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Inferring the most probable maps of undergroundutilities using Bayesian mapping modelBilal, Muhammad; Khan, Wasiq; Muggleton, Jennifer; Rustighi, Emiliano; Jenks, Hugo;Pennock, Steve R.; Atkins, Philip; Cohn, AnthonyDOI:10.1016/j.jappgeo.2018.01.006

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Journal of Applied Geophysics 150 (2018) 52–66

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Journal of Applied Geophysics

j ourna l homepage: www.e lsev ie r .com/ locate / j appgeo

Inferring themost probablemaps of underground utilities using Bayesianmapping model

Muhammad Bilal a,⁎, Wasiq Khan f, Jennifer Muggleton c, Emiliano Rustighi c, Hugo Jenks d, Steve R. Pennock d,Phil R. Atkins e, Anthony Cohn b

a University of California, Center for Environmental Implications of Nanotechnology (UCCEIN), Los Angeles, USAb School of Computing, University of Leeds, Leeds, United Kingdomc Institute of Sound and Vibration Research, University of Southampton, Southampton, United Kingdomd School of Electronic and Electric Engineering, University of Bath, Bath, UKe School of Electronic, Electrical and Computing Engineering, University of Birmingham, Birmingham, United Kingdomf Manchester Metropolitan University, Manchester, United Kingdom

⁎ Corresponding author.E-mail address: m.bilal@ucla.edu (M. Bilal).

https://doi.org/10.1016/j.jappgeo.2018.01.0060926-9851/© 2018 The Authors. Published by Elsevier B.V

a b s t r a c t

a r t i c l e i n f o

Article history:Received 13 February 2017Received in revised form 23 December 2017Accepted 11 January 2018Available online 31 January 2018

Mapping the Underworld (MTU), a major initiative in the UK, is focused on addressing social, environmental andeconomic consequences raised from the inability to locate buriedundergroundutilities (such aspipes and cables)by developing amulti-sensormobile device. The aim ofMTU device is to locate different types of buried assets inreal time with the use of automated data processing techniques and statutory records. The statutory records,even though typically being inaccurate and incomplete, provide useful prior information on what is buriedunder the ground and where. However, the integration of information from multiple sensors (raw data) withthese qualitative maps and their visualization is challenging and requires the implementation of robust machinelearning/data fusion approaches. An approach for automated creation of revisedmapswas developed as a Bayes-ian Mapping model in this paper by integrating the knowledge extracted from sensors raw data and availablestatutory records. The combination of statutory records with the hypotheses from sensors was for initial estima-tion of what might be found underground and roughly where. The maps were (re)constructed using automatedimage segmentation techniques for hypotheses extraction and Bayesian classification techniques for segment-manhole connections. Themodel consisting of image segmentation algorithm and various Bayesian classificationtechniques (segment recognition and expectation maximization (EM) algorithm) provided robust performanceon various simulated as well as real sites in terms of predicting linear/non-linear segments and constructing re-fined 2D/3D maps.

© 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Keywords:MTU sensorsMost probable mapsBayesian data fusionImage processingBayesian regression

1. Introduction

The costs associated with street works in the UK is of critical consid-eration due to the vast majority of utilities buried underneath the roadsand their repair/(re)installation (£7b annual) (Mcmahon et al., 2005).The types of utilities buried under the ground are diverse and theiramount is notoriously large which makes excavation a challengingtask in order to upgrade these underground networks. In addition, thestatutory records of underground networks are typically incompleteand inaccurate particularly for old street works (Burtwell and E. A.,2004). An important undertaking is to develop schemes to detectwhat is buried underground that could be associated to their recordsand could become cost savior. A multi-sensor mobile laboratory MTU

. This is an open access article under

(Underworld, 2011) was developed which consists of multiple sensorscapable of deploying several approaches to detect different types of bur-ied infrastructure. The MTU device, was designed to assess the feasibil-ity of a range of potential technologies that can be combined into asingle device to accurately locate buried pipes and cables. The potentialtechnologies included ground penetrating radar (GPR), low-frequencyquasi-static electromagnetic fields (LFEM), passive magnetic fields(PMF) and low frequency vibro-acoustics (VA) and significant advanceshave already been made (Royal et al., 2011; Royal Acd et al., 2010).

The location estimation approaches combined by MTU provide sig-nificant advantages over other commercially available techniques(Ashdown, n.d.) for detecting wide variety of utilities and control trialswere taken for test commercial sites. As a result, excavations necessaryformaintenance and repair can be largely reduced using such device. Animportant undertaking is to use heterogeneous information from thesesensors and build refinedmaps of buried utilities in real time. However,due to the heterogeneity in features of utilities and ground properties, it

the CC BY license (http://creativecommons.org/licenses/by/4.0/).

53M. Bilal et al. / Journal of Applied Geophysics 150 (2018) 52–66

is challenging to develop a general technique that could assess hetero-geneous information and handle the uncertainties associated to thistask. The integration of information obtained from multiple sensors onMTU is of critical importance in order to make sense of the data beforeproviding a precise information on a site. The knowledge obtainedfrom different sensors presents itself non-symbolically i.e. the delivereddata is essentially an image representing what the sensor “sees” under-ground. In contrast, utility records are almost universally representedsymbolically i.e. they are stored in a spatial database as records with avectorized representation of their spatial position, along with attributeinformation (such as material, diameter). It is therefore challenging toprovide a useful and accurate representation of the data acquired froma variety of sensors. Therefore, a data fusion approach consisting of au-tomated techniques for data extraction and integration was imperative.

The map (re)construction model developed in this work was an im-provement over (Chen and Cohn, 2011) which was initially designedonly for 2D construction of themap assuming that it consists of only lin-ear segments. In addition, the data preprocessing for hypotheses extrac-tion in (Chen and Cohn, 2011) was not combined as a complete modeland it was assumed that the hypotheses were extracted from GPR im-ages using an iterative clustering/classification techniques prior todata fusion tasks. Simple clustering/classification algorithms for hy-potheses extraction such as k-means or Dbscanwere restricted in sever-al ways for asset classification problem when developing real timemaps. For example, traditional k-means clustering algorithm createsthe clusters based on Euclidean distance of each data point to the cen-troids (initially selected randomly). Also, the number of clusters to becreated is known in k-means algorithm. Depending on statutory recordsto identify the number of segments was not reliable as, even providingvaluable information, they are inaccurate and may contain incompleteinformation. Dbscan (Sander et al., 1998) also separates the clustersbased on Euclidean distance without providing the desired number ofclusters to be generated as prior. However, Dbscan requires radius inorder to differentiate the clusters that is used as a criterion for decisionmaking on number of clusters. The Euclidean distance between param-eters is important in both approaches which is helpful in situationswhere clustering is only distance based.

