Detection of linear objects in GPR data
Introduction
Detecting, localizing and assessing buried or hidden objects in a non-destructive and cost-effective fashion is a problem of great interest for a variety of application areas that range from structural engineering to medical and defense.
The ground penetrating radar (GPR) is widely considered an excellent non-destructive method for the detection of underground objects such as pipes, beams, tunnels, buried walls, etc. Typical data are 2D vertical sections (slices) of the ground, where hyperbolic patterns reveal the presence of scattered objects. The detection of targeted objects in such data, however, is often left to a human operator, due to the presence of intense noise, artifacts, and interfering objects (e.g. stones). Nonetheless, many attempts to automatize this pattern recognition task have been proposed in the literature (see, for example, [6], [9], [27]), but they are usually limited to a 2D domain (volume slices) and, therefore, they do not take advantage of the interdependence between aligned views. In order to overcome this limitation it is thus necessary to work directly on the 3D data set obtained by packing together all the available parallel slices. In general, this is accomplished by first applying a migration1 operator to the 3D data set, in order to obtain a data set that is able to describe the object shapes in a metrically consistent fashion. This approach is particularly convenient with linear target objects, in which case the hyperbolic surfaces generated by such targets collapse into roughly cylindrical shapes that approximate the objects to be detected. This helps the user distinguish the real targets from other non-elongated interfering objects (see Fig. 1, Fig. 2, Fig. 3).
Detection of linear objects is a problem of great interest, particularly for application of industrial/civil engineering (localization of pipes, metal rods, etc.). In the past decade, methods for linear object detection have appeared in the remote sensing literature for 2D data (see, for example, road detection techniques in SAR [18] or LADAR [25] images. Such line detection techniques, however, have little use for 3D data obtained with GPR, which looks more like a noisy collection of aligned elongated spots (see Fig. 1, Fig. 2). In fact, the lack of continuity and the non-negligible thickness of the “blobs” that constitute the data relative to each target line are likely to cause serious difficulties to traditional line detection methods based on local data analysis. In order to overcome these problems we must turn to solutions based on a more “global” approach.
Examples of global analysis tools that seem appropriate for the data that we are interested in are Hough and Radon transforms. There is a twofold reason why such transforms can provide us with a viable approach to the solution of the faced problem. The former is their intrinsic robustness against data discontinuities. In fact, they could help detect linear targets even if they appear as a series of aligned but isolated blobs. The latter reason that motivates our interest in such transforms is their intrinsic robustness against the impact of undesired scattering objects such as stones.
The Hough transform (HT) was originally conceived as a tool for detecting lines in 2D images, but numerous extensions of this algorithm can be found in the literature for the detection of more general shapes that belong to specific parametric families, such as ellipses [1], [17]. Further results are also available for the detection of non-parametric shapes (see generalized HT [4], [8], [16]). Unfortunately, computational cost and memory requirements make HT-based solutions extremely sensitive to the number of parameters that are needed to model the shapes to be detected. For these reasons, the literature is rich with techniques aimed at the optimization of the basic algorithms (see fast linear HT [13], iterative HT [16], adaptive HT [12], fast adaptive HT [10], randomized fuzzy HT [17], etc.). An interesting example of this sort is presented in [7] and [3], which propose a hierarchical and multi-resolution approach to HT analysis.
An example of application of a 3D HT to the analysis of GPR data sets was recently proposed in [2].
In this work we propose a solution based on the 3D radon transform (RT), which has been shown to be equivalent to the Hough Transform for the detection of lines [5], [24]. It is well known that the RT is commonly used for the generation of 3D tomographic data from 3D slices [14], [26], but it has also been used for detection of lines in both 2D and 3D spaces [15], [19].
In the next section we will provide the basics on the Radon transform and the extension of the RT to the 3D domain. Such concepts will then be applied to the analysis of 3D data sets. We will also provide criteria to correctly interpret the RT of complex data (see Section 3). The proposed solutions will be tested on both simulated and real data (see Section 4).
Section snippets
2D radon transform
Let f(x,y) be an image and g(γ,u) its 1D projection along the direction γAccording to this definition, g(γ,u) is the line integral of the image intensity, computed along a line l whose distance from the origin is u and whose angle from the X-axis is γ (Fig. 4). All points (X,Y) on the line l satisfy the equationand this allows us to rewrite the projection function g(γ,u) aswhere δ(·) is the Dirac function. The family
An iterative approach
Due to the presence of overlapping regions in the parameter space, the simultaneous identification of more than one scattering object is often too much of a complex problem. Furthermore, peaks in parameter space are often generated by lines that pass through “blobs” of various scattering objects. In order to be able to cope with these problems, we can make the process iterative and detect only the leading target at each step. In fact, once the most likely target is detected, it can be removed
Experimental results
The proposed approach has been tested on a variety of synthetic and natural data sets, with voxset sizes ranging from 50×50×70 to 100×100×200 voxels.
