Road Rutting Measurement Using Mobile Lidar Systems Point Cloud

International Journal of Geo-Information

Article Road Rutting Measurement Using Mobile LiDAR Systems Point Cloud

Luis Gézero 1,2,* and Carlos Antunes 1,3 1 Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal 2 LandCOBA, Digital Cartography Consulting Lda, Av. 5 de Outubro, 323, 1649-011 Lisboa, Portugal 3 Instituto Dom Luiz, Universidade de Lisboa, 1749-016 Lisboa, Portugal * Correspondence: [email protected]

Received: 23 August 2019; Accepted: 9 September 2019; Published: 11 September 2019

Abstract: Road rutting caused by vehicle loading in the wheel path is a major form of asphalt pavement distress. Hydroplaning and loss of skid resistance are directly related to high road rutting severity. Periodical measurements of rut depth are crucial to maintenance and rehabilitation planning. In this study, we explored the feasibility of using point clouds gathered by Mobile LiDAR systems to measure the rut depth. These point clouds that are collected along roads are usually used for other purposes, namely asset inventory or topographic survey. Taking advantage of available clouds to identify rutting severity in critical pavement areas can result in considerable economic and time saving and thus, added value, when compared with specific expensive rut measuring systems. Four different strategies of cloud points aggregation are presented to create the cross-section of points. Such strategies were established to improve the precision of individual sensor measurements. Despite the 5 mm precision of the used system, it was possible to estimate rut depth values that were slightly inferior. The rut depth values obtained from each cross-section strategy were compared with the manual field measured values. The cross-sections based on averaged cloud points sensor profile aggregation was revealed to be the most suitable strategy to measure rut depth. Despite the fact that the study was specifically conducted to measure rut depth, the evaluation results show that the methodology can also be useful for other mobile LiDAR point clouds cross-sections applications.

Keywords: Mobile LiDAR systems; point clouds; LiDAR proﬁles; rutting; pavement distress

1. Introduction Rutting is a longitudinal, permanent pavement deformation along roads created by repetitive vehicle loading in the wheel path. Water accumulation on ruts reduces skid resistance and increases the danger of hydroplaning [1–4]. Usually, three levels of severity are used for rut classification (low, medium, and high), however, there is no consensus regarding the rut severity classification thresholds among countries and agencies [2,3,5]. Regardless of the classification values that are used, there is a wide-ranging consensus of the direct correlation between rut depth severity and increased traffic accidents. Therefore, periodical measurement of road rut depth values is essential for road maintenance intervention plans, avoiding road safety degradation and saving money [1–5]. The manual method to measure the rut depth is performed by placing a straight edge across a rut and measuring the distance between the straight edge and the rut bottom [4]. Along with being a slow procedure, this task usually requires safety measures, which implies use disruptions or even road use interruption. One of the procedures specifically used to perform the rut depth measurement includes a vehicle with a discrete number of laser beams installed on a bar perpendicular to the direction of the road. By comparing the different distances to the ground, the rut depth measurement can be performed by a

ISPRS Int. J. Geo-Inf. 2019, 8, 404; doi:10.3390/ijgi8090404 www.mdpi.com/journal/ijgi ISPRS Int. J. Geo-Inf. 2019, 8, 404 2 of 16 ISPRS Int. J. Geo-Inf. 2019, 8, x FOR PEER REVIEW 2 of 16 minimuma minimum of threeof three laser laser beams—one beams—one in each in each wheel wheel path path and anotherand another in the in car’s the center.car’s center. However, However, since thesince system the system vehicle vehicle does not does have not the have means the tomeans ensure to thatensure the that wheels the arewheels always are inalways the rut’s in the deepest rut’s point,deepest the point, number the of number laser beams of laser is directly beams correlated is directly with correlated the precision with the of the precision rut depth of measurement.the rut depth Themeasurement. lower the number The lower of laserthe number beams, theof laser lower beams, the chances the lower of the the rut’s chances deepest of the point rut’s being deepest detected point andbeing measured detected and, and consequently, measured and, the consequently, rut depth can the be underestimated.rut depth can be Initially underestimated. having three Initially laser beams,having thisthree number laser beams, has increased, this number for example, has increased, Serigos for et example, al. [6] mention Serigos a et 37-laser al. [6] mention beams system. a 37-laser beamsAnother system. rut depth measurement specific technique includes the use of continuous 3D laser systems.Another Such systemsrut depth allow measurement the measurement specific of techniqu thousandse ofincludes points inthe each use profile, of continuous increasing 3D the laser rut depthsystems. precision. Such systems However, allow these the systems measurement are developed of thousands specifically of points for pavementin each profile, distress increasing assessment the and,rut depth consequentially, precision. they However, are very these expensive systems [7]. Figureare developed1 shows schematic specifically representations for pavement of manualdistress discreteassessment laser and, profilers consequentially, and continuous they laser are systems very methodologies. expensive [7]. Figure 1 shows schematic representations of manual discrete laser profilers and continuous laser systems methodologies.

(a)

(b)

(c)

FigureFigure 1.1. SchematicSchematic transversaltransversal roadroad proﬁleprofile andand rutrut depthdepth measurementmeasurement techniques.techniques. ((aa)) ManualManual methodmethod usingusing aa straightstraight edgeedge acrossacross thethe rut.rut. ((bb)) DiscreteDiscrete laserlaser beambeam proﬁlerprofiler installedinstalled inin aa frontfront carcar transversaltransversal bar.bar. ((cc)) ContinuousContinuous laserlaser system system installed installed in in the the car’s car’s back.back.