Bayesian data fusion models have been utilized for numerous appli-cations and there is a large body of literature proposing Bayesianmodel-ing for data fusion and uncertainty management, thus, providingmotivation for the work proposed in this study. To date, Bayesianmodeling has been successfully implemented in similar applications,such as seismic/Magnetotelluric inversion (Dettmer et al., 2014; Guoet al., 2011), water distribution management, modeling for rock-physics analysis, gas and buried near-surface utility mapping (Ristićet al., 2017; Ji et al., 2016; Wang and Lu, 2016; Ren et al., 2017;Aleardi et al., 2017; Fernández-Martínez et al., 2013). Among severalimpactful studies using Bayesian modeling, the approach of combiningmultiple data sources and Bayesian data fusion for bedrock trackinghas been of significant interest such as (Fiannacca et al., 2017;Christensen et al., 2015; Oldenborger et al., 2016). These studies pro-posed automated tracking of bedrock depth and orientation by combin-ing data from different inversion models, borehole data (Christensenet al., 2015), and the utilization of time-domain electromagnetic data(Oldenborger et al., 2016) to systematically handle uncertainties indata of heterogeneous nature and reconstruct estimated maps of bed-rocks. An application of Bayesian data fusion approach for thepredictionof water pipe failures was developed by (Oldenborger et al., 2016) withthe capability to be integrated with the geographical information sys-tem of water resources and automatically predicting pipes of potentialfailures. Another application of neural networks and pattern recognitionwas developed utilizing only ground penetrating radar (GPR) data (im-ages) to train the model on hyperbolic features (of buried objects) andpredict the locations and depths of buried solid objects followed by au-tomatic construction of the maps of underground solid objects (pipesand cables) (Ristić et al., 2017; Al-Nuaimy et al., 2000). It is noted that,

in addition to the inclusion of GPR image analysis as proposed by (Al-Nuaimy et al., 2000), the work proposed in this paper provides widerapplicability due to the inclusion of multiple sensors of the MTU deviceand the application of Bayesian models being capable of incorporatingincremental learning (unlike neural networks) upon the acquirementof new knowledge.

In other similar works, Neira (Neira and Tardos, 2001) developed adata association model for addressing the problem of robust data asso-ciation for simultaneous vehicle localization and map building whichwas an improvement over gated nearest neighbor (NN) (Bar-Shalom,1987) for tracking problems that successfully rejects spuriousmatchingandprovides optimal solutions in terms of pairs ofmatching in clutteredenvironments. The correlation betweenmeasurement prediction errorsin 2D space in cluttered environment provides robust data associationwith an efficient traversal of the solution space. However, the direction-al errors (linearity) causedmismatching of the segmentswithmanholesusing the hypotheses extracted from the sensors. Abhir and Roland(Bhalerao andWilson, 2001) also used aMulti-resolution Fourier Trans-form (MFT) for capturing sufficient shape and orientation of objectswithin a given image. The use of statistical analysis and camera projec-tions to estimate the location/orientations of line segments in 3D imagewas also implemented for similar linear segment construction problems(Dong-Min and Dong-Chul, 2009; Chen and Wang, 2010). However,these approaches are only limited to an image of objects and segmentswhich is used to reconstruct a 3D image. MTU mapping, on the otherhand, is multi-source data fusion approach to integrate informationfrom multiple sources and produce most probable maps utilizing ad-vanced machine learning/data mining techniques. For linear segmentfitting, significant amount of literature report the use of different regres-sion models including EM algorithm that can efficiently fit at higher ac-curacy levels (Ward et al., 2009; Ester et al., 1996; Sanquer et al., 2011;Delicado and Smrekar, 2007; Werman and Keren, 1999; Friedman andPopescu, 2004). The classification of data samples based on its sourceas distinguished by MTU sensors is, however, lacking in these ap-proaches as these algorithms were developed for regression scenarios.In addition, the connection establishment (manhole-segment) wasnot considered as an underlying issue as only the general regressionwas covered.

The Bayesian mapping model is capable of using automated tech-niques for hypotheses extraction, classification, segment recognitionand connection establishment with the associated manholes. We as-sociate a probability distribution with every such hypothesisreflecting possible errors in the measurements (uncertainty due tothe fusion of data from multiple sources) and hypothesis extractionprocess. These geographical positions (x, y) and depths (z) wereused as input to the next stage of the mapping system. A variety ofArtificial Intelligence (AI) techniques and algorithms were imple-mented such as Bayesian Data Fusion (BDF), image segmentation, or-thogonal distance hyperbolic fitting, and weighted variation. Thealgorithms for automated data processing and map (re)constructionwere developed for real time operative capability of MTU device. Acomplete use case can be tested using real time mapping modelwhere hypotheses extraction techniques were combined with itera-tive connection establishment and visualization techniques. Severalsimulated as well as real sites were tested, and it was demonstratedthat the model is robust in various conditions where statutory re-cords were unavailable, and the sensor readings were sparse. Thesegments were recognized and noise was removed successfully invarious situations for mapping the utilities demonstrating the abilityof model to work in real time complex situations.

2. Materials and methods

Themodel for Bayesianmapping followed theworkflow depicted inFig. 1. The sequential steps inmodel workflowwere as follows; (1) datapreprocessing, (2) segment recognition, and (3) segment-manhole

Fig. 1. Model Workflow (Data preprocessing for hypotheses extraction following segment recognition, Bayesian segment connection and refined map visualization.

54 M. Bilal et al. / Journal of Applied Geophysics 150 (2018) 52–66

connection. The datasets consisted of both qualitative (raw images fromMTU sensor device, statutory records (utility maps)) as well as quanti-tative information (manhole surveys providing information on

Fig. 2. Images taken from MTU sensors and processed to mark the hypotheses (hyperbolae and(b) Passive Magnetic Field, (c)MTU GPR, and (d) Vibro acoustics. (Right) Images (b) and (d)wit

directions and depths). More details are given in Section 2.1.2 (MTUsensor raw data). The data from these sources were integrated togetherin the form of positions (x, y), depths (z) and orientations (Ɵ) as an

circles). The images were created from the raw data collected from (a) Commercial GPR,h backgrounds subtracted using image segmentation technique to extract hypotheses.

Fig. 3. (a)MTU scan lines on the surface to record reflections w.r.t. surface excitation and referencemeasurement location. (b) Correlated functions to create raw images using frequencydomain transformation, and (c) hypotheses extracted from raw images using adaptive image segmentation techniques, and integrated with utility records for segment recognitionalgorithm.

55M. Bilal et al. / Journal of Applied Geophysics 150 (2018) 52–66

input for segment recognition algorithm. The geometrical measure-ments (i.e., readings of slope distances in horizontal and vertical planes)with respect to spatial survey structure were acquired using the TotalStation Theodolite (TST). The relative positions of the MTU mobile lab-oratory were, therefore, called the survey lines at given (x, y) coordi-nates from the TST. Manhole surveys were helpful in determining thetypes of buried utilities at a site and estimating their orientations anddepths. Bayesian recursive algorithm as known as EM was developedfor segment-manhole connection. EM is an iterative algorithm for find-ing themaximum-likelihood estimation of a set of parameters for a spe-cific distribution in a statistical model when it contains unobservedlatent variables (Do and Batzoglou, 2008). Based on partially connectedinformation from different sources and segments recognized from

Fig. 4. Clusters with curvatur

segment recognition, EM algorithm was used to identify most probableconnections of segments with assets and connect them in an iterativemanner. The depth information from manholes and sensor readingswere then used in conjunction with EM output to produce refined 2D/3D maps of an investigated site.

