Point coordinates extraction from localized hyperbolic reflections in GPR data

    Point Coordinates Extraction from Localized Hyperbolic Reflections in GPR Data ˇ Aleksandar Risti´c, Zeljko Bugarinovi´c, Milan Vrtunski, Miro Govedarica PII: DOI: Reference:

S0926-9851(17)30567-0 doi:10.1016/j.jappgeo.2017.06.003 APPGEO 3288

To appear in:

Journal of Applied Geophysics

Received date: Revised date: Accepted date:

8 July 2016 6 June 2017 10 June 2017

ˇ Please cite this article as: Risti´c, Aleksandar, Bugarinovi´c, Zeljko, Vrtunski, Milan, Govedarica, Miro, Point Coordinates Extraction from Localized Hyperbolic Reflections in GPR Data, Journal of Applied Geophysics (2017), doi:10.1016/j.jappgeo.2017.06.003

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ACCEPTED MANUSCRIPT POINT COORDINATES EXTRACTION FROM LOCALIZED

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HYPERBOLIC REFLECTIONS IN GPR DATA

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Authors: Aleksandar Ristića, Željko Bugarinovića, Milan Vrtunskia, Miro Govedaricaa

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a. Faculty of technical sciences, University of Novi Sad, Trg Dositeja Obradovića 6,

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21000 Novi Sad, Serbia

ABSTRACT

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In this paper, we propose an automated detection algorithm for the localization of apexes and points on the prongs of hyperbolic reflection incurred as a result of GPR

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scanning technology. The objects of interest encompass cylindrical underground

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utilities that have a distinctive form of hyperbolic reflection in radargram.

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Algorithm involves application of trained neural network to analyze radargram in the form of raster image, resulting with extracted segments of interest that contain hyperbolic reflections. This significantly reduces the amount of data for further analysis. Extracted segments represent the zone for localization of apices. This is followed by extraction of points on prongs of hyperbolic reflections which is carried out until stopping criterion is satisfied, regardless the borders of segment of interest. In final step a classification of false hyperbolic reflections caused by the constructive interference and their removal is done. The algorithm is implemented in MATLAB environment.

ACCEPTED MANUSCRIPT There are several advantages of the proposed algorithm. It can successfully recognize true hyperbolic reflections in radargram images and extracts coordinates, with very

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low rate of false detections and without prior knowledge about the number of

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hyperbolic reflections or buried utilities. It can be applied to radargrams containing

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single and multiple hyperbolic reflections, intersected, distorted, as well as incomplete (asymmetric) hyperbolic reflections, all in the presence of higher level of

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noise. Special feature of algorithm is developed procedure for analysis and removal of

associated with the utilities.

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false hyperbolic reflections generated by the constructive interference from reflectors

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Algorithm was tested on a number of synthetic and radargram acquired in the field

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survey. To illustrate the performances of the proposed algorithm, we present the characteristics of the algorithm through five representative radargrams obtained in

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real conditions. In these examples we present different acquisition scenarios by varying the number of buried objects, their disposition, size, and level of noise. Example with highest complexity was tested also as a synthetic radargram generated by gprMax. Processing time in examples with one or two hyperbolic reflections is from 0.1 to 0.3 s, while for the most complex examples it is from 2.2 to 4.9 s. In general, the obtained experimental results show that the proposed algorithm exhibits promising performances both in terms of utility detection and processing speed of the algorithm.

ACCEPTED MANUSCRIPT Keywords: GPR, hyperbolic reflection, automated extraction, neural networks,

INTRODUCTION

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1.

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MATLAB

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In recent period, GPR technology has become more accessible and more present in engineering applications. This led to an increased amount of data being

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collected with GPR (Birkenfeld, 2010). In addition, interpretation of results from the

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radargram (e.g., underground utility detection) is a complex task in terms of operators’ knowledge and skills. Therefore, the increased amount of data and

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complex interpretation are pre-conditions for the development of automated procedures for detection and interpretation of anomalies in radargrams. Ground

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Penetrating Radar (GPR) is one of the most significant and advanced geophysical

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technique that detects changes in electromagnetic properties and provides high resolution data (Daniels, 2004; Jol, 2009). The technology of underground structure scanning involves the interaction of GPR device characteristics, signal propagation media and the object that is to be detected. Transmitting antenna emits a conical beam of electromagnetic waves, so the object is detected even before the antenna is directly above the axis of the object (Fig. 1). The time needed for the electromagnetic wave to reach the boundary surface and to reflect back to the reception area is two-way travel time tp [ns]. Measured twoway travel time and wave propagation velocity v [cm/ns] are used to calculate the depth of the object z [cm] as given in (1)

ACCEPTED MANUSCRIPT z

t p v

(1)

2

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The vector of reflections (intensities on the radargram image) measured at one

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certain position for different travel times is called an A-Scan. The radargram image, the B-Scan, is a sequence of consecutive A-Scans and can be considered as a matrix of

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intensities with rows corresponding to the travel time and columns corresponding to

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horizontal positions. B-Scans are usually pictured as gray scale images (Janning et al.,

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2014).