SeveralSeveral studiesstudies regardingregarding discretediscrete andand continuouscontinuous laserlaser systemssystems comparisoncomparison andand precisionprecision evaluationevaluation havehave beenbeen publishedpublished [[6,8].6,8]. BesidesBesides thethe threethree methodologiesmethodologies illustratedillustrated inin FigureFigure1 1,, other other approachesapproaches toto measuremeasure thethe rutrut depthdepth usingusing geoinformationgeoinformation havehave beenbeen presented.presented. InIn [[9–11],9–11], closeclose rangerange terrestrialterrestrial photogrammetryphotogrammetry principlesprinciples areare usedused toto measuremeasure thethe rutrut depthdepthin in forestforest areas. areas. UsingUsing camerascameras suspendedsuspended byby manuallymanually carriedcarried poles,poles, thethe rutrut depthdepth measurementmeasurement isis performedperformed overover thethe three-dimensionalthree-dimensional createdcreated point point cloud. cloud. More recently, Unmanned Aerial Vehicles (UAV) have been found to be an economic method to efficiently take high resolution photos along large road areas. Marra et al. [11] show how the rut

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More recently, Unmanned Aerial Vehicles (UAV) have been found to be an economic method to efficiently take high resolution photos along large road areas. Marra et al. [11] show how the rut depth in a forest path is measured from the automatically created point cloud [11]. Several authors have used UAV to assess pavement distress through image processing, however they did not include rut depth measurements [12–14]. Existing grass, logging residues, and water along ruts are referred to as the main factors that compromise the precision of the photogrammetric methods. Still, in forest paths, a methodology to measure the rut depth using a 2D laser is presented in [15]. The respective obtained results suggest that a LiDAR sensor mounted on a forest vehicle can be a viable method for rut depth data as part of normal forestry operations. It should be noted that all these studies were conducted on unpaved forest roads where the precision requirements are smaller due to the terrain nature and the fact that the ruts are much deeper than in paved roads. In [16–18], recent reviews of pavement distress detection and measurements, including rutting, are presented. Few studies have contributed to rut depth measurement by using LiDAR point cloud data. Li et al. [19] introduce a real-time 3D scanning specific system for pavement distortion inspections. The system uses a simple yet robust structured light method for 3D profile generation. The authors conclude that rutting can be reliably detected from 3D transverse profiles and the real-time measurements and 3D visualization of these distortions can be an output for a pavement management system. Li et al. [20] demonstrate the application of random forest classification to identify pavement distress based on the use of UAV LiDAR point cloud data. The data quality used does not allow the identification of slight pavement distresses, therefore, a classification method mainly for severe pavement distresses was established. Due to the similarity between subsidence, rutting, and cracks, they are all regarded as the same type of distress in the classification, which prevents any type of distinction between the pavement pathologies. Even so, a satisfactory classification with an accuracy of 92.3% was achieved. Mobile LiDAR Systems (MLS) have emerged in recent years as a new source of precise and very detailed georeferenced information. The gathered point clouds with a few thousand of points per square meter represent the road pavement and surrounding area with high spatial resolution. These point clouds become very popular for the collection of accurate objects geometry and their related attributes. Many country’s road agencies are using MLS point clouds to extract road assets’ geometry, attributes, and condition. These systems reveal to be much faster and cheaper than the traditional survey methods [21]. Another MLS advantage is the extraction of many asset types from the same point cloud, gathered with just one road passage and without any road traffic disruptions. Several studies support the general idea of MLS point clouds as a solution for road inventory [22–24]. Che et al. [25] present a complete and recent state of the art review regarding the object’s extraction methods from MLS point clouds. Given the MLS efficiency, it is expected that the object types and extraction methodologies from the gathered point clouds will continue to increase [26]. This will result in a large amount of existing point clouds covering the entire road pavement. Using this available data, an efficient methodology to identify road areas with high rut depth values can clearly be of added value, speeding up the process of problematic areas detection, without the need of specific laser systems for pavement distress detection. Apart from reducing the cost of the process, it can anticipate road interventions and diminish traffic accidents. At first glance, the rut depth measurement can easily be performed through cross-sections along the MLS point cloud. However, different strategies for grouping the point clouds to get the profile points can lead to very different results. Also, the lower accuracy of the commercial MLS systems when compared with the specific laser systems can compromise the rut depth measurement quality. In this work, a comparative study of different strategies to group the cloud points in order to create the cross-sections is presented. By comparing different strategies, it is intended that the precision improvement regarding the individual system sensor measurement can be evaluated. On the one hand, ISPRS Int. J. Geo-Inf. 2019, 8, 404 4 of 16 statically, by increasing the number of cloud points used for each cross-section point computation. ISPRSOn the Int. other J. Geo-Inf. hand, 2019 taking, 8, x FOR advantage PEER REVIEW of the system operating principles knowledge, grouping the 4cloud of 16 points by individual laser rotation. Thus, Section2 includes an MLS working principles description, principlesfollowed by description, each proposed followed strategy by description. each proposed Finally, strategy Sections description.3 and4 presents Finally, the discussionSection 3 ofand the 4 presentsresults, main the discussion conclusions, of the and results, future work.main conclusions, and future work.

2.2. Materials Materials and and Methods Methods SinceSince rutting rutting has has a a longitudinal longitudinal development, development, the the most most obvious obvious way way to to measure measure the the rut rut depth depth is is throughthrough the the creation creation of of road road tran transversalsversal cross-sections. cross-sections. However, However, to to evaluate evaluate the the potential potential precision precision improvementimprovement of thethe sensor’ssensor’s individualindividual measurement, measurement, four four strategies strategies to to aggregate aggregate the the cloud cloud points points for forcreating creating those those cross-sections cross-sections were were set out.set out. The The proposed proposed strategies strategies will will be described be described in this in this section section and andjustiﬁcation justification of choices of choices will be will included be included in the discussionin the discussion of the results. of the Sinceresults. some Since deﬁned some strategies defined strategiesare related are to related the way to the the data way are the gathered, data are agathered, resumed adescription resumed description of the MLS of working the MLS principles working principlesare presented. are presented.

2.1.2.1. MLS MLS Working Working Principles Principles AnAn MLS MLS consists consists of of a a set of devices and sensors, installed in a moving platform. These These systems systems allowallow gathering gathering georeferenced georeferenced points reflected reﬂected on the surface of the surrounding objects. TheThe data data registered registered by MLS sensors is classified classiﬁed in two types: • TrajectoryTrajectory—includes datadata collected collected by by the the system system sensors sensors to compute to compute the most the accurate most trajectory.accurate • trajectory.Namely, Global Namely, Navigation Global Navigation Satellite System Satellite (GNSS) System antennas, (GNSS) Inertial antennas, Measurement Inertial Measurement Unit (IMU), Unitand high-resolution(IMU), and high-resolution Distance Measuring Distance Instrument Measuring (DMI).Instrument (DMI). • LaserLaser—a—a set set of distances and angles to to compute the the points points coordinates coordinates in in space space regarding regarding the the • laserlaser sensor sensor position. position.