2.1. Data preprocessing

Data for model developmentwere collected from following sources;

2.1.1. Statutory recordsThe utility/statutory records consisted of maps of buried assets as

ground truth which provided information on approximate orientations

e of hyperbolic features.

Fig. 5. Separation of hypotheses into cluster of linear clusters and curved clusters. For clusters with circular features, a three-point circle fitting was used, as in Fig. A-1 (Appendix).

56 M. Bilal et al. / Journal of Applied Geophysics 150 (2018) 52–66

and positions of these assets. Since these records are inaccurate, theirposition information was not included in segment recognition algo-rithm. However, the information pertaining to the type of buried assetand their approximate directions was helpful in segment-assetconnection algorithm. Therefore, the positions and orientations (x, y,Ɵ)T from these records were used for segment-manhole connectionestablishment.

2.1.2. MTU sensor raw dataThe raw data included heatmaps (Fig. 2) of investigated sites that

were produced from various MTU and commercial sensors. The sensorsused in MTU mobile apparatus include Ground Penetrating Radar(GPR), Passive Magnetic Field (PMF), Vibro Acoustic, and Low Frequen-cy Electro-Magnetic (LFEM). Briefly, the sensors and their functionality

Fig. 6. Segment recognition algorithm fitting

are explained in this section. Detailed information on each sensor can befound elsewhere (Dutta et al., 2013; Muggleton et al., 2011; Thomaset al., 2009).

2.1.2.1. Ground penetrating radar (GPR).GPR locates buried utilities (me-tallic and non-metallic) by transmitting electromagnetic waves into theground and collecting the response (waves reflected from the objectsunderground) (Ristić et al., 2017; Al-Nuaimy et al., 2000). A GPR scanproduces an image as a collection of multiple A-scans of reflectedwaves received at different wave-travel times and integrating theminto a B-scan. In B-scan, the rows represent depth (by utilizing thereflected waves) and columns represent horizontal positions of scanlines.

linear segments in groups of hypotheses.

Table 1Settings for simulated and real sites (S#= simulated site #, R#= real site #).

Data # Manholes # Pipes & cables # Sensor readings

S1 10 13 28S2 12 16 30S3 26 46 87R1 19 8 18R2 8 12 25

57M. Bilal et al. / Journal of Applied Geophysics 150 (2018) 52–66

2.1.2.2. Passive magnetic field (PMF). PMF is useful for detecting the ca-bles by utilizing the magnetic field generated by current in a cable aswell as neighboring objects which generate magnetic field (may alsobe from current flow leak from a buried cable). The cluster centroids(Fig. 2c) are multiplied by the surveyed map dimensions (m × nimage) which are then divided by surveyed lengths and depths, respec-tively, to calculate the (x, y, z) coordinates on the map.

2.1.2.3. Vibro acoustic (VA) sensors.VAdevice at theMTUuses seven geo-phones for recording the reflected velocities of the waves that are gen-erated by exciting the surface. The response received at the surface isutilized to create a cross-sectional image with respect to the referencemeasurement used near the exciting location. The cross-sectionalimage is created via the time-domain transformation of the correlationfunctions between geophone and reference measurement recordings(Figs. 2d, 3). The images are then analyzed to extract hypotheses usingadaptive image segmentation techniques (Section 2.1.4, Hypothesesextraction).

Fig. 7. Simulated datasets with hypotheses points and initial maps for (a) S1, (b) S2, and (c)

2.1.2.4. Low frequency electromagnetic field (LFEM). LFEM approach isbased on injecting the current into the ground and measuring the volt-age on the surface via coupled platesmoved along the surface. The LFEMapproach at MTU is operated in a targeted grid location and theresulting image represents the underground structure.

Using the above approaches, qualitative raw images consisting of (x,y, z)T information (x-axis as the length of scan line and y-axis as thedepth of the investigated surface (typically 2–4 mdeep))were collectedand processed to extract hypotheseswhichwere utilized for 2D/3Dmapreconstruction. The orientation of MTU sensor device provides approx-imate direction of buried asset as the survey is usually taken in the di-rection perpendicular to the orientation of asset.

2.1.3. Manhole surveyManhole surveys for real sites were conducted to collect supporting

information on estimated orientations and depths of buried assets. Inaddition, the types of buried assetswere also recorded to distinguish be-tween themwhen constructing site maps. The quantitative informationfrommanhole surveys therefore included (x, y, z,Ɵ)T aswell as the typeof buried asset as qualitative information.

2.1.4. Hypotheses extractionHypotheses (processed coordinates of the location detected byMTU

sensors) extraction was implemented on raw sensor image data to au-tomatically estimate the positions from surveyed locations. The imageswere segmented into clusters of foreground (hypotheses) and back-ground pixels using unsupervised image segmentation techniques.The adaptive image segmentation was used to highlight and quantify

•••

•••

S3. Squares correspond to manholes (legend) and circles correspond to sensor readings.

58 M. Bilal et al. / Journal of Applied Geophysics 150 (2018) 52–66

regions of high thresholds in the image (Nobuyuki Otsu, 1979). Imageswere initially enhanced based on histogram equalization in order to in-crease image contrast (Krishna, 2013; Gonzalez, 2008). Subsequently,the adaptive segmentation algorithm (Nobuyuki Otsu, 1979), whichregards an image as a data clustering scenario, was applied to dividethe image into clusters of two classes (foreground and background)which iteratively finds the threshold that minimizes the weightedwithin-class variance and thus, maximizing the between-class variance.The centroids of clusters were identified as approximate positions of as-sets (e.g., Fig. 2(b and d) and their backgrounds subtracted (Fig. 2(right))). Sensor output image is often noisy andmaynot provide an ac-curate location. Additionally, multiple hypotheses locations may be re-ported in close proximity when different types of assets (or a non-asset object) are present as given in Fig. 1 (hypotheses extraction). Itis noted that the sensory scan lines may consist of multiple hypothesesof different types or a single hypothesis given the ground truth(i.e., utility map in Fig. 1). Accordingly, the image segmentation algo-rithm provides clusters (regions) of possibly one or more locationsgiven (i) the type of buried material from utility map, and (ii) raw im-ages provided by differentMTU sensor. Frommultiple images of a singlesurveyed location, themost probable locations of assets were estimatedusing Bayesian weighted average technique, i.e.

h xið Þ ≈ N x; μ;Λð Þ ð1Þ

In the above equation, xi denotes the relative location of hypothesis i(w.r.t. MTU scan line) collected from the image, μ is themeanof selectedhypotheses, and Λ is covariance matrix of the hypotheses. Maximum A

Posteriori (MAP) position of an asset was obtained using hðxÞ ¼ arg

max Πn

i¼1ðhðxiÞÞ where n is the number of hypotheses.