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Fig. 1. Generation of hyperbolic reflection (Ristic et al., 2009)

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Each anomaly, whether it is a manmade object or an inhomogeneity, has a specific shape of reflection in radargram (Ristic et al., 2009, 2010, 2012). Radargrams of cylindrical underground objects (Fig. 1) have specific hyperbolic shapes (hyperbolic reflections) (Ristic et al., 2009).The specific shape of hyperbolic reflection resulting from the scanning of cylindrical objects with GPR technology provides an opportunity for development and application of automated methods for their detection in radargram. The main tasks of processing radargram are in the localization of hyperbolic reflection, extraction of coordinates that characterize the apices and the points on prongs of a hyperbolic reflection, as well as parameter estimation as shown in (Ristic

ACCEPTED MANUSCRIPT et al., 2009). This paper proposes a procedure for solving the first two problems, without parameter estimation.

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Our method relies on neural networks. It differs from the previous ones in speed and the efficiency of finding the unique coordinates of apices and points on the

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prong. In addition, the algorithm gives good results with radargrams with noise, as

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well as identification and elimination of interfered hyperbolic reflection.

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2. RELATED WORK

Procedures for radargram examination for the needs of automated detection

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can be performed by either analyzing the full, dense radargram image or by analyzing

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a thresholded sparse version of it (Janning et al., 2014). It is possible to apply unsupervised procedures (Hough transform, for instance) and supervised procedures

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(e.g., Artificial Neural Networks – ANN) if dense radargram is analyzed. According to the authors’ best knowledge, all existing strategies for hyperbolic reflections detection involve application of algorithms that implement Hough transform (Illingworth and Kittler, 1988; Falorni et al., 2004; Windsor et al., 2005; Simi et al., 2008; Borgioli et al., 2008; Windsor et al., 2014; Li et al., 2016), Wavelet transform (Zhou et al., 2005), Radon transformation (Dell’Aqua et al., 2004), standard algorithms for pattern recognition, such as Support Vector Machines (SVM) (Passoli et al., 2009; Xie et al., 2013), or ANN (Youn and Chen, 2002). The Hough transform is a kind of a computationally intensive brute force method and has a cubic time complexity (Janning et al., 2014). ANNs are easiest to train after radargram simplification has

ACCEPTED MANUSCRIPT been done by edge detection (Shaw et al., 2005) or binarization (Gamba and Lossani, 2000). ANNs can be trained using signal processing statistical data descriptors (Shihab

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et al., 2002), Welch power spectral density estimate of signal segments (Al-Nuaimy et

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conditions (Giannopoulos, 2005; Frezza et al., 2013).

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al., 2000) or generated data sets which model EM waves propagation in specific

The basic problem of automated localization of hyperbolic reflection on

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radargram is high level of interference and noise in radargram which is a result of the

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complex disposition of a large number of underground utilities made of different materials and with different diameters in inhomogeneous soil (Rossini, 2003).

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In (Mertens et al., 2015) the authors propose an automated method for

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identifying hyperbolic reflection in inhomogeneous surrounding soil. The algorithm

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detects peaks of hyperbolae by setting analytically defined function of a hyperbola on a profile of edge points detected using the Canny filter. The existence of hyperbola is defined by a series of carefully selected criteria in order to match the zone of interest. Processing time is about 56s for 10,000 edge points detected in the image obtained from a radargram created by antenna 900 MHz, and 228s with an antenna 400 MHz (laptop Intel Core i5-3320M 1.90 GHz CPU). This time depends on the complexity of the image (Mertens et al., 2015). Ayala-Cabrera et al. (2011) used transformation multi-agent methodologies where the initial radargram (raw data) is based on the wave amplitude parameter. The obtained results show the viability of multi-agent methods for locating (plastic)

ACCEPTED MANUSCRIPT pipes in simple and complex cases. In paper (Dutta et al., 2013) authors proposed and investigated multi-sensor image fusion frame work using dynamic Bayesian network

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for automatic detection of buried underground infrastructure. The approach was

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applied successfully to produce 3D buried map. Meschino et al. (2013) presented the

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use of smart antenna techniques for the localization of a single buried object. The localization procedure reveals to be robust even if the target is in a peripheral

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position with respect to the array of the receiving antennas, in most of the cases it is

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successfully localized.

A large number of methods is based on common characteristics of image

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segments, where the trained neural network is used (Gamba and Lossani, 2000; Al-

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Nuaimy et al., 2000; Shihab and Al-Nuaimy, 2002; Birkenfeld, 2010; Cui et al., 2010; Khan et al., 2010; Maas and Schmalzl, 2013; Núñez-Nieto et al., 2014). The main

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objective of this approach is the quality image segmentation in order to narrow the search area. To reduce the need for a large database, the authors in (Passoli et al., 2009) use simulated data for the training set. In (Youn and Chen, 2002) the authors illustrate how different levels of noise can affect the performance of detection approach based on neural networks. In (Chen and Cohn, 2010) the authors propose an algorithm that can perform identification of hyperbola in GPR data in real time, as well as the calculation of the depth and size of the underground cylindrical objects.

ACCEPTED MANUSCRIPT The edge detector is often used in processing after the image segmentation. Edge detection is done using "canny" operator that finds the edges by local maximum

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of image (radargram) gradient, which is calculated using Gauss filter (Canny, 1986).