ByBy merging merging these these two two data data types, types, georeferenced georeferenced po pointint clouds clouds representing representing all all objects objects at at a a sensor sensor rangerange are are created. created. ToTo ensure a full surrounding coverage, two two type typess of of movement movement are are applied applied to to the the laser laser pulse pulse direction.direction. The The first first is is a a rotational rotational movement movement 360 360 degrees degrees around around the the sensor sensor axis, axis, creating creating a a single single profile.profile. The The second second is is the the vehicl vehiclee movement, movement, which which allows allows consecutive consecutive profiles profiles and and the the point point cloud cloud effect.effect. Figure Figure 2 illustrates thethe MLSMLS pointpoint cloudcloud gatheringgathering process.process.

Figure 2. Mobile LiDAR Systems (MLS) point cloud effect creation by consecutive sensor profiles and vehicleFigure movement. 2. Mobile LiDAR Systems (MLS) point cloud effect creation by consecutive sensor profiles and vehicle movement. Along this work, two profile types are recurrently mentioned, the original sensor cloud points profilesAlong described this work, in Figuretwo profile2, and types the road are recurrently transversal mentioned, profiles used the for original measuring sensor the cloud rut depth.points profiles described in Figure 2, and the road transversal profiles used for measuring the rut depth. The term profile will always be used when referring to the first type and the term cross-section when referring to the second type.

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profile cross-section The termIn order towill increase always the be surround used whening objects referring area to coverage, the first type the andplatform the term laser sensor installationwhen referringis typically to the performed second type. in a way that the profiles direction performs a 45 degree angle regarding the systemIn order trajectory to increase direction, the surrounding as shown in objectsFigure 2. area coverage, the platform laser sensor installation is typically performed in a way that the profiles direction performs a 45 degree angle regarding the system2.2. Cross-Section trajectory direction, Points Creation as shown Strategies in Figure 2. 2.2. Cross-SectionAn MLS point Points cloud Creation dataset Strategies gathered along a highway was used to compare the cross-sections points creation strategies. The used system was a Trimble MX8 with the sensor RIEGL VQ-250 An MLS point cloud dataset gathered along a highway was used to compare the cross-sections configuration. In Table 1, the main sensor characteristics are presented. points creation strategies. The used system was a Trimble MX8 with the sensor RIEGL VQ-250 configuration. In Table1, the main sensor characteristics are presented. Table 1. Riegl VQ-250 sensor main characteristics.

TableCharacteristics 1. Riegl VQ-250 sensor main characteristics.Values Accuracy1 10 mm Characteristics Values Precision2 5 mm 1 MaximumAccuracy measurement rate 300,00010 points/second mm Precision 2 5 mm MaximumNumber measurement of sensor profiles rate Up 300,000 to 200 points profiles/second/second 1 Accuracy is the degreeNumber of conformi of sensorty profilesof a measured Upquantity to 200 to profiles its actual/second (true) value. One sigma at 1 Accuracya 50 m range is the under degree test of conformity conditions. of a measured quantity to its actual (true) value. One sigma at a 50 m range under test conditions. 2 Precision or repeatability is the degree to which further measurements show the same result. 2 OnePrecision sigma at aor 50 repeatability m range under is test the conditions. degree to which further measurements show the same result. One sigma at a 50 m range under test conditions. TheThe point point clouds clouds were were obtained obtained to to perform perform the the highway highway asset asset inventory. inventory. The The strategy strategy goal goal was was to evaluateto evaluate the the use use of those of those point point clouds clouds to additionallyto additionally measure measure the the rut rut depth. depth. The The data data was was already already processedprocessed using using the the IMU IMU and and GNSS GNSS data data and and subsequent subsequent integration integration of of distances distances and and angles angles were were collectedcollected by by the the laser laser sensor. sensor. The The obtained obtained georeferenced georeferenced point point cloud cloud was was exported exported to to LAS LAS format, format, versionversion 1.2. 1.2. InIn Figure Figure3, 3, a samplea sample point point cloud cloud gathered gathered along along a highwaya highway is presented.is presented. To To describe describe each each proposedproposed strategy, strategy, the the red red line line drawn drawn transversal transversal to the to roadthe road will bewill used. be used. An image An image of the of yellow the yellow area willarea be will enlarged. be enlarged. Thus, theThus, continuous the continuous cloud e ffcloudect will effect be lost,will andbe lost, the originaland the cloudoriginal points cloud profiles points willprofiles be exposed will be (Figuresexposed 4,(Figures 6, 8 and 4,6,8,10). 10). The The distance distance between between those those profiles profiles depends depends on on the the vehicle vehicle velocityvelocity and and on on the the sensor sensor rotation rotation frequency, frequency, while while each each profile profile point point density density depends depends on on the the sensor sensor measurementmeasurement rate rate frequency frequency and and on on the the distance distance between between the the reflection reflection point point and and the the sensor. sensor. AlongAlong the the gathering gathering process, process, both both maximum maximum system system frequencies frequencies were were used used and and the the vehicle vehicle velocityvelocity was was always always kept kept below below 50 km 50/h, which,km/h, consideringwhich, considering the system the rotation system frequency, rotation guarantees frequency, aguarantees maximum distancea maximum between distance consecutive between profilesconsecutive of less profiles than 7 of cm. less than 7 cm.

FigureFigure 3. 3.MLS MLS point point cloud cloud and and red red cross-section cross-section line line sample. sample.

2.2.1. Cross-Section Line Projected Points The first proposed approach to create the cross-section points is probably the most intuitive. That is, project in the cross-section line segment all cloud points below a perpendicular predefined

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2.2.1. Cross-Section Line Projected Points The first proposed approach to create the cross-section points is probably the most intuitive. That is,ISPRS project Int. J. inGeo-Inf. the cross-section2019, 8, x FOR PEER line REVIEW segment all cloud points below a perpendicular predefined distance 6 of 16 of that line. Figure4 shows the zoomed yellow area indicated in Figure3 with the red cross-section line.distance A lower of that point line. cloud Figure density 4 shows can the be zoomed observed yellow along area the indicated sensor profiles in Figure on the 3 with left sidethe red since cross- the vehiclesection trajectoryline. A lower is closer point to cloud the right density side. can be observed along the sensor profiles on the left side since the vehicle trajectory is closer to the right side.