Prior to segment recognition from groups of hypotheses, the identi-fication of noisewas conducted in terms of pointswith nomanhole con-nection within a given previously tested threshold (δ = 2 m). Eachhypothesis point was validated using: (1) point to line (nearest buriedutility in statutory record) distance and (2) manhole orientations. Thedistance djh (Fig. 3c top right) from each pipe segment j to the point h(Fig. 2d (white circle, Fig. 3b) was calculated using

djh ¼xje−xjs� �

yjs−yh� �

− xjs−xh� �

yje−yjs� ���� ���ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

xje−xjs� �2 þ yje−yjs

� �2r ð2Þ

where (xjs,yjs) and (xje,yje) are the start and end points of the pipe seg-ment j respectively, and (xh,yh) is the location of hypothesis point. Thepoint h was considered an orphan point if its distance from a pipe

Fig. 8. Segments recognized for (a) S1, (b) S2 and (c) S3. Squares in thefigures correspond to difof the references to color in this figure legend, the reader is referred to the web version of this

segment j was greater than δ. i.e. h ¼ orphan if dhk1Nδanddhk2Nδhr otherwise

� where dh, ks and dh, k

e are the distances between of kmanhole (with posi-tion (xk, yk), where the segment of same type exists (i.e., a pipeconnection matching pipe segment j in this case)) from the segmentstart and segment end, respectively. The probability that the point h be-longs to a segment j was then calculated as Sj ¼ arg max

jðPhjÞ where

Phj = F(h→ j|djh)≈ N(h,djh.)

2.2. Segment recognition

The hypotheses obtained from above step were given as input to seg-ment recognition algorithmwhich estimated the segments by joining hy-potheses together based on their positions and orientations. The input tosegment identification algorithm included the hypotheses and the orien-tations in which the surveys were taken (usually from left-to-right). Thelinear segments were iteratively classified from the groups of hypotheseswhich were located within the range of an angle of up to ε= ± 0.08(i.e., wider sensitivity of up to 4.5 degrees). The algorithm starts withfirst two chosen hypotheses as assigned to first class (starts with class= 1), and the orientation from thefirst hypothesis to all other hypothesesare calculated. The next point is chosen and assigned to the same class iftheir difference in orientations is ≤ ε otherwise the chosen point isassigned a new class. The algorithm is repeated for each hypothesis andprovides the output as points assigned to a class which are then joinedusing least squares, circle and/or polynomial fitting techniques. Theworkflow of the algorithm is given in Algorithm 1.

Algorithm 1. Segment recognition algorithm (Pseudo code).

ferentmanholes (legend) and red circles correspond to sensor readings. (For interpretationarticle.)

Fig. 9. 3D map construction for segment-manhole connection (S1(a), S2(b) and S3(c)).

59M. Bilal et al. / Journal of Applied Geophysics 150 (2018) 52–66

To separate the clusters of linear segments from curved segments, thegoodness of fit (R2) was checked and compared to threshold ε1 ≥ 0.99(0.99 confidence). Each cluster with R2 ≥ 0.99 was separated as a linearpipe segment and the remaining clusters were considered as curved orcircular segments. For each hypothesis point in curvature analysis,the tip of the vector r(t)= b x(t), y(t) N traces out a path in the planewhere t representedMTU survey line and y represented the change in po-sitions represented by hypotheses. The relative positions of the hypothe-ses points were therefore represented as follows r′(t)= b x′(t), y′(t) N

where x0ðtÞ ¼ ∂x∂t and y0ðtÞ ¼ ∂y

∂t . The unit tangent vector was calculated

as T ¼ r0ðtÞkr0ðtÞk, where kr0ðtÞk ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffix0ðtÞ2 þ y0ðtÞ2

q. In order to determine the

variation in the position (y) with respect to (x), the difference intervalwas obtainedusingη ¼ k arg max

i∈NðTiÞ− arg min

i∈NðTiÞk. Testing data clus-

ters of various curvatures led to the selection of approximate curvaturethreshold to 0.15. The segments were assigned as curved using

Curved ¼ true if T∈ −R;þR½ � or T∈ þR;−R½ �ð Þand Curvature ¼ 1false Otherwise

�ð3Þ

whereCurvature ¼ 1 if η≥0:150 Otherwise

� andR is the quantitativemeasure of

the change in y (Fig. 4).The curvature detection algorithm was tested on various groups of

hypotheses which demonstrated robust performance in terms of

Fig. 10. Real Site 1. Blue lines represent simulated utility record based onmanhole and sensor rinterpretation of the references to color in this figure legend, the reader is referred to the web

separating curved segments from linear ones (four of the groups givenin Fig. 5)

2.3. Segment-manhole connection using expectation maximizationalgorithm

The connection of segments recognized from previous sectionwith manholes was categorized as a classification problem whereeach segment was to be classified as a segment connected to twomanholes. The EM algorithm was proposed for segment-manholeconnection establishment which has been used in wide range of ma-chine learning and data mining scenarios such as classification(Klautau, 2003; Sander et al., 1998), Image Processing (HuanhuanChen, 2010) and unsupervised clustering (Bailey and Elkan, 1994;Buntine, 2002; Salojarvi et al., 2005). The inputs from sensor read-ings, estimated asset orientations from manholes, statutory recordsand segments recognized from previous step were used to identifysuitable connections between segments and manholes. Combiningthe inputs created a data fusion scenario where hidden informationfrom different sources was integrated and the probability of segmentclassification was updated until the algorithm converged (or thenumber of iterations reaches). Therefore, based on the probabilitydistribution drawn from EM algorithm, the local maximum ofsegment-manhole connection provided an optimal solution thatwas then compared with prior information from statutory records.Using EM, each segment can be assigned to a pair of manhole

eadings. Red lines represent segment-manhole connections established by themodel. (Forversion of this article.)

Fig. 11. Real survey site 2 (a) pipe detected by MTU sensors, (b) pipe detected by PMF sensor due to electric cable buried closely, (c) data from different sensors integrated together forsegment-manhole connection, (d) 3D view of segments detected by Bayesian Mapping model.

60 M. Bilal et al. / Journal of Applied Geophysics 150 (2018) 52–66

connections given the above parameters. EM consists of two stepsthat are (1) Expectation and (2) Maximization. Expectation calcu-lates the probability distribution of a target outcome given a set ofparameters while the maximization step updates the distributiongiven the parameters which are updated from expectation at each it-eration. The EM algorithm is explained as follows:

1) For a given hypothesis point h, get nearest segment Sj from statutoryrecord. Get manhole locations and the depths. Initialise the prior foreach manhole connection with Pi as uniform distribution. Initialisecovariance matrix

Λ ¼ diag Δd; θ j−θk ; θk−θhkk k; θ j−θhk

; Zh−Zkk k� �where Δd ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðxSj−xkÞ2 þ ðySj−ykÞ2

q, θj = orientation of Sj, θk = ori-

entation of segment of same type as of Sj from manhole k's cover,θhk = orientation from manhole k to h, zh = depth of h fromsensor, zk = depth of the segment of same type as of Sj frommanholek's cover, Θ = (K,X,Y,Z,xh,yh, zh,Sj)T for K manholes with [X,Y,Z] asposition and depth.