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The method uses two threshold values in order to detect strong and weak edges, and

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includes weak edges into output result only if they are connected with strong edges. The probability that the function with canny parameter will be misguided by the noise

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is lower, while the probability that true weak edges will be detected is higher.

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Application of functions for edge detection results in smaller amount of data that needs to be processed and makes this system functional in real time (Al-Nuaimy et al.,

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2000).

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The analysis of the papers related to these technologies yields the conclusion that the search through the dense radargram is very demanding in terms of time and

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computation resources and sensitive to noise and hyperbolic segments interference as well. Furthermore, it can be noticed that the majority of the procedures is directed towards the analysis of simplified radargram, which can be done in two ways (Birkenfeld, 2010):

1. Simplification of dense radargram and extraction of the data from the hyperbolic reflection 2. Segregation of small two-dimensional sections from dense radargram (called segment of interest) and extraction of the data from the hyperbolic reflection

ACCEPTED MANUSCRIPT From a technical point of view, software detection of anomalies (hyperbolic reflections, for instance) in radargram is more difficult because:

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 Various types of media surrounding the objects (different geological environments and volumetric moisture content)

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 Incomplete or noisy hyperbolic reflections (conditions of acquisition, media inhomogeneities)

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 Interference of neighboring hyperbolic reflections (estimation of affiliation)

EXTRACTION

POINTS

FROM

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REFLECTIONS

OF

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The procedure presented in this paper is based on the application of the procedure with segregation of segments of interests (SOI) from dense radargram.

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Such procedure retains maximum possible data resolution from the radargram in one or more segregated SOIs. When the data is extracted from SOI it is possible to apply each of the aforementioned techniques for data extraction regardless of their complexity, because the amount of data is significantly reduced. The proposed algorithm is done in seven steps and is given as a workflow map in Fig. 2. Its implementation is described in Table 1.

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Fig. 2. Workflow map of the algorithm

Step 1: basic pre-processing of radargram in terms of time-zero offset and *.dzt to *.bmp conversion. Radargrams were converted in *.bmp raster data

ACCEPTED MANUSCRIPT format. Number of columns depends of scanning resolution [scans/m] and real antenna trajectory. Number of rows depends of sampling resolution

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[sample/scan]. For most of examples, we use 100 [scan/m] and 512

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[sample/scan].

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Step 2: detection of SOI (initial set of rectangular boundary boxes S1) in dense radargram using ANN, that is Cascade Object Detector trained on previously

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formed sets of samples (Fig. 8) which contain hyperbolic reflections (positive

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targets) and ones that do not contain hyperbolic reflections (negative targets). Step 3: rejection of false isolated boundary boxes from initial set S1 by

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calculating the ratio of minimum and maximum pixel intensity within a

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bounding box. Remaining boxes form the set S2.

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Step 4: rejection of doubled boundary boxes from the set S2. Each bounding box containing other box is eliminated. Remaining boxes form the set S3. Step 5: extraction of data points. In the first stage (5.1), coordinates of apices are determined, forming the set P. In the second stage (5.2), coordinates of points of prongs are extracted, forming the set H. Step 6: checking of intersections between different hyperbola prongs. Coordinates of crossing points form the set O. Step 7: removal of hyperbolic reflections originated from constructive interference. Remaining reflections form the set H_out.

ACCEPTED MANUSCRIPT Table 1. Algorithm implementation ALGORITHM

Convert radargram to raster image

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(*.dzt to *.bmp) described in sub-section 3.1.2

Use COD to obtain on initial set of rectangular boundary boxes (bbox), S1

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For each bbox  S1

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described in sub-section 3.2

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STEP 2

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STEP 1

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Compute Ratio (Equation 2) IF Ratio  THOLD (0.68) REJECT bbox(i)

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S2 = bbox  bbox  S1  RATIO
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STEP 4

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Compute overlap condition (Equation 3) IF condition is satisfied REJECT outer bbox

Set of remaining bboxes, S3 described in sub-section 3.3.2

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For each remaining bbox  S3 5-1 HYPERBOLA APEX EXTRACTION Divide bbox into 2x3 rectangular sub-region (see Fig. 16) and in middle upper sub-region detected apex as described in sub-section 3.3.3, P - Set of apex coordinate pairs 5-2 DETECTED HYPERBOLA PRONGS Extract prongs - Separate left (Lp) and right (Rp) H = Lp U Rp described in sub-sections 3.3.4 and 3.3.5

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CROSSING POINTS ON INTERSECTED PRONGS Denote the set of all crossing points, O described in sub-section 3.3.6 For each o  O

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STEP 7

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Detect interfered hyperbolas and remove them from H The remaining hyperbolas form set H_out

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3.1 INPUT DATA AND CONVERSION

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described in sub-section 3.3.6

3.1.1 Input radargrams

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To examine the performances of the algorithm, a number of radargrams was used. A

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set of five representative radargrams obtained in real conditions was selected to be showed in the paper (Table 2). These examples contain different number of buried

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objects with different disposition, size, and level of noise. Sixth radargram is synthetic one (generated by gprMax), based on same geometry as Example 5. It is analyzed in order to emphasize the complexity of Example 5. Table 2: examples in paper and their description Example Radargram

Description

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sasa012a

One hyperbolic reflection, low noise level

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file028

Two hyperbolic reflections, different depths, no interference, low noise level

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testpit

Nine hyperbolic reflections, different depths, no interference, lower noise level

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file270

Two hyperbolic reflections, same depth, moderate interference, moderate level of noise

ACCEPTED MANUSCRIPT fivtanks

Five hyperbolic reflections, same depth, high level of constructive interference from hyperbolic reflectors associated with USTs, moderate level of noise

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Five_tanks

Synthetic radargram, same parameters as in example 5, low level of noise. Used to compare with Example 5 and to emphasize complexity of Example 5.