FigureFigure 4. Strategy 4. Strategy 1 schematic 1 schematic top view. top Each view. point Each cloud point inside cloud distance inside L is distance projected L isin projectedthe cross-section in the line. cross-section line. In Figure 4, P1 and P2 are the two end points of the cross-section line, P is a random cloud point and QIn is Figure the P4 ,projection P1 and P2 in are the the cross-section two end points line. of The the two-dimensional cross-section line, Euclidian P is a random distance cloud between point andP and Q Q is are the represented P projection by in D, the and cross-section L is the maximum line. The threshold two-dimensional distance Euclidianvalue below distance which between the cloud P andpoints Q are representedconsidered. by D, and L is the maximum threshold distance value below which the cloud pointsThe are point considered. Q XY-coordinates can then be computed by The point Q XY-coordinates can then be computed by

⃗ 𝑄 =𝑋 + .(𝑋 −𝑋)  ⃗  = + −−→P1Q ( . ) (1)  Qx X1 |⃗ | . X2 X1  − 𝑄 =𝑌 + P−−→1.(𝑌P2 −𝑌)  |⃗ | . (1)   −−→P1Q  Q = Y + | | .(Y Y ) After Q coordinates determination, y the distance1 D can2 be1 calculated by applying the Euclidian P P − distance formula to the P and Q points coordinates.|−−→1 2| AfterThe cross-section Q coordinates points determination, XY coordinates the distanceare calcul Dated can using be calculated (1), and bythe applying Z-coordinate the Euclidian from the distanceoriginal cloud formula point to theare Pkept, and Qi.e., points each coordinates.cloud point under distance L is projected in the cross-section plan.The cross-section points XY coordinates are calculated using (1), and the Z-coordinate from the originalOnly cloud the cloud point arepoints kept, with i.e., D each distance cloud less point than under L and distance of which L is their projected projection in the cross-sectionis over the profile plan. line segmentOnly the are cloud considered. points with The D required distance restrictions less than L andthat ofapply which to theirthe point projection clouds is are over presented the proﬁle in lineEquation segment 2. are considered. The required restrictions that apply to the point clouds are presented in Equation (2).  𝐷≤𝐿  D L  𝑋 ≤𝑄≤ ≤𝑋 (2) X1 Qx X2 (2)  𝑌 ≤𝑄 ≤𝑌  ≤ ≤ Y1 Qy Y2 In Figure 5, profile views of three projected≤ points’≤ cross-section using L=0.025, 0.05, and 0.1 m are presented.In Figure5 ,Obviously, proﬁle views more of threecloud projected points will points’ be considered cross-section for using each Lcross-section= 0.025, 0.05, when and 0.1the mL arevalue presented. increases. Obviously, more cloud points will be considered for each cross-section when the L value increases.

ISPRS Int. J. Geo-Inf. 2019, 8, 404 7 of 16 ISPRS Int. J. Geo-Inf. 2019, 8, x FOR PEER REVIEW 7 of 16 ISPRS Int. J. Geo-Inf. 2019, 8, x FOR PEER REVIEW 7 of 16

Figure 5. Profile view of strategy 1 sample results using L = 10, 20, and 50 mm. Figure 5. Profile view of strategy 1 sample results using L=10, 20, and 50 mm. Figure 5. Profile view of strategy 1 sample results using L=10, 20, and 50 mm. 2.2.2. Averaged Grouped Cloud Points 2.2.2. Averaged Grouped Cloud Points 2.2.2.In Averag the seconded Grouped proposed Cloud strategy, Points a specific number of cross-section points are predefined. The Z-coordinateIn the second of proposed each of those strategy, points a resultsspecificfrom number the averageof cross-section cloud points points Z-coordinate are predefined. within Thea definedZ-coordinate distance of R.each An of example those points of nine results cross-section from the points average is presented cloud points in Figure Z-coordinate6. withinwithin aa defined distance R. An example of nine cross-section points is presented in Figure 6.

Figure 6. Second strategy schematic top view. The cloud points’ Z-coordinates at distance R are FigureFigure 6.6. SecondSecond strategystrategy schematicschematic top view. The The cloud cloud points’ points’ Z-coordinates Z-coordinates at at distance distance R R are are averaged and assigned to the Z-coordinate of the centered cross-section point. The M value represents averagedaveraged and and assigned assigned toto thethe Z-coordinateZ-coordinate ofof the centeredcentered cross-section point. The The M M value value represents represents the distance between the cross-section points (M is a predefined value). thethe distance distance between between the the cross-sectioncross-section pointspoints (M(M isis aa predeﬁnedpredefined value).

MM is is the the distance distance betweenbetween twotwo sequentialsequential cross-sectioncross-section points. To To establish establish each each cross-section cross-section point,point, the the azimuth azimuth of of P2 P2 from from P1P1 isis used,used,

𝐴(𝑃1, 𝑃2) =𝐴𝑡𝑎𝑛X2 ( X1). (3) A(𝐴P1,(𝑃1,P2) =)𝑃2 =𝐴𝑡𝑎𝑛Atan( (− )). . (3) (3) Y2Y1 −

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ISPRS Int. J. Geo-Inf. 2019, 8, x FOR PEER REVIEW 8 of 16 ISPRSThe Int. XY-coordinatesJ. Geo-Inf. 2019, 8, x FOR of each PEER point REVIEW can then be calculated by 8 of 16 ( The XY-coordinates of each point canX then= X1 be+ calculatedM.Sin(A) by The XY-coordinates of each point cani then be calculated by. (4) Yi = Y1 + M.Cos(A) 𝑋 =𝑋1+𝑀.𝑆𝑖𝑛(𝐴) 𝑋 =𝑋1+𝑀.𝑆𝑖𝑛(𝐴). (4) 𝑌 =𝑌1+𝑀.𝐶𝑜𝑠(𝐴). (4) In Figure7, the proﬁle views of the same𝑌 =𝑌1+𝑀.𝐶𝑜𝑠(𝐴) cross-section, using di ﬀerent values of R, are presented. In allIn samples, Figure 7, 50 the cross-section profile views points of the same were cross-section, used, being Musing= W different/50, where values W of is R, the are cross-section presented. In Figure 7, the profile views of the same cross-section, using different values of R, are presented. lineIn all length. samples, 50 cross-section points were used, being M =W/50, where W is the cross-section line In all samples, 50 cross-section points were used, being M =W/50, where W is the cross-section line length. length.