2) E-step: Likelihood for each manhole k connection

L Ck Λ;Θjh i ¼ 1

2π Λj jð Þ3=2exp −

12

C h;kð ÞTΛ−1C h;kð Þ� ��

where C(h,k)= [Δd,‖θj− θk‖,‖θk− θhk‖,‖θj− θhk‖,‖zh− zk‖]. The Maxi-

mum Likelihood Estimate (MLE) is then given by γk ¼ LhCk jΛ;ΘiXKk¼1

LhCkjΛ;Θi

3) M-Step: Maximization of likelihood

Λ ¼ diag

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi∑k

YKk¼1

Δd:L CkjΛ;Θh ið Þ !2

Xkk¼1

L CkjΛ;Θh i

vuuuuuuuut ;

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi∑k

YKk¼1

θ j−θk :L CkjΛ;Θh i� � !2

Xkk¼1

L CkjΛ;Θh i

vuuuuuuuut

;

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi∑k

YKk¼1

θk−θhkk k:L CkjΛ;Θh ið Þ !2

Xkk¼1

L CkjΛ;Θh i

vuuuuuuuut ;

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi∑k

YKk¼1

θ j−θhk :L CkjΛ;Θh i� � !2

Xkk¼1

L CkjΛ;Θh i;

vuuuuuuuut zh−zkk k

0BBBBBBBBBBBBBBBBBB@

1CCCCCCCCCCCCCCCCCCA

4) Repeat 2–3 until converged (log likelihood converges to 10−4)

5) Maximum A Posteriori (MAP) for connection of k with Sj is Ch→k ¼arg max

k∈KðγkÞ

TheMLE γk in step 2 provides bestmatch between amanhole k and asegment Sj. The algorithm is repeated for connection from both ends of Sjto a pair of best matchingmanholes. At the test site, it is possible for sen-sors to contain noise (containing spatial location and direction error) aspart of the hypotheses. A point h was considered noise when it's likeli-

hood of manhole connections (k→ and k←) fell below a threshold α ¼∑h∈OPðLjh;k→ ;k←Þ

32O

where P(L|h,k→,k←) ≈ N(L,h,σo). Here, σo(=0.4) is the

variance (meters) calculated from (x,y,z) of O. The noise from aboveset of hypotheses points was identified using

h ¼ noise if P L h; k→; k←jð Þ b αh otherwise

�ð4Þ

Table 2Directional (D(Ѳ)), Spatial (S(x,y)) and connection errors compared to JCBB. EM\L =without segment recognition algorithm, EM\U=without utility records.

Error EM\L EM\U EM JCBB U E(JCBB) E(EM)

S(x,y)S1 1.3514 1.7923 0.4132 3.1548 2.8 1 0D(Ѳ)S1 3.3371 4.4451 1.2526 6.1112 4S(x,y)S2 2.1334 3.5691 1.005 7.4324 2.5 0 0D(Ѳ)S2 4.3351 6.4321 1.1129 10.9813 5S(x,y)S3 3.1058 6.9471 2.0591 12.6976 6.5 5 0D(Ѳ)S3 4.6131 8.8195 2.0031 16.9115 6S(x,y)R1 4.3291 8.7795 1.6531 11.1125 5 1 0D(Ѳ)R1 3.9973 6.9553 1.8533 8.8134 4S(x,y)R2 2.4415 3.1101 1.0051 4.9518 3 0 0D(Ѳ)R2 2.3705 3.1781 0.8109 4.1136 3

Fig. 12. (a) JCBB Connection Error in water pipes (b) JCBB Connection Error in gas pipes.

61M. Bilal et al. / Journal of Applied Geophysics 150 (2018) 52–66

The clusters of segments formanhole connections from (4) consistedof the hypotheses points and the connected manhole positions whichare: Cj = [k→ {h ∈ O : h→ Sj} k←]

3. Results and discussion

Dataset for model validation included five sites of simulated data (3sets) aswell as real data (2 sets). Themodel was developed and validatedusing MATLAB 2011(b) where the most probable maps were generatedgiven 3 different sources of information: (i) sensor readings, (ii) manholesurveys, and (iii) the statutory records. In order to validate themodel, hy-potheses extraction, accurate segment identification (with noise remov-al) and segment-manhole connection were tested. Several variations inthe parameters and data qualitywere considered in order to verify the ro-bustness of the model. The hypotheses were extracted from raw sensorimages using image segmentation techniques. A segment recognition al-gorithmwas developed to identify linear and curved pipe/cable segmentsbased on the direction of survey taken byMTUmachine, and orientationsestimated from hypotheses when they were combined together. Total of4 initial use cases of hypotheses (Fig. 6) tested in order to evaluate theperformance of segment recognition algorithmwhere the number of seg-ments in each use case were known.

The simulated datasets (S1, S2, and S3) consisted of locations ofmanholes as well as pipes from ArcGIS (Esri, 2015) and simulatedhypotheses (simulated readings from MTU sensors). The real sites(R1 and R2) consisted of measurements from MTU sensor readingsand statutory records. For noise removal in simulated sets, whitenoise was addedwith the following: (1) Spatial noise of the locationsof manholes and pipes was up to 2 × 2 m, (2) Noise in hypotheses lo-cations was up to 0.4 m and (3) Noise in pipe directions was up to 8degrees.

3.1. Bayesian mapping model for simulated data

The model was initially tested on 3 simulated datasets (S1, S2 andS3) with varying numbers of manholes, sensor data points, and seg-ments from statutory records (Table 1). For simulated datasets, the hy-potheses were manually generated and the initial maps were obtainedfrom ArcGIS (Esri, 2015). Initial simulated datasets with initial mapsare depicted in Fig. 7.

(a) Segment recognition: Segment recognition algorithm showed robustperformance for all datasets and the noise was removed from groupsof hypotheses in S1 and S2. The absence of statutory records did not

affect the capability of the model to draw accurate segments due tothe segment recognition algorithm. In addition, the segments weredrawn in 3D due to the inclusion of depth information from man-holes and sensor readings. However, the uncertainty increased inthe absence of statutory records as they provided useful informationon the number of buried assets and their directions. The segmentsdrawn by automated segment recognition algorithm for simulateddatasets are given in Fig. 8.

(b) Segment-manhole connection: The segment recognition algorithmprovided advantages over (Chen and Cohn, 2011) in terms of basisfor accurate connection with manholes and construction of 3Dmaps. The segments were used by EM algorithm for segment-manhole connection establishment. Using the parameters from dif-ferent sources (Materials andMethods), it was observed that the al-gorithm successfully created connections for segments that led tothe reconstruction of 3D map. Among the segments generatedfrom step (a) a few segments had single end connecting to a man-hole. Such situations were also tested for the validation of EM algo-rithm. The maps of simulated datasets were generated which aredepicted in Fig. 9.