We first considered synthetic data sets that included two pipes of different diameters, placed in different positions and with different orientations. The diameters in the tests were 3, 5 and 7 voxels, and we used a 5-pixel wide mask for the low-pass filter on the projection planes (see Section 2.3).
We initially set all voxels to zero except for
Implementation issues
We implemented our algorithm in a Windows environment, using C++ and MATLABTM. The MATLAB module manages the graphic interface, while a Dynamic Linkage Library (DLL) written in C++ carries out all computational tasks.
In order to optimize the algorithm from the computational standpoint, particular attention has been paid to the implementation of DLL. The result is, in fact, very encouraging, considering the size of the data sets and the number of operations needed to compute the RT. In order to
Conclusions
In this paper we proposed a semi-automatic approach to the detection of linear scattering objects in geo-radar data sets, based on the 3D radon transform (RT).
One of the main features of our algorithm is the robustness and the reliability of the detection of the targets, even in the presence of data affected by heavy noise, artifacts and other undesired scattering objects.
The solution that we propose is iterative, as each detected target is removed from the data set before the next iteration,
References (27)
Generalizing the hough transform to detect arbitrary shapes
Pattern Recognition
(1981)Randomized Hough transformimproved ellipse detection with comparison
Pattern Recognition Lett.
(1998)- et al.
Detection and characterization of planar fractures using a 3d hough transform
EURASIP Signal Processing
(2002) - A.S. Aguado, M.S. Nixon, A new hough transform mapping for ellipse detection, Technical Report, Research Journal...
- W. Al-Nuaimy, H. Lu, S. Shihab, Automatic 3-dimensional mapping of features using GPR, Ninth International Conference...
Multiresolution hough transform—an efficient method of detecting patterns in images
IEEE Trans. Pattern Anal. Mach. Intel.
(1992)Hough Transform from the Radon Transform
IEEE Trans. Pattern and Mach. Intell.
(1981)- S. Delbò, P. Gamba, D. Roccato, A fuzzy approach to recognize hyperbolic signatures in subsurface radar images, IEEE...
- C. Espinosa, M.A. Perkowski, Hierarchical Hough transform based on pyramidal architecture, Northcon, Portland, 1–3...
- P.F. Fung, W.S. Lee, I. King, Randomized generalized hough transform for 2-D grayscale object detection, Thirteenth...
Neural detection of pipe signatures in Ground Penetrating Radar data
IEEE Trans. Geosci. Remote Sensing
Cited by (42)
A CNN model for predicting size of buried objects from GPR B-Scans
2022, Journal of Applied GeophysicsCitation Excerpt :Different strategies have been used on the topic of hyperbola detection. Fitting algorithms like Radon (Dell'Acqua et al. (2004)), wavelet (Windsor et al. (2005)) and Hough (Chen and Cohn (2010); Liu et al. (2019)) have been used for feature extraction in GPR images. Other feature extractors like Sobel operators (Li et al. (2016)) and Canny operators (Mertens et al. (2015); Bugarinović et al. (2020)) are also used as a pre-processing step.
Integration of modern remote sensing technologies for faster utility mapping and data extraction
2017, Construction and Building MaterialsCitation Excerpt :It is possible to apply unsupervised procedures (Hough transform, for instance) and supervised procedures (e.g., Artificial Neural Networks – ANN) if dense radargram is analyzed [15]. Existing strategies for hyperbolic reflections detection involve application of algorithms that implement Hough transform [16–19], Wavelet transform [20], Radon transformation [21], standard algorithms for pattern recognition, such as Support Vector Machines (SVM) [22,23] or ANN [24]. The Hough transform is a computationally intensive method and has a cubic time complexity [15].
Point coordinates extraction from localized hyperbolic reflections in GPR data
2017, Journal of Applied GeophysicsCitation Excerpt :It is possible to apply unsupervised procedures (Hough transform, for instance) and supervised procedures (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'Acqua 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).
Advanced multi-frequency GPR data processing for non-linear deterministic imaging
2017, Signal ProcessingCitation Excerpt :It should not come as a surprise that ground penetrating radar (GPR) is nowadays recognized as one of the most effective, versatile, and robust tools for subsurface investigations [1–12].
Sensitivity and accuracy in rebar diameter measurements from dual-polarized GPR data
2013, Construction and Building MaterialsCitation Excerpt :Steel bar corrosion effects in concrete can also be detected with high frequency antennas and advanced processing techniques [7,8]. Rebars buried in concrete represent such an easy target for GPR that detection and location can be assigned to fully automatic algorithms [9,10]. Nevertheless, rebar diameter cannot be estimated through a geometrical analysis of radar images since the wavelength at the frequencies normally used for concrete inspections (1–2 GHz) is in the order of a 5–10 cm, i.e. quite larger than the diameter of the rebars.
Compressive sensing of underground structures using GPR
2012, Digital Signal Processing: A Review Journal