FigureFigure 7. 7.Profile Profile view view of of second second strategy strategy twotwo samplesample results,results, usingusing LL=40,= 40, 50, 50, and and 60 60 mm. mm. Figure 7. Profile view of second strategy two sample results, using L=40, 50, and 60 mm. 2.2.3.2.2.3. OriginalOriginal SystemSystem ProfileProfile 2.2.3. Original System Profile TheThe third third proposedproposed strategystrategy usesuses oneone singlesingle originaloriginal system sensor profile. profile. The The closest closest point point of of The third proposed strategy uses one single original system sensor profile. The closest point of thethe cross-section cross-section centercenter lineline isis determineddetermined and the originaloriginal sensor sensor profile profile that that contains contains the the point point is is the cross-section center line is determined and the original sensor profile that contains the point is used.used. FigureFigure8 8shows, shows, in in blue, blue, the the used used originaloriginal sensorsensor profile.profile. used. Figure 8 shows, in blue, the used original sensor profile.

Figure 8. Third strategy schematic top view. The blue cloud points represent the nearest center cross- FigureFigure 8.8. ThirdThird strategy strategy schematic schematic top top view. view. The Theblue blue cloud cloud points points represent represent the nearest the nearest center cross- center section sensor profile. cross-sectionsection sensor sensor profile. proﬁle. Since the sensor is installed at about 45 degrees regarding the vehicle direction, the original Since the sensor is installed at about 45 degrees regarding the vehicle direction, the original sensor profiles are not parallel to the cross-section line. Since drastic longitudinal variations in rut sensor profiles are not parallel to the cross-section line. Since drastic longitudinal variations in rut

ISPRS Int. J. Geo-Inf. 2019, 8, 404 9 of 16 ISPRS Int. J. Geo-Inf. 2019, 8, x FOR PEER REVIEW 9 of 16 ISPRS Int. J. Geo-Inf. 2019, 8, x FOR PEER REVIEW 9 of 16 depthSince values the are sensor not isexpected, installed the at about rut depth 45 degrees value regarding obtained thein the vehicle sensor direction, direction the should original be sensor very depth values are not expected, the rut depth value obtained in the sensor direction should be very profilessimilar to are the not one parallel obtained to thealong cross-section the cross-section line. Since line. Besides, drastic longitudinal this strategy variationsallows one in to rut evaluate depth similar to the one obtained along the cross-section line. Besides, this strategy allows one to evaluate valuesthe point are clouds not expected, behavior the along rut depth a single value sensor obtained profile. in the sensor direction should be very similar to the point clouds behavior along a single sensor profile. the oneAs obtaineda way to identify along the the cross-section cloud points line.of the Besides, original this profile strategy sensor, allows the variable one to evaluate GPS epoch the stored point As a way to identify the cloud points of the original profile sensor, the variable GPS epoch stored cloudsfor each behavior cloud point along was a singleused. Based sensor on profile. the MLS working principles, the points are time sequentially for each cloud point was used. Based on the MLS working principles, the points are time sequentially obtainedAs a along way to the identify original the profil cloudes. points The time of the interval original between profile consecutive sensor, the variable points are GPS defined epoch by stored the obtained along the original profiles. The time interval between consecutive points are defined by the forsensor each shooting cloud point frequency, was used. and Based the time on interval the MLS that working it takes principles, to complete the a points 360 degrees are time sensor sequentially profile sensor shooting frequency, and the time interval that it takes to complete a 360 degrees sensor profile obtaineddepends on along the thesensor original rotation profiles. frequency. The time After interval the cross-section between consecutive center line nearest points areto the defined point bycloud the depends on the sensor rotation frequency. After the cross-section center line nearest to the point cloud sensorbeing identified, shooting frequency, sequential and cloud the points time interval belonging that to it takesits sensor to complete profile acan 360 be degrees identified, sensor applying profile being identified, sequential cloud points belonging to its sensor profile can be identified, applying dependsthe following on the restrictions: sensor rotation frequency. After the cross-section center line nearest to the point cloud the following restrictions: being identified, sequential cloud points belonging to its sensor profile can be identified, applying the following restrictions: || 𝐷𝑖 ≤ (𝐸𝑖) q− || 𝐷𝑖 ≤ (𝐸𝑖)− 2 P 1 P 2 2 (5)  Di (Ei) | | (5) |𝑇𝑐 − 𝑇𝑖|≤≤  , 𝑤ℎ𝑒𝑟𝑒− 2  <𝑓 (5) |𝑇𝑐 −Tc 𝑇𝑖| ≤ Ti , 𝑤ℎ𝑒𝑟𝑒∆, where  <𝑓∆ < f where Di and Ei are, respectively, the |perpendicular− | ≤ distance and the Euclidian distance of each cloud where Di and Ei are, respectively, the perpendicular distance and the Euclidian distance of each cloud wherepoint to Di the and profile Ei are, line respectively, center. Tc represents the perpendicular the GPS distance epoch of and the theC cloud Euclidian point distance (nearest ofto eachthe profile cloud point to the profile line center. Tc represents the GPS epoch of the C cloud point (nearest to the profile pointline center) to the and profile Ti represents line center. the Tc GPS represents epoch theof each GPS cloud epoch point. of the The C cloud Δ time point threshold (nearest value to the depends profile line center) and Ti represents the GPS epoch of each cloud point. The Δ time threshold value depends lineon the center) rotation and sensor Ti represents frequency. the GPS In summary, epoch of each the cloudfirst restriction point. The ensures D time thresholdthat the projected value depends cloud on the rotation sensor frequency. In summary, the first restriction ensures that the projected cloud onpoints the lie rotation in the sensorcross-section frequency. line and In summary, the second the ensures first restriction that only ensuresthe points that belonging the projected to the cloudsame points lie in the cross-section line and the second ensures that only the points belonging to the same pointsoriginal lie profile in the sensor cross-section are considered. line and the second ensures that only the points belonging to the same original profile sensor are considered. originalSince profile the original sensor aresensor considered. profile is not coincident with the profile line, a projection of the cloud Since the original sensor profile is not coincident with the profile line, a projection of the cloud points,Since as described the original in section sensor 2.2.1, profile was is notperformed. coincident Figure with 9 theshows profile the line,resulting a projection single sensor of the profile cloud points, as described in section 2.2.1, was performed. Figure 9 shows the resulting single sensor profile points,after the as describedcross-section in Section points 2.2.1 had, wasbeen performed. projected. Figure It should9 shows be the noted resulting that singlethe line sensor projection profile after the cross-section points had been projected. It should be noted that the line projection afterapplication the cross-section deforms the points rut hadshape been (the projected. points distance It should is beshortened). noted that However, the line projection the rut depth application value application deforms the rut shape (the points distance is shortened). However, the rut depth value deformswill be the the same. rut shape (the points distance is shortened). However, the rut depth value will be the same. will be the same.