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1. As example of the simplest case radargrams containing one and two clearly notable

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hyperbolas (Fig. 3 – Courtesy of Faculty of Technical Sciences). Also, the noise level

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is very low. The prongs of neighboring hyperbolas have no common points and radargrams contain no interfered reflections. Radargram in Figure 3a represents

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gas line metal pipe 14” (R=35.56cm), while in the second radargram (Fig. 3b) two

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steel pipes are represented (R=50cm and R=35cm).

Fig. 3. Radargrams with one (a) and two hyperbolas (b)

2. Medium complexity radargram contains several hyperbolic reflections at various depths and with different intensity of the reflection (Fig. 4 - Radargram example from RADAN: "TestPit.dzt", courtesy of GSSI). Regarding interference, disposition of upper two hyperbolas on the right side (in red frame) may result in occurrence of interfered hyperbola below. But lower hyperbola in the red frame is real so this

ACCEPTED MANUSCRIPT step leads to the conclusion that geometric disposition is not sufficient condition

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for occurrence of interference.

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Fig. 4. Radargram with multiple hyperbolas

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3. Radargram 'file_270.dzt' presented on Fig. 5. contains two hyperbolic reflections

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that have a crossing point. This radargram was formed by scanning a pair of district heating line pipes, both with diameter of 250mm. Antenna with central frequency

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of 200MHz was used, scanning was done in real conditions (not in experimental field) and with significant level of noise.

Fig 5. Radargam 'file_270.dzt' containing two intersecting hyperbolic reflections

ACCEPTED MANUSCRIPT 4. In terms of processing, one of more demanding radargrams which is used in this paper is shown in Fig. 6, radargram example from RADAN: "fivtanks.dzt", courtesy

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of GSSI. Radargram represents a scan of five Underground Storage Tanks (UST's)

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with same diameter of 1.5m, on total depth 3m and UST offset of 2m. It is distinct

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for several reasons:  There is a number of hyperbolic reflections

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 On 4 locations real hyperbolic reflections are crossed

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 The last hyperbola is of irregular shape and contains high level of noise on one part

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 Present interference (4 false reflections beneath the points of prongs

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crossings)

Fig. 6. Disposition of tanks (left image – five tubes), radargram (right image) For the same geometry, a synthetic radargram Five_tanks was created by using gprMax application (Fig. 7). Being synthetic, the level of noise is much lower than in fivtanks.dzt. This example is used for comparative analysis with example obtained in real conditions in order to represent the difference in application of algorithm on synthetic and real data.

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Fig. 7. Synthetic radargram Five_tanks, obtained by using gprMax application,

3.1.2 Conversion to raster format

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containing 600 scans

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DZT data format represents binary file, in encrypted format, which contains raw data collected with GPR. In realization of proposed procedure it is necessary to

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convert data to *.bmp format, according to previously defined parameters (see

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abstract). Free software rad2bmp1was used. It is possible to extract a part of an image. First and last scan and first and last sample of the part to be extracted have to be defined (‘sub range information’). Conversion is possible for both 8 and 16-bit radargrams.

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http://www.geophysical.com/softwareutilities.htm

ACCEPTED MANUSCRIPT 3.2 Locating of hyperbolic reflection using trainCascadeObjectDetector Recognition of hyperbolic reflections in radargrams is done using MatLAB

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GUItrainCascadeObjectDetector2 (ComputerVisionSystem toolbox). Reflections are recognized and selected as boundary boxes.

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3.2.1 Training set

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Cascade Object Detector (COD) is well known algorithm for machine learning. It is based on Viola-Jones learning algorithm. First, the classifier has to learn to identify

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an object. It is done by training during which many positive (containing an object hyperbolic reflection) and negative (not containing an object - without hyperbolic

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reflection) sample images are analyzed (Fig. 8). Once the training is carried out,

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output classifier is used to recognize object. During the detection process input

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images are divided into many subimages which can be classified as object or noobject (Maas and Schmalzl, 2013).