3.2. Bayesian mapping model for real data

Real sites (R1 and R2) with sensor readings and manhole surveyswere tested for model validation. Table 1 provides information on theinputs to model for simulated sites as well as real sites. There were 18sensor readings taken at R1 which included readings for linear pipes

Fig. 13. Impact of spatial and directional error on survey sites S2 and S3.

62 M. Bilal et al. / Journal of Applied Geophysics 150 (2018) 52–66

and an electricity cable. Raw images from sensors were manipulated toextract hypotheses which were used for automatic segmentrecognition. There were no connection errors for R1 using EM basedsegment-manhole connection algorithm for linear segments (SeeFig. 10).

Real site R2 consisted of straight linear pipes with an electric cablefor which the sensor readings were taken (Fig. 11a). There was nonoise detected in the sensor readings and segments were successfullyconnectedwithmanholes. PMF sensor usually detects objectswith elec-trical current such as electric cables. At R2, The PMF sensor detected awater pipe (rectangle in Fig. 11b) in the survey. This was due to therun of an electric cable in a close proximity of that water pipe whichemits the electrical current.

3.3. Connection and spatial errors in mapping models

For manhole connection establishment process, the proposed algo-rithm was also compared with Joint Compatibility Branch & Bound(JCBB)which calculates theMahalanobis distance between the observa-tions and the predictions and accepts a connection if the Mahalanobisdistance is smaller than a validation gate (Yangming Li et al., 2013).The segment-manhole connection problem was similar to the spatialdata association problem in robotics (Bailey and Durrant-Whyte,2006). Using the data fusion technique, noise removal and the iterativerefinement of posterior probability using EM algorithm, the analysisshowed better results compared to JCBB for both simulated sets aswell as real sites. JCBB suffered in connecting segments in simulated sce-narios with manholes when more than one segments were located inclose proximity in the map. In tested datasets, JCBB also suffered fromconnection errors at the manhole locations where directional errorexceeded five degrees. There were total five manhole connection errorsrecorded when JCBB was run on S3 as shown in Fig. 12 where Fig. 12ashows the connection errors forwater pipes and Fig. 12b shows the con-nection errors for gas pipes.

The analysis with segment recognition algorithm significantly re-duced the spatial errors (in meters) and directional errors (in de-grees) when modeling for mapping the underground utilities. Themean directional error using EM algorithm was smaller comparedto JCBB. The connection errors (i.e., false positives (number of man-holes connections predicted for the wrong segment)) are given inTable 2 which are denoted as E(JCBB) for JCBB and E(EM) for EMalgorithm.

A noticeable impact on the voxel prediction for each pipe was ob-served when this error rate was increased from 8 to 14 degrees. The in-creased directional error in S1 and S3 had significant effect withinaccurate segment-manhole connections in the maps. In addition, thespatial error resulted in variations in voxel classification as shown inFig. 13a and b. The black circles show directional errors and the red cir-cles show spatial error.

4. Conclusions

The traditional approaches formap generation given in the literaturerequire information from statutory records and provide solutions formostly 2Dmap generation. Additionally, the information frommultiplesensors require extensive processing and statutory records should alsobe integrated that provide prior knowledge about buried utilities. Re-cent analyses/studies on the abilities to locate underground utilitiesstressed the needs of a system capable of generating real time mapswith the help of heterogeneous information. However, current tech-niques are limited to either generating 2D maps of linear segments orunable to detect different types of utilities. This paper addresses theseproblems by proposing a Bayesian mapping model by implementingvariousmachine learning techniques for real time3Dmap (re)construc-tion. The segment recognition algorithm is robust in identifying groupsof hypotheses forming linear/curved segments that are helpful in estab-lishing connections with manholes. In order to improve utility classifi-cation and refined map generation, noise removal facilities wereembedded in the system that improved performance in distinguishingbetween hypotheses and noise. The Bayesian Mapping model is aimedto overcome critical issues related to efficient and real-time location ofburied assets that could provide valuable underground informationand be cost effective. Further online analysis will also validate modelperformance at higher levels and its ability to generate refined mapsat real time.

Contributions

The research and development activities were conducted mainlyat the University of Leeds, under the supervision of Professor Antho-ny G. Cohn. First author conducted the analysis, prepared results andthe manuscript under the supervision of Prof. Anthony Cohn, secondauthor conducted major revisions and improvements in the paper,while other authors at partner institutions contributed to the

63M. Bilal et al. / Journal of Applied Geophysics 150 (2018) 52–66

development of MTU sensors and providing raw data from Wiganand Blagdon test sites.

Conflicts of interest

The authors do not have any conflict of interest.

Acknowledgements

This research is supported by EPSRC grants (EP/F06585X/1 and EP/K021699/1): Mapping the Underworld: Multisensory Device Creation,Assessment, Protocols (http://www.mappingtheunderworld.ac.uk).We are thankful to the projectmanagement, especially, Mark Hamilton,for all site visits, collaboration and management of the efforts from allproject partners.

Appendix A. Appendix

For curved segments, the three-point circle fitting was applied as il-lustrated in Fig. A-1.

A. Most probable segment estimation

In order to refine the output of linear segment fitting without sig-nificant impact on model performance, the least squares fitting wasperformed on the above sets of hypotheses and manhole connec-tions. Even though the data from multiple sources was integratedfor Bayesian mapping, the sensor readings may contain small non-negligible noise which may also affect the performance of leastsquares linear fitting algorithm. Fig. A-2 shows a simple scenariowhere the point containing noise in its location causes an increasedangular difference with the orientation from connecting manhole.Also, the segment approximation fails to find the most probablelinear segment without crossing any other segment in closeproximity.

It is critical to develop an approach for above mentioned scenariossince it is common that the street surveys contain more than one pipesburied in close proximity and the chances of having the overlaps betweenthose segments are higher. In order to overcome such challenge, a proba-bility distribution over the space of three possible lines Li (i = 1,2,3) was

Fig. A-1. (a) Circular hypotheses, (b) Circle fit for circular points, (c) N

created and described by discrete random variables. Li is the ith line ofvoxels given the specific attributes which are the locations of the pointsof clusters defined in previous section. We need to find

arg maxl

Ygll¼1

P yl L1; L2; L3jð Þð Þ ðA1Þ

and

arg maxl

Ygll¼1

P zl L1; L2; L3jð Þð Þ ðA2Þ

where l ∈ gl is the voxel chosen from a set gl of voxels fitted for thequantized line. The probability distribution for three observed possible3D positions of each line Li were created and combined given x, y andz information. For each voxel of a line Li, two equal spaced perpendicularline segments ℊp were drawn along the y-axis for Eq. (A1) and z-axis forEq. (A2). This set of linear segments is denoted byG. For the calculationof themost probable voxel at each quantised position of each line Li, weuse two terminologies. For Eq. (A1), the pixel pil of Li is the (xl, yl) and forEq. (A2), the pixel pil of Li is the (yl, zl). Therefore Eq. (A1) is used for de-termining the most probable yth position of the voxel and Eq. (A2) isused to determine the zth position of the voxel in the map. For all kvoxels defined by gl, the joint probability distributions are given by

P yl L1; L2; L3jð Þ ¼YLi¼1

P yl Lijð Þ for L ¼ 3

P zl L1; L2; L3jð Þ ¼YLi¼1

P zl Lijð Þ for L ¼ 3

where

P yl Lijð Þ ¼Xgll¼1

Xy∈G

1∇yk k exp −

y−pli 2

gp 2

( )ðA3Þ

on-circular Hypotheses, (d) Polynomial fit for non-circular points.