Figure 9. Strategy three sample results, profile view. FigureFigure 9. 9. StrategyStrategy three three sample sample results, results, profile proﬁle view. view. 2.2.4. Time Grouped Cloud Points 2.2.4. Time Grouped Cloud Points The lastlast strategystrategy to to be be tested tested combines combines the the point point average average coordinates coordinates and theand cloud the cloud points points GPS epoch. GPS The last strategy to be tested combines the point average coordinates and the cloud points GPS Forepoch. each For sensor each profilesensor crossingprofile crossing the cross-section the cross-se line,ction the line, cloud the points cloud Z-coordinate points Z-coordinate that lies withinthat lies a epoch. For each sensor profile crossing the cross-section line, the cloud points Z-coordinate that lies definedwithin a distance defined aredistance averaged. are averaged. Figure 10 illustratesFigure 10 theillustrates resulting the points resulting obtained points from obtained this method. from this within a defined distance are averaged. Figure 10 illustrates the resulting points obtained from this method. method.

Figure 10. FourthFourth strategy strategy schematic schematic top top view. view. Each Each cross- cross-sectionsection point results from individual sensor Figure 10. Fourth strategy schematic top view. Each cross-section point results from individual sensor proﬁleprofile averaged cloud points.points. profile averaged cloud points.

ISPRSISPRS Int.Int. J. Geo-Inf. 2019, 8, 404x FOR PEER REVIEW 1010 of of 16

Each point represented along the profile line in Figure 10 results from the averaged cloud point coordinatesEach point of the represented individual along original the sensor profile profiles. line in Figure To identify 10 results those from points, the averagedsimilar restrictions cloud point of coordinatesSection 2.3.1 of and the 2.3.3 individual are used, original as sensor profiles. To identify those points, similar restrictions of Sections 2.2.1 and 2.2.3 are used, as ( 𝐷𝑖 ≤ 𝐿 Di L ≤ (6) |𝑇𝑗 − 𝑇𝑖| ≤Tj  , Ti ∆ , | − | ≤ where TjTj represents thethe firstfirst pointpoint ofof eacheach sensor profile.profile. Since the points are ordered in the cloud by GPS epoch, the firstfirst cloud point of which distance Di is less than L is considered as the firstfirst profileprofile point. Then, all subsequent cloud points are considered as part of that profileprofile until the GPS epoch didifference,fference, regarding that firstfirst point, is lower than ∆ (sensor (sensor rotationrotation frequency).frequency). TheThe firstfirst pointpoint thatthat does not satisfy the second restriction is used as a new first first sensor profile profile point and and the the cycle cycle restarts. restarts. In thisIn strategy, this strategy, besides besides Z-coordinates, Z-coordinates, the XY-coordinates the XY-coordinates of the of profile the profile points points are also are averaged, also averaged, and andthe resulting the resulting point point is very is very close close to the to the profile profile line line since since the the sensor sensor profile profile cloud cloud points points tend tend to be symmetric to that line. However, to help the displaydisplay and comparison and to eliminate the points of which their projection isis outside the profileprofile line, thethe averaged points are projected in the cross-section line, following thethe descriptiondescription ofof SectionSection 2.2.12.3.1.. Figure 11 shows the profile profile view of the resulting points using didifferentfferent LL values.values.

FigureFigure 11. 11.Proﬁle Profile viewview ofof strategystrategy fourfour samplesample results, results, using using L L=10,= 10, 20, 20, and and 50 50 mm mm

ISPRS Int. J. Geo-Inf. 2019, 8, 404 11 of 16 ISPRS Int. J. Geo-Inf. 2019, 8, x FOR PEER REVIEW 11 of 16

3. Results and Discussion 3. Results and Discussion To evaluate the proposed strategies’ results, a set of 10 manual field measurements were made. To evaluate the proposed strategies’ results, a set of 10 manual ﬁeld measurements were made. The measurements were performed along a highway right lane, using a straight edge across a rut, The measurements were performed along a highway right lane, using a straight edge across a rut, like like described in Section 1. Only the right lane was considered, since, due to the heavy truck traffic, described in Section1. Only the right lane was considered, since, due to the heavy truck tra ﬃc, deeper deeper ruts were expected. ruts were expected. In Table 2, the left and right wheel rut depth values, which were manually obtained in the right In Table2, the left and right wheel rut depth values, which were manually obtained in the right lane, are listed. The values were measured with 100 m intervals, with the highway kilometric point lane, are listed. The values were measured with 100 m intervals, with the highway kilometric point (PK) used as a reference. (PK) used as a reference.

TableTable 2. 2. RutRut depth depth manual manual field field measurement measurement values. values. Right depth rut Left depth rut PKPK Right Depth Rut Value (mm) Left Depth Rut Value (mm) value (mm) value (mm) 52 + 800 12 9 52 + 90052 + 800 13 12 9 11 53 + 00052 + 900 13 13 11 10 53 + 10053 + 000 10 13 10 8 53 + 20053 + 100 11 10 8 10 53 + 300 15 12 53 + 200 11 10 53 + 400 11 9 53 + 50053 + 300 14 15 12 11 53 + 60053 + 400 14 11 9 10 53 + 70053 + 500 8 14 11 7 53 + 600 14 10 The first step to compare53 + 700 the proposed strategies 8 with the manual 7 measured values was the materializationThe first step of to the compare cross-section the proposed lines in thestrategi samees locations with the wheremanual manual measured measurements values was were the materializationperformed. Perpendicular of the cross-section lines to lines the in highway the same direction, locations with where the manual lane width, measurements were designed. were performed.The hectometers Perpendicular vertical signs lines that to the exist highway along the dire highwayction, with allow the one lane to ensurewidth, thatwere the designed. cross-section The hectometerslines are in thevertical exact signs place that where exist the along manual the highwa measurementsy allow one were to made. ensure Figure that the 12 cross-section shows the sample lines areprofile in the lines’ exact locations place where along thethe highway. manual measurements were made. Figure 12 shows the sample profile lines’ locations along the highway.