Fig. 8. Example of positive (left) and negative (right) training samples

An object becomes true positive when positive sample image is correctly classified and false positive when negative sample image is misclassified as positive. An object

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http://www.mathworks.com/matlabcentral/fileexchange/39627-cascade-trainer--specify-ground-truth--traina-detector

ACCEPTED MANUSCRIPT becomes false negative when positive sample image is misclassified as negative. In order for algorithm to work correctly, each stage in the cascade must have a low rate

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of false negative objects. COD algorithm supports three training models: Haar-like features

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LBP – Local Binary Patterns

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HOG – Histograms of Oriented Gradients

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Each of these models has its advantages and disadvantages, so experimental

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evaluation of their applicability has been done, under the same conditions. All used pieces of data are real (not generated) and collected in real conditions (urban and

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suburban area), not on test-fields (which have strictly defined parameters and

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acquisition conditions). The radargrams are collected using 200, 400 and 900MHz antennas, with several variations in terms of type of soil, homogeneity and volumetric moisture content. Fig. 9 represents comparative analysis of the results of the mentioned models application. In the Fig. 9, the radargram is shown as *.bmp with time-zero offset removed. The radargram is formed on a soil with low volumetric moisture content with two pipes of large diameter (50 and 35cm) in it.

ACCEPTED MANUSCRIPT Fig. 9. Results of COD algorithm trained on three data set models (a – Haar, b – LBP, c – HOG)

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Fig. 9a (Haar model) shows that in represented example 3 ‘false’ objects are

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registered, while the time for training was 238 seconds. Fig. 9b (LBP) shows that, in

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represented example, 6 ‘false’ objects are registered, while the time for training was 7 seconds. Finally, Fig. 9c (HOG) shows that not a single ‘false’ object was registered in

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this example, while the time for training was 52 seconds. The number of stages of

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COD mainly depends on the quality of trained ANN, the number of hyperbolic reflections and SNR in the radargram. Better trained ANN and higher SNR yield less

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stages, while more reflections yield more stages. In most examples presented in this

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paper the number of COD stages was around 20. Since the analisys is done on real radargrams it is necessary to create the

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training set with a number of examples in order to apply it on a large number of radargrams. One result of detection on training set 2 is shown on Fig. 10.

Fig. 10. Detected boundary boxes containing hyperbolic reflections, by using COD (radargram Testpit.dzt)

ACCEPTED MANUSCRIPT 3.2.2 Problems with boundary box The main problem when selecting with boundary boxes is that boundary boxes

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often select interfered hyperbolic reflections (Fig. 11 – red rectangle). These

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reflections have the same shape as the real ones and, based on training set, are

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selected as positive samples. Also, it is often that one reflection is selected by two different boundary boxes. These problems are solved by creating the functions that

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recognize these cases and process them in adequate manner.

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Fig. 11. Detected boundary boxes containing hyperbolic reflections, by using COD (radargram fivtanks.dzt)

3.3 Processing of boundary boxes in MATLAB Resulting boundary boxes along with radargram in the form of raster are the input data for further processing (Fig. 12). First and second column of resulting boundary box determine the coordinates of the upper left pixel. Third column determines the width while the last one determines the height of the boundary box. This way, hyperbolic reflections are approximately located so the search area is reduced.

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Fig. 12. The result of hyperbolic reflections detection in the form of boundary boxes

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3.3.1 Recognition and elimination of false isolated boundary boxes As a result of the recognition of hyperbolic reflections based on the trained network,

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in addition to boundary boxes (bboxes) containing reflections, false isolated zones of

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the radargram can be obtained (Fig. 9a, 9b). In the first steps of the algorithm it is necessary to recognize false isolated zones for the purpose of their elimination. The

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task of this segment of the algorithm is to remove zones that are too homogenous in terms of ratio of pixel intensity contained within the bbox, so theoretically they could not contain useful information. To resolve this problem, falsely obtained bboxes are particularly analyzed as well as bboxes that contain hyperbolic reflections. In bboxes containing hyperbolic reflections there is stronger reflection from underground infrastructure facilities compared with the surrounding ground, so the ratio of min and max pixel intensity values in the isolated zone is greater, unlike the homogeneous zones where this ratio is small. These features are used to find the limit value for

bbox rejection, with the emphasis on keeping the positive bbox samples. Calculating the ratio is done by the equation:

ACCEPTED MANUSCRIPT Ratio 

min(bboxi ) max(bboxi )

(2)

By analyzing a larger number of radargrams and training set led to the optimum limit

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value (0.68) for the rejection of false bboxes. Bboxes which have the ratio of min and max greater than the specified limit value are rejected as falsely selected. Figure 13

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shows a radargram with frames of bboxes where the yellow represents the frames of

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bboxes which are rejected, while the retained ones are black. This step allows for greater freedom of the algorithm and the quality of its work even

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in cases where the trained network does not give ideal results.

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Fig. 13. The result of removing false isolated bboxes (yellow – removed bboxes, black – retained bboxes)

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3.3.2 The checkout of double boundary boxes

In the second step it is checked whether there are extracted boundary boxes

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that contain other boundary box. If there are, they are eliminated. To solve this

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problem the differences between upper left and lower right coordinates are

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calculated (Fig. 14) and then they are used to check if the conditions are met. Coordinate differences are calculated between every two bounding boxes. If the

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conditions are satisfied, the outer frame of boundary box is deleted. Figure 15 shows

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a result of the elimination of doubled bounding boxes.