Fig. A-2. Pipe segment fitted from hypotheses crossing another closed segment in the map.

64 M. Bilal et al. / Journal of Applied Geophysics 150 (2018) 52–66

pil is the lth pixel (xl, yl) of Li

P zl Lijð Þ ¼Xgll¼1

Xz∈G

1∇zk k exp −

z−pli 2

gp 2

( )ðA4Þ

pil is the lth pixel (yl, zl) of LiCalculating P(yl|Li) and P(zl|Li) provide the probabilities P(yl|L1,L2,L3)

and P(zl|L1,L2,L3) respectivelywhich are used to calculate themost prob-able voxel position for the map using

P Ly L1; L2; L3j� � ¼ arg maxl

Ygll¼1

P yl L1; L2; L3jð Þð Þ ðA5Þ

and

P Lz L1; L2; L3jð Þ ¼ arg maxl

Ygll¼1

P zl L1; L2; L3jð Þð Þ ðA6Þ

Fig. A-3. Perpendicular quantised linear points created from the point and the linearsegment.

An example of this is shown in Fig. A-3 where three lines(L1,L2,L3) are drawn from three techniques and the quantizedlines on y-axis and z-axis are drawn to calculate Eqs. (A5) and(A6).

At each step in themap, the voxel with the highest probability giventhree lines as input was taken as the most probable voxel. The set of allvoxels at the end created a line in 3D spacewhichwas considered as themost probable linear segment approximation. This algorithm was ap-plied for the approximation of each linear segment in the performanceevaluation of the algorithm.

B. Cardinal spline fitting

In addition to the linear and curved pipe segments which mayinclude sewer pipes, gas pipes and water pipes, the street mapsalso included electric cables buried underground which need tobe approximated. The difference of the cables from the otherpipe segments is their non-linear behavior. The cable can be buriedin an arbitrary order without satisfying linearity condition forwhich line fitting or curve approximation may represent inappro-priate solutions. The Passive Magnetic Field (PMF) sensors reportthe sequence of the survey locations when performing street sur-vey. For fitting cables and non-linear segment, Cardinal Spline al-gorithm was implemented which was capable for fitting the linesto points in both 2D and 3D. The detailed explanation of CardinalSpline algorithm is provided elsewhere (Ali Khan and Sarfraz,2011).

C. Probabilistic voxel classification

Errors in the linearity of segment lines vary depending on thenoise added in sensor and manhole readings. In addition, thepresence of multiple closely-buried assets is challenging when rec-ognizing the number of segments. In order to address these chal-lenges, linear approximation algorithm was useful as it integratedinformation from multiple sources and provided most probable esti-mation of voxel classification. Bayesian probabilistic voxel classifica-tion showed improved results in terms of fitted lines when comparedto least squares fitting.

Fig. C1. Lines regressed for two pipes with and without using probabilistic approximation algorithm

65M. Bilal et al. / Journal of Applied Geophysics 150 (2018) 52–66

References

Aleardi, M., Ciabarri, F., Mazzotti, A., 2017. Probabilistic estimation of reservoir propertiesby means of wide-angle AVA inversion and a petrophysical reformulation of theZoeppritz equations. J. Appl. Geophys. 147 (Supplement C):28–41 Available at:.http://www.sciencedirect.com/science/article/pii/S0926985117301192.

Ali Khan, M., Sarfraz, M., 2011. Motion tweening for skeletal animation by cardinal spline.In: Abd Manaf, A., Sahibuddin, S., Ahmad, R., Mohd Daud, S., El-Qawasmeh, E. (Eds.),Informatics Engineering and Information Science. Springer, Berlin Heidelberg.

Al-Nuaimy, W., et al., 2000. Automatic detection of buried utilities and solid objects withGPR using neural networks and pattern recognition. J. Appl. Geophys. 43 (2):157–165Available at. http://www.sciencedirect.com/science/article/pii/S0926985199000555.

Ashdown 2000. Mains Location Equipment – A State of the Art Review and Future Re-search Needs. In: UKWIR (Ed.). (ISBN: 1 84057 233 7).

Bailey, T., Durrant-Whyte, H., 2006. Simultaneous localization and mapping (SLAM): partII. IEEE Robotics & Automation Magazine 13 (3), 108–117.

Bailey, T.L., Elkan, C., 1994. Fitting a mixture model by expectation maximization to dis-cover motifs in biopolymers. Proceedings International Conference on Intelligent Sys-tems for Molecular Biology. 2, pp. 28–36.

Bar-Shalom, Y., 1987. Tracking and Data Association. Academic Press Professional, Inc.,San Diego, CA, USA.

Bhalerao, Abhir, Wilson, R., 2001. A Fourier Approach to 3D Local Feature Estimation fromVolume Data (2001). British Machine Vision Conference. pp. 461–470.

Buntine, W., 2002. Variational Extensions to EM and Multinomial PCA. In: Elomaa, T.,Mannila, H., Toivonen, H. (Eds.), Machine Learning: ECML 2002. Springer BerlinHeidelberg.

Burtwell, M., E. A., 2004. Locating underground plant and equipment - proposals for a re-search programme. UKWIR (ISBN: 1-84057).

Chen, Huanhuan, A. G. C, 2010. Probabilistic robust hyperbola mixture model forinterpreting ground penetrating radar data. The 2010 International Joint Conferenceon Neural Networks (IJCNN). IEEE, Barcelona.

Chen, H., Cohn, A.G., 2011. Buried utility pipeline mapping based on multiple spatial datasources: A Bayesian data fusion approach. IJCAI Retrieved from. https://doi.org/10.5591/978-1-57735-516-8/IJCAI11-402.

Chen, T.W., Wang, Q., 2010. 3D line segment detection algorithm for large-scale scenes.2010 International Conference on Audio, Language and Image Processing:pp. 1056–1061 https://doi.org/10.1109/ICALIP.2010.5685113.

Christensen, C.W., et al., 2015. Combining airborne electromagnetic and geotechnical data forautomated depth to bedrock tracking. J. Appl. Geophys. 119 (Supplement C):178–191Available at:. http://www.sciencedirect.com/science/article/pii/S0926985115001585.

Delicado, P., Smrekar, M., 2007. Mixture of nonlinear models: a Bayesian fit for principalcurves. 2007 International Joint Conference on Neural Networks:pp. 195–200https://doi.org/10.1109/IJCNN.2007.4370954.

Dettmer, J., et al., 2014. Trans-dimensional finite-fault inversion. Geophys. J. Int. 199 (2):735–751 Available at. https://doi.org/10.1093/gji/ggu280.