FigureFigure 12. 12. SampleSample cross-section cross-section lines lines distribution distribution along along the the highway’s highway’s right right lane. lane.

AnAn important important aspect aspect that that affects affects the the rut rut depth depth value value is is the the measurement measurement method method used. used. Different Different measurementmeasurement methods methods based based on on the the same same cross-section cross-section of of data data may may lead lead to to rut rut depth depth estimation estimation that that areare not not always always consistent. consistent. A A comprehensive comprehensive study study of of the the method method influence influence in in the the measured measured rut rut depth depth valuevalue is is presented presented in in [27]. [27]. In In Figure Figure 13, 13 ,three three distinct distinct illustration illustration methods methods to to measure measure the the rut rut depth depth areare presented. presented. In this work, all rut measurements were performed manually over the created cross-sections. For each cross-section, an auxiliary line was manually drawn between the two higher points of each individual wheel rut side, as is illustrated by the middle green line method in Figure 13. That method was chosen because that was the straight edge position used in the field manual measurements. Different parameters values were evaluated for each strategy, and successively increased values were tested. The ones that reached the best results were used. For strategy one, the value L = 30 mm has been used. For strategy two, 50 points were used, as presented in Figure7 with R = 30 mm. Strategy three had no parameters, and only the nearest middle cross-section sensor profile point clouds

ISPRS Int. J. Geo-Inf. 2019, 8, 404 12 of 16 were used. For strategy four, the value L = 30 mm was also used. In strategies three and four, GPS epoch values of each cloud point were obtained from the LAS ﬁle. The LAS are in version 1.2, to which theISPRS standard Int. J. Geo-Inf. format 2019, is 8, describedx FOR PEER inREVIEW [28]. 12 of 16

Figure 13. Different rut depth measurement methods. Figure 13. Different rut depth measurement methods. These parameters were set based on the uses of MLS rotation and measurement frequency. A lower In this work, all rut measurements were performed manually over the created cross-sections. rotation frequency will increase the distance between the consecutive scan profiles and, for example, in For each cross-section, an auxiliary line was manually drawn between the two higher points of each strategy four, less cross-section points would be obtained. This can, however, be compensated with a individual wheel rut side, as is illustrated by the middle green line method in Figure 13. That method lower vehicle velocity. A lower measurement rate will decrease the point density and a higher value of was chosen because that was the straight edge position used in the field manual measurements. L can be more suitable. Different parameters values were evaluated for each strategy, and successively increased values In Table3, the left and right wheel rut depth measured values for each proposed strategy are were tested. The ones that reached the best results were used. For strategy one, the value L=30 mm listed, rounded to the nearest integer millimeter value. has been used. For strategy two, 50 points were used, as presented in Figure 7 with R = 30 mm. Strategy threeTable had 3. noLeft parameters, and right wheel and rut only depth the measured nearest valuesmiddle for cross-section each proposed sensor strategy. profile point clouds were used. For strategy four, the value L= 30 mm was also used. In strategies three and four, GPS epoch values of eachStrategy cloud point 1 wereStrategy obtained 2 from theStrategy LAS file. 3 The LASStrategy are in 4 version 1.2, to which the standard formatLeft is describedRight inLeft [28]. Right Left Right Left Right PK These parameters (mm)were set(mm) based on(mm) the uses(mm) of MLS(mm) rotation(mm) and measurement(mm) (mm) frequency. A lower rotation52 + frequency800 5 will increase 3 the 7 distance 5 between 4 the consecutive 4 8 scan profiles 6 and, for example, in52 strategy+ 900 four, 5 less cross-section 2 7 points 4 would 5 be obtained. 4 This 9 can, 8 however, be compensated53 with+ 000 a lower 4 vehicle 4velocity. 8 A lower 4measurement 4 rate 3 will decrease 11 the 7 point density 53 + 100 4 3 6 3 5 3 8 6 and a higher53 value+ 200 of L can 3 be more 3 suitable. 6 4 4 2 8 8 In Table53 3,+ 300the left and 6 right 5wheel rut 8 depth 4measured 5 values 3for each 13 proposed 9 strategy are listed, rounded53 + to400 the nearest 3 integer 3 millimeter 6 value. 5 4 2 7 7 53 + 500 4 4 7 3 5 3 11 7 53Table+ 600 3. Left and 4 right wheel 3 rut depth 6 measured 4 values 5 for each 2 proposed 10 strategy. 8 53 + 700 3 3 4 6 4 3 7 5 Strategy 1 Strategy 2 Strategy 3 Strategy 4 Left Right Left Right Left Right Left Right It shouldPK be noted that although the used system has 5 mm precision (Table1), it was possible to (mm) (mm) (mm) (mm) (mm) (mm) (mm) (mm) estimate lower values over the created cross-sections. Despite the low significance of these values, 52 + 800 5 3 7 5 4 4 8 6 for a matter of comparison, it was decided that they would be included in Table3. 52 + 900 5 2 7 4 5 4 9 8 Based on the obtained values, it is possible to represent the longitudinal evolution of rut depth 53 + 000 4 4 8 4 4 3 11 7 values along the highway. Figures 14–16 represent, respectively, the left, right, and maximum rut depth 53 + 100 4 3 6 3 5 3 8 6 values of the field measurements and each strategy’s obtained results. 53 + 200 3 3 6 4 4 2 8 8 Table4 presents the strategy’s list, ordered by Root Mean Square (RMS) of the maximum rut 53 + 300 6 5 8 4 5 3 13 9 depth differences to the field measurements. 53 + 400 3 3 6 5 4 2 7 7 53 + 500 4 4 7 3 5 3 11 7 53 + 600 4 3 6 4 5 2 10 8 53 + 700 3 3 4 6 4 3 7 5

It should be noted that although the used system has 5 mm precision (Table 1), it was possible to estimate lower values over the created cross-sections. Despite the low significance of these values, for a matter of comparison, it was decided that they would be included in Table 3.