Fig. 14. Boundary boxes with coordinates of upper left and right corner

The conditions that have to be met: ΔX1 = X1 – X3ΔX1 < 0 ΔY1 = Y1 – Y3ΔY1 < 0 ΔX2 = X4 – X2ΔX2 < 0 ΔY2 = Y4 – Y2ΔY2 < 0

(3)

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Fig. 15. The result after elimination of doubled bounding boxes (yellow – removed isolated bbox, red – removed doubled bbox, black – retained bboxes)

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3.3.3 Hyperbola apex extraction After doubled boundary boxes are eliminated hyperbola apex is determined. As a simplest solution a pixel with the maximum positive intensity (considering that reflecting surface is metallic, as in all examples in this paper) in the middle column of the boundary box can be considered apex. However, this is entirely based on the geometry of boundary box which depends on the way training set is created, and this approach doesn’t always yield satisfying result. Therefore, the proposed solution yields better results while minimally relying on boundary box frame. Analysis of representative radargrams shows that boundary boxes have several common features, which are:

ACCEPTED MANUSCRIPT  Resulting boundary boxes often don’t select complete hyperbola prongs, but alwas contain hyperbola apex.

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 Radargram analysis in frequency domain (Al-Nuaimy, 1999) – by applying short-

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time Fourier transform (STFT). Each scan is divided in several time-segments

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and maximum values of their spectra higher than defined threshold are represented in frequency image (Fig. 16). It can be noticed that maximum

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values are, in most cases, at the upper segments of hyperbola prongs.

Fig. 16. Thresholded STFT frequency image corresponding to file028

Mentioned conditions are used to detect the hyperbola apex:  Searching starts from the pixel with maximum intensity located in the column between first and second third of the boundary box, width-wise (Fig. 17 – left),  Around found pixel submatrix with dimensions 3x2 is formed (Fig. 17 – middle),  Within the pixels of interest next pixel with maximum value is found,

ACCEPTED MANUSCRIPT  Procedure is done iteratively, with search window moving from the begining to the end of the second third of the boundary box (Fig. 17 – right), with current

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pixel always in the second row of the first column.

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 From the resulting local maximums row and column of hyperbola apex is

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determined.

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Fig. 17. Division of boundary box, sub matrix 3x2 and resulting local maximums

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Pixels with minimum row index indicate the row where apex is located. However, due to the noise that can occur, it is possible that minimal indexes of extracted rows are starting and ending index of extracted array. Since the apex is expected to be in the middle of the array, algorithm checks ending pixels and if there are such they are discarded. Also, there is a limit in terms of tolerance which is calculated automatically. The limit is used to eliminate pixels with very low intensity of reflection, which theoretically cannot be hyperbola apex. When all these criteria are taken into account from the remaining pixels the row with minimal index is separated and accepted as a row of hyperbola apex.

ACCEPTED MANUSCRIPT After the row is determined it is needed to determine the column of hyperbola apex. If there is a single pixel with maximum value in previously selected row, its

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column can be adopted as the column of the apex. However, it is often that apex

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contains several pixels with the same maximum value. Also frequency and magnitude

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image indicate that maximum does not have to be exactly at the apex. Therefore it is not the best solution to adopt the mean value of pixels for the apex column. To

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determine the apex column, the first step is to find the row with maximum

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numeration which is on both sides of hyperbola (Fig. 18 – left).

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Fig. 18. Row with maximum numeration (left), pixels on left and right side (center), hyperbola apex (right)

Then it is checked whether these rows contain more pixels in array. If there are, their mean value is calculated (Fig. 18 – center). After that, resulting pixels on the left and right side are used to calculate mean value which is adopted as the final column. The final result is a single pixel characterized with previously determined row and column. Selected pixel is the hyperbola apex (Fig. 18 – right).

ACCEPTED MANUSCRIPT 3.3.4 Point extraction from hyperbolic reflection. Dealing with asymmetrical raw data.

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After hyperbola apex is found, the points that represent hyperbola prongs have

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to be determined. It is favorable to enable determination of characteristic points for

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non-symmetric hyperbolas, determine points after the crossing with neighboring hyperbola. In order to perform this step successfully, hyperbola is divided into two

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column where the apex is found (Fig. 19).

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parts and points are determined separately for each part. Division is done along the

Fig. 19. Division of the hyperbola prong and its area of search.

Selected half will often contain prongs of neighboring hyperbolas or crossings with them, so it is needed to separate the hyperbola which is related to resulting boundary box. The start of the search is the upper right corner, for the left half, and the upper left corner for the right half (Fig. 20). The pixel adopted as hyperbola apex is starting pixel. Local maximum is searched in a 2x2 window so that current pixel is in upper right corner for left prong or in upper left corner for right prong. This way it is unable to pass onto neighboring prongs of hyperbola and point are correctly determined to

ACCEPTED MANUSCRIPT the crossing with neighboring hyperbolas. Within this step it is necessary to define stopping criterion, taking into account that prongs very often have different lengths.

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The main guideline is, based on known parameter (hyperbola apex), to determine the

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limit of tolerance, as upper boundary for determination of characteristic pixels of one

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prong.

