varying soil moisture and different dielectric permittivity?

Response 3 and 4: Thank you for those questions. Due to the multifaceted topic in our article, we did not add a soil analysis while the following explains why this additional extensive analysis was not undertaken.

In the research in this publication, we focused on a homogeneous soil environment (gravelly sands - gravelly sands of fluvial origin - fluvial genesis) in order to obtain more reliable underground infrastructure detection results. Maintaining a homogeneous soil environment was intended to eliminate the influence of different soil types on the penetration of electromagnetic waves in variable geological mediums and on the results of analysis and comparison of results. In addition, if moisture and physico-chemical conditions are constant, consistency and comparability of results regarding radargram quality assessment can be ensured. Different types of soils would introduce another variable, and this research aspect is our aim to solve in future research.

In addition, the study area where we had the opportunity to acquire GPR data is dominated by soils of gravelly sands (gravelly sands) of fluvial genesis.

In conclusion, with a focus on controlling the conditions for testing the quality of GPR images, as well as taking into account technological constraints (the possibility of obtaining data for testing) and practical considerations (i.e. time and budget), we were forced to use GPR data in a specific area. Consideration of a homogeneous ground environment thus ensured more consistent and reliable results in assessing the impact of image quality on the detection of underground infrastructure on radargrams.

The proposed method of radargram selection was tested in an area with equal dielectric permittivity of soil type. However, it is worth noting that in the study area there were different types of underground infrastructure characterized by different values of dielectric constants. A detailed description of the dielectric constants of different soil types and underground objects was presented by the authors in their publications:

• Karsznia, K.R.; Onyszko, K.; Borkowska, S. Accuracy Tests and Precision Assessment of Localizing Underground Utilities Using GPR Detection. Sensors2021, 21, 6765. https://doi.org/10.3390/s21206765.
• Onyszko, K.; Fryśkowska-Skibniewska, A. A New Methodology for the Detection and Extraction of Hyperbolas in GPR Images. Remote Sens.2021, 13, 4892. https://doi.org/10.3390/rs13234892.

Comments 5: The presentation of the results shown in Figure 2 should be better explained in the text.

Response 5: Thank you for the proper remark. We added better explanation in the text.

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

Comments 6: The article does not clearly specify the range of hyperbola curvature to which the method can be applied. If the hyperbola that localizes the subsurface object is only slightly curved, will the algorithm still detect it?

Response 6: Thank you for the proper remark. We added better explanation in the text and below.

The presented method for the detection of hyperbolas, representing underground infrastructure, was developed by the authors in a prior publication, i.e. Automatic classification of underground utilities in Urban Areas: A novel method combining ground penetrating radar and image processing. Archives of Civil Engineering 2024, 70, https://doi.org/10.24425/ace.2024.14985. This publication explains in detail the geometric conditions introduced for the detection of hyperbolas of appropriate curvature, depth and size:

„The proposed method for the detection of hyperbolas is based on the extraction of hyperbolas that meet the predefined geometric conditions: (1^st condition) the size of the object (C_S) is larger than 45 px, (2st condition) the curvature of the object (C_C) falls within the range of <0.016; 0.160>, (3st condition) the depth of the object (C_D) is larger than 13 px. Entering these conditions means that all hyperbolas not meeting these conditions will be removed from the image.” [Pasternak, K.; Fryśkowska-Skibniewska, A. Automatic classification of underground utilities in Urban Areas: A novel method combining ground penetrating radar and image processing. Archives of Civil Engineering 2024, 70, https://doi.org/10.24425/ace.2024.14985].

In this paper, we have added an abbreviated description of the hyperbola detection method, which was explained in detail in our previous publication:

Based on the research conducted by the authors Pasternak, K., Fryskowska-Skibniewska, A. the paper [52], predefined geometric conditions were determined that are meet by hyperboles representing underground infrastructure: (1^st condition) the size of the object (C_S) is larger than 45 px, (2^st condition) the curvature of the object (C_C) falls within the range of <0.016; 0.160>, (3^st condition) the depth of the object (C_D) is larger than 13 px [52].

Comments 7: Did the authors conduct experiments to determine the maximum depth at which the proposed method remains effective for hyperbola localization?

Response 7: Thank you for this question. Due to the multifaceted topic in our article, we did not add a depth analysis while the following explains why this additional extensive analysis was not undertaken.

Our proposed method for the detection of hyperbolas, representing underground infrastructure, was developed on the basis of radargrams acquired to a depth of 5 m. The authors focused mainly on maintaining the condition of minimum location of underground infrastructure, as the authors explained in our previous publication: Onyszko, K.; Fryśkowska-Skibniewska, A. A New Methodology for the Detection and Extraction of Hyperbolas in GPR Images. Remote Sens. 2021, 13, 4892. https://doi.org/10.3390/rs13234892:

„The legal basis for the determination of the criterion of the depth of the location of an underground object is technical guidelines. They contain the minimum values of cover thickness for underground network installations according to their type (Table 2).

Table 2. Minimum depths of installing underground networks.

Type of Underground Network	Minimum Depth (m)
separate telecommunication duct systems	0.5
mains telecommunication duct systems and in-ground cables	0.7
power supply cables up to 1 KV and over 1 KV	0.7–1.0
lighting cables	0.5
remotely controlled heating ducts starting from the manhole cover	0.5
gas networks	1.0–1.2
water supply networks (depending on pipe diameter)	1.4–1.8
sewers—the depth is calculated so as to maintain the proper inclination of these points	1.4

Assuming that the underground utility network is detected in an area where the operator does not know the position of the given objects, the minimum depth (common for all types of networks) is 0.5 m.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

ACCEPT