Do, C.B., Batzoglou, S., 2008. What is the expectation maximization algorithm? Nat.Biotechnol. 26:897. https://doi.org/10.1038/nbt1406.

Dong-Min, W., Dong-Chul, P., 2009. 3D line segment detection based on disparity data ofarea-based stereo. Intelligent systems, 2009. GCIS '09.WRI Global Congress on, 19–21May 2009, pp. 219–223.

Dutta, R., Cohn, A.G., Muggleton, J.M., 2013. 3Dmapping of buried underworld infrastruc-ture using dynamic Bayesian network based multi-sensory image data fusion. J. Appl.Geophys. 92:8–19 Available at:. http://www.sciencedirect.com/science/article/pii/S0926985113000311.

Esri, 2015. Put Your Maps to Work with ArcGIS, the Mapping Platform for Your Organiza-tion [Online]. Esri Available:. https://www.arcgis.com.

Ester, M., Kriegel, H.-P., Sander, J., Xu, X., 1996. A density-based algorithm for discoveringclusters a density-based algorithm for discovering clusters in large spatial databases

with noise. Proceedings of the Second International Conference on Knowledge Dis-covery and Data Mining. AAAI Press, pp. 226–231.

Fernández-Martínez, J.L., et al., 2013. From Bayes to Tarantola: new insights to under-stand uncertainty in inverse problems. J. Appl. Geophys. 98 (Supplement C),62–72.

Fiannacca, P., et al., 2017. IG-Mapper: A new ArcGIS® toolbox for the geostatistics-basedautomated geochemical mapping of igneous rocks. Chem. Geol. 470 (Supplement C),75–92.

Friedman, J., Popescu, B., 2004. Gradient Directed Regularization for Linear Regression andClassification (Retrieved from citeulike-article-id:3142778).

Gonzalez, R.C., 2008. Digital Image Processing. Third Ed.Guo, R., et al., 2011. Non-linearity in Bayesian 1-D magnetotelluric inversion. Geophys.

J. Int. 185 (2), 663–675.Ji, Y., et al., 2016. Frequency-domain sparse Bayesian learning inversion of AVA data for

elastic parameters reflectivities. J. Appl. Geophys. 133 (Supplement C), 1–8.Klautau, Aldebaro, N. J. A. A. O, 2003. Discriminative Gaussian mixture models: a compar-

isonwith Kernel classifiers. In: Mishra, T.F.A.N. (Ed.), Proceedings of the 20th Interna-tional Conference on Machine Learning (ICML-03).

Krishna, A.S., Rao, G.S., 2013. Contrast enhancement techniques using histogram equaliza-tion methods on color images with poor lightning. Int. J. Comput. Sci. Eng. Appl.15–24.

Mcmahon, W., Burtwell, M.H., Evans, M., 2005. Minimising street works disruption: thereal costs of street works to the utility industry and society. UKWIR.

Muggleton, J.M., Brennan, M.J., Gao, Y., 2011. Determining the location of buried plasticwater pipes from measurements of ground surface vibration. J. Appl. Geophys. 75(1), 54–61.

Neira, J., Tardos, J.D., 2001. Data association in stochastic mapping using the joint compat-ibility test. IEEE Trans. Robot. Autom. 890–897.

Oldenborger, G.A., et al., 2016. Bedrock mapping of buried valley networks using seismicreflection and airborne electromagnetic data. Journal of Applied Geophysics 128(Supplement C), 191–201.

Otsu, Nobuyuki, 1979. A threshold selection method from gray-level histograms. IEEETrans. Syst. Man Cybern, SMC-9 62–66.

Ren, H., et al., 2017. Bayesian inversion of seismic and electromagnetic data for marine gasreservoir characterization using multi-chain Markov chain Monte Carlo sampling.J. Appl. Geophys. 147 (Supplement C), 68–80.

Ristić, A., et al., 2017. Point coordinates extraction from localized hyperbolic reflections inGPR data. J. Appl. Geophys. 144 (Supplement C), 1–17.

Royal Acd, R. C., Atkins Pr, Brennan Mj, Chapman Dn, Chen H, Cohn Ag, Curioni G, FooKy, Goddard K, Hao T, Lewin Pl, Metje N, Muggleton Jm, Naji A, Pennock Sr,Redfern Ma, Saul Aj, Swingler Sg andWang P 2010. Mapping the Underworld: Lo-cation, Mapping and Positioning Without Excavation. In: Control, C. (Ed.). (Mid-dle East, Singapore).

Royal, A.C.D., Atkins, P.R., Brennan, M.J., Chapman, D.N., Chen, H., Cohn, A.G., Foo, K.Y.,Goddard, K.F., Hayes, R., Hao, T., Lewin, P.L., Metje, N., Muggleton, J.M., Naji, A.,Orlando, G., Pennock, S.R., Redfern, M.A., Saul, A.J., Swingler, S.G., Wang, P., Rogers,C.D.F., 2011. Site assessment of multiple-sensor approaches for buried utility detec-tion. Int. J. Geophys. 2011, 19.

Salojarvi, J., Puolamaki, K., Kaski, S., 2005. Expectationmaximization algorithms for condi-tional likelihoods. Proceedings of the 22nd International Conference on MachineLearning. ACM, Bonn, Germany.

Sander, J., Ester, M., Kriegel, H.-P., Xu, X., 1998. Density-based clustering in spatial data-bases: the algorithm GDBSCAN and its applications. Data Min. Knowl. Discov. 2,169–194.

Sanquer, M., Chatelain, F., El-Guedri, M., Martin, N., 2011. A reversible jump MCMC algo-rithm for Bayesian curve fitting by using smooth transition regressionmodels. Acous-tics, Speech and Signal Processing (ICASSP). 2011 IEEE International Conference on,22–27 May 2011, pp. 3960–3963.

66 M. Bilal et al. / Journal of Applied Geophysics 150 (2018) 52–66

Thomas, A.M., et al., 2009. Stakeholder needs for ground penetrating radar utility location.J. Appl. Geophys. 67 (4), 345–351.

Underworld, M.T., 2011. Mapping the Underworld [Online]. Available:. http://www.mappingtheunderworld.ac.uk, Accessed date: 13 September 2015.

Wang, Y., Lu, W., 2016. Discontinuity enhancement based on time-variant seismic imagedeblurring. J. Appl. Geophys. 135 (Supplement C), 155–162.

Ward, G., Hastie, T., Barry, S., Elith, J., Leathwick, J.R., 2009. Presence-only data and the em al-gorithm. Biometrics 65 (2):554–563. https://doi.org/10.1111/j.1541-0420.2008.01116.x.

Werman, M., Keren, D., 1999. A novel Bayesian method for fitting parametric and non-parametric models to noisy data. Computer Vision and Pattern Recognition, 1999.IEEE Computer Society Conference on 1999 Vol. 2, pp. 1–558.

Yangming Li, S.L., Song, Quanjun, Liu, Hai, Meng, M.Q.-H., 2013. Fast and robust data asso-ciation using posterior based approximate joint compatibility test. IEEE Transactionson Industrial Informatics, pp. 331–339.