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Fig. 20. Starting pixels of the left and right prong

Points on the prongs are selected as long as difference between intensities of

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the apex and current pixel becomes too large. If only pixels are compared it is very difficult to define the threshold of tolerance for each hyperbola, so mask with dimensions 5x5 is formed. In the first iteration mask is formed around the apex (reference mask) and mean value of intensities of pixels within the mask is calculated. In each following iteration around the pixel selected as local maximum 5x5 mask is also formed and mean value is calculated (current mask) (Fig. 21). Point determination is done until the ratio of mean values in current and reference mask is lower than tolerance limit. Here it has to be emphasized that the point extraction is continued outside the boundary box until the stopping criterion is satisfied.

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Fig. 21. Determining points on the hyperbola prongs with 5x5 mask

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3.3.5 Skipping routine for fewer interruptions of data (inhomogeneous data) in intersection zone of two different hyperbolic reflections (crossed hyperbolic

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reflections)

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In the crossing zones pixel intensity steeply drops which causes algorithm to stop. Analysis showed that the maximum width of the critical zone is 10 pixels. In

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critical zone pixels do not satisfy the tolerance so algorithm stops. In proposed solution when this situation occurs, the search is continued in the direction of local maximum while the critical zone is skipped (in red circle on Fig. 22). If mean value of the next current mask satisfies given tolerance the determination of points continues, otherwise previous iteration is the last one. Figure 22 shows the result before and after the code is modified with the part for solving the situation of two hyperbolas crossing.

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Removing of false reflections caused by constructive interference of the

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Fig. 22. Extraction of points on prongs without skipping routine (left) and with skipping routine applied (right)

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hyperbolic diffractions - Removing interference Interfered hyperbolas are the consequence of scanning technology and utilities

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disposition. They need to be eliminated from further processing. In Fig. 23 some

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similarities between radargrams with and without interference can be noticed. In both situations the disposition of three central hyperbolas is almost identical. Interfered hyperbola is in the middle of upper two, and the same layout has hyperbola 3b which is not interfered. Also, distances from hyperbolas 1a and 2a to the apex of hyperbola 3a are almost equal as distances from 1b and 2b to 3b. It follows that the condition of geometric layout is not sufficient to conclude whether the hyperbola is interfered or not. The difference that can be noticed is that hyperbolas 1a and 2a have the crossing point, while 1b and 2b have not. The necessary condition for occurrence of visible interference is that the end of the prongs must spread at least under the apices of 2 hyperbolas on the top. Due to the

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point is tested. In the second step it is examined whether the apex of possible

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interfered hyperbola is in approximately the same column as the crossing point.

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Fig. 23. Similarities between real and interfered hyperbolas

To conclude if the hyperbola is interfered or not crossing points have to be found. If hyperbola apex is below the crossing point that hyperbola is considered to be interfered and is eliminated. To determine crossing points all pairs of left prongs (as numerations of row and column) are stored in a matrix. The same procedure is for the right prongs. After that it is checked if there are pairs whose absolute values difference is close to zero or one. If there are, they are considered to be crossing points. This approach is derived from the way point of left and right prongs are determined. Namely, when 2x2 search

ACCEPTED MANUSCRIPT window is moved for left and right prong separately it is possible that the pixels of the neighboring prongs pass over (Fig. 25). Found pixels which determine left prong of

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hyperbola in Fig. 25 are colored bright green, and right prong dark green. Also it can

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be seen that the prong pass over, that is there is no point of their crossing although

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they are crossed. Since the maximum difference between row and column of the pixel at the position of left and right prong crossing is one, this condition is taken as an

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optimum. Besides, it is possible that the apex is moved few pixels to the left or right

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while scanning, and this approach takes this tolerance into account as well. Crossing points are stored in separate nx2 matrix (green circles in Fig. 24), and then it is

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checked whether columns of crossing points contain apex which is located under the

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crossing point. If they do, that hyperbola is considered interfered.

Fig. 24. Detected crossing points (green circles)

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Fig. 25. Pixels pass over

4. EXPERIMENTAL RESULTS ANALYSIS

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The results of the implemented algorithm are represented on specified

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characteristic radargrams. In the first case the simplest examples from Fig. 3 are

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processed. These radargrams contain one and two clearly notable hyperbolas. Existing hyperbolic reflections representing cylindrical objects are successfully detected and processed in an adequate manner (Fig. 26).

Fig. 26. Processed radargram containing one (a) and two metal pipes (b)

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In example shown on Fig. 27 nine reflections were detected.

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Fig. 27. Processing results of radargram "TestPit.dzt" with several hyperbolic reflections

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Two hyperbolic reflections were detected in example ‘file_270.dzt’ (Fig. 28). Unlike previous examples, this one contains the crossing point of two hyperbolas. Points on prongs of both hyperbolas were extracted beyond the crossing point.

ACCEPTED MANUSCRIPT Fig. 28. Processing results of radargram "file_270.dzt" with two intersecting hyperbolic reflections

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Radargram Five_tanks is synthetic and therefore contains high SNR, but four interfered hyperbolas can be noticed. Proposed algorithm detected apices and

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crossing points and also extracted points on the prongs of five real hyperbolas. Apices of two interfered hyperbolas and the crossing point between them was also detected,

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but the algorithm recognized those were interfered hyperbolas and didn’t extract

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points on their prongs (Fig. 29).

Fig. 29. Processing results of synthetic radargram "Five_tanks" with five intersecting hyperbolic reflections Last example represents more complicated radargram previously shown on Fig. 6, which contains real hyperbolas crossings and interfered hyperbolas. In this example two interfered hyperbolas with higher intensity were detected and five real

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determined after the crossing points. The third interfered hyperbola was not selected

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as positive sample of training set, considering it contains higher level of noise and

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reflection intensity is low. Also, the last hyperbola on the right side is noisy. Despite that, this hyperbola apex and points on the prongs were successfully determined,

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considering that the hyperbola is recognized as a positive sample.

Fig. 30. Radargram "FiveTanks.dzt" processing result: hyperbola apices and prongs (a) and crossing points and apices of interfered hyperbolas (b)

If results obtained on synthetic and radargram obtained in real conditions are compared, it can be noticed that, although the geometry is the same and the radargrams themselves different, the results are similar. In both cases proposed algorithm successfully detected real hyperbolas. Apices of interfered hyperbolas were also detected, but were recognized as false and therefore algorithm didn’t extract points on prongs, on both radargrams. Therefore it can be stated that the proposed algorithm showed high level of robustness to interference.

ACCEPTED MANUSCRIPT The result of the recognition of hyperbolic reflections depends on the quality and quantity of training samples. In paper (Gamba and Lossani, 2000) it was shown

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that the neural networks can be applied to locate the hyperbolic reflection, as well as

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to obtain satisfactory results with a relatively small number of training samples. It

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should be stressed that frames of training results in this paper serve only for approximate localization of a hyperbolic reflection. The coordinates of the points that

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characterize the prongs are found separately for the left and right prong, wherein the

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extracted points may go outside the frames of the obtained boundary boxes. Since the coordinates of points on the prong are determined separately, the

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algorithm is also successful with hyperbolic reflections with asymmetrical prongs.

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The algorithm also successfully localizes the coordinates of points in the cross-

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sectional area of two adjacent hyperbolic reflections (Fig. 30, right). Moreover, the coordinates of the points on prongs are also being determined after the cross section of the adjacent prongs of hyperbolic reflections. In addition, the algorithm has proven to be successful with finding and eliminating interfered hyperbolic reflections. The embedded function in MATLAB, etime, was used for measuring the speed of processing of the training results. The average speed is obtained as the mean value of ten consecutive measurements of processing time (Table 3). All analyzes in the paper were carried out on a PC with Intel Core i3-4130 CPU with 3.40 GHz with

ACCEPTED MANUSCRIPT MATLAB environment (The Mathworks). Average speed depends on the number of detected hyperbolic reflections on radaragram.

Average processing speed [s]

Description

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Example Radargram

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Table 3. The average processing speed of the representative radargrams

sasa012a

0.1113

One hyperbolic reflection, low noise level

2

file028

0.2894

Two hyperbolic reflections, different depths, no interference, low noise level

3

testpit

4.1767

Nine hyperbolic reflections, different depths, no interference, lower noise level

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file270

0,1890

Two hyperbolic reflections, same depth, moderate interference, moderate level of noise

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fivtanks

2.2428

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Five_tanks

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1

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4,952

Five hyperbolic reflections, same depth, high interference with ghost hyperbolic reflections, moderate level of noise

Synthetic radargram, same parameters as in example 5, low level of noise. Used to compare with Example 5 and to emphasize complexity of Example 5.

5. CONCLUSIONS

In this paper, the process of localization of the apex and points on the prongs of hyperbolic reflections is addressed through seven steps. The algorithm is based on the approximate localization of hyperbolas and separation of segments of interest from radargram relying on neural networks. Following that, the localization of unique apex coordinates is done, and then the points which characterize prongs of hyperbolic reflections. Finally, a classification of possible interfered hyperbolic reflections is carried out and extraction of the algorithm results.

ACCEPTED MANUSCRIPT Functionality of algorithm was tested on a number of synthetic and radargram obtained in real conditions. Based on the obtained results it was shown that the

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with low processing time and low rate of false detections.

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majority of hyperbolic reflections is successfully detected and properly processed,

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A step further achieved in the presented method for the localization of the coordinates of apices and points on the prongs is its successful application on

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hyperbolic reflections with asymmetric prongs (high noise level). As a part of the

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solution, the procedure to recognize the interference of two or more hyperbolic reflections is defined so, if the effect is present, useful data is properly classified and

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extracted.

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This approach accelerates the processing of radargrams and facilitates making the

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final decisions for the user. The proposed solution could be implemented into existing software packages in this area, or standard functions could be provided in MATLAB for automated radargram processing.

Acknowledgment

This work has benefited from the network activities carried out within the EU (European Union) funded COST (European Cooperation in Science and Society) Action TU1208 "Civil Engineering Applications of Ground Penetrating Radar"

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1009-1012.

ACCEPTED MANUSCRIPT Highlights

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1. Localization of hyperbolic reflections from GPR profiles relying on neural

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networks.

2. Extraction of coordinates of hyperbola apex and prongs.

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3. Tested on radargams with various complexity levels (asymmetrical, interfered

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data).