ISPRS Int. J. Geo-Inf. 2019, 8, x FOR PEER REVIEW 13 of 16

ISPRSBased Int. J. Geo-Inf. on the 2019 obtained, 8, x FOR values, PEER REVIEW it is possible to represent the longitudinal evolution of rut 13 depth of 16 values along the highway. Figures 14, 15 e 16 represent, respectively, the left, right, and maximum ISPRS Int. J. Geo-Inf. 2019, 8, x FOR PEER REVIEW 13 of 16 rut depthBased values on the of obtained the field values, measurements it is possible and eachto represent strategy’s the obtained longitudinal results. evolution of rut depth values along the highway. Figures 14, 15 e 16 represent, respectively, the left, right, and maximum Based on the obtained values, it is possible to represent the longitudinal evolution of rut depth rut depth values of the field measurements and each strategy’s obtained results. valuesISPRS Int. along J. Geo-Inf. the 2019highway., 8, 404 Figures 14, 15 e 16 represent, respectively, the left, right, and maximum13 of 16 rut depth values of the field measurements and each strategy’s obtained results.

Figure 14. Longitudinal representation of the left rut depth wheel path. Figure 14. Longitudinal representation of the left rut depth wheel path. Figure 14. Longitudinal representation of the left rut depth wheel path. Figure 14. Longitudinal representation of the left rut depth wheel path.

Figure 15. Longitudinal representation of the right rut depth wheel path. Figure 15. Longitudinal representation of the right rut depth wheel path. Figure 15. Longitudinal representation of the right rut depth wheel path. Figure 15. Longitudinal representation of the right rut depth wheel path.

Figure 16. Longitudinal representation of the maximum value between the left and right rut depth Figurewheel 16. paths. Longitudinal representation of the maximum value between the left and right rut depth wheel paths. FigureTable 16. 4. LongitudinalOrdered Root representation Mean Square(RMS) of the valuesmaximum of the va maximumlue between rut the depth left diandﬀerences right rut between depth eachwheel Tablestrategy 4 andpresents the ﬁeld the manual strategy’s measurements. list, orderedpaths. by Root Mean Square (RMS) of the maximum rut Figure 16. Longitudinal representation of the maximum value between the left and right rut depth wheel depth differences to the field measurements. Strategypaths. RMS Value Table 4 presents the strategy’s list, ordered by Root Mean Square (RMS) of the maximum rut depth differences to the field measurements.4 3.2 Table 4 presents the strategy’s list, ordered2 by Root 5.6 Mean Square (RMS) of the maximum rut depth differences to the field measurements.3 7.9

1 8.3

The first proposed strategy is probably the most instinctive solution to create a plane cross-section using cloud points. By projecting in the cross-section line, the profile cloud points, under a defined

perpendicular distance, is obtained. However, since in the MLS data case, each profile’s absolute ISPRS Int. J. Geo-Inf. 2019, 8, 404 14 of 16 position is calculated using the auxiliary sensors’ trajectory (GNSS, IMU, DMI etc.), this strategy mixes the points from different sensor profiles (Figure4). Despite the typical trajectory smoothing processes, the absolute error value of each profile is different. Consequently, the mixed cloud points from different sensor profiles increases the inconsistency between the cross-section consecutive points. Further, that inconsistency is proportional to L distance value (Figure5). To smoothen the cross-section, the second proposed strategy uses a limited number of cross-section points, with the Z-coordinate cloud points averaged within a defined distance L. The point’s number of predefined cross-section influences the measured rut depth, since less points decreases the chance of the higher depth being measured. On the other hand, an increase in the number of points requires a higher L distance. Otherwise, some cross-section points use only few or no cloud points to Z-coordinate average. Higher L values smooth the cross-section and underestimate the rut depth values (Figure7(R = 60 mm)). Strategy three intends to verify the single profile sensor internal consistency. The obtained results show that even the points from a single sensor profile present inconsistency (Figure9). Those inconsistencies result from sensor precision limitation (Table1) and asphalt rugosity. Based on that, strategy four averages the individual sensor profile point cloud coordinates. The resulting points are then projected in the cross-section line. Strategies two and three present as very inconsistent over the consecutive Z-coordinate cross-section points, which makes it very difficult to measure the rut depth over the resulting cross-sections independently of the parameters’ values used. Strategy two results in less cross-section points, facilitating rut depth measurements. However, the exclusively spatial criteria smooth the cross-section, underestimating the rut depth value. The fourth proposed strategy takes advantage of the MLS gathering information, averaging the cloud points by individual sensor profile. This strategy clearly presents the closest result of the manual field reference measurements (Table4). Additionally, concerning the similar results between the field manual measurements and strategy four, this strategy presents a consistent proportionality, demonstrated in Figure 14, Figure 15, and Figure 16. It shows that the point clouds gathered by MLS systems can be used to identify road rut depth in critical areas. Those critical areas can afterwards be tested using specific and more precise systems. This methodology avoids the need for a full road verification by those expensive systems, allowing a more frequent rut depth monitorization. Without the need of special requirements, any available road MLS point cloud can be used to evaluate rut depth. This capability conjugated with rational procedures for rut depth intervention [3] can improve road agencies’ intervention plans. Apart from lower costs, by anticipating the identification of rutting severity areas, this allows better intervention planning, increasing road security. In futures works, the terrain ruggedness index developed by Riley et al. [29] can be an added value to detect the rut depth measurement. By creating a grid based on the cloud points elevation values and comparing the amount of elevation difference between adjacent cells, the roughness values can be mapped [30]. Using the correlation between higher roughness and deeper rut values, these maps can be a huge asset for efficient rut severity areas identification. It should be noted that the measured rut depth values in this work are very small according to any severity classification thresholds values [2,3,5]. In future work, deeper rut depth values should be tested. Also, more exhaustive reference field measurement datasets should be used to confirm the presented results.

4. Conclusions This work presents an evaluation study between different strategies to aggregate the point clouds in a way to create cross-sections. The cross-sections are used to measure the rut depth values. The best RMS results were obtained by the strategy that takes advantage of the cloud point disaggregation in the original sensor profiles. By using the GPS epoch stored for each cloud point, the individual profile cloud points coordinates are averaged. Based on the obtained results, the MLS point clouds can be an efficient and reliable source for anticipating critical road rutting areas identification. This study was specifically focused on the ISPRS Int. J. Geo-Inf. 2019, 8, 404 15 of 16 measurement of rut depth. However, it is believed that the evaluation results are useful for other mobile LiDAR point clouds cross-sections applications, namely topographic cross-sections for digital terrain models creation.

Author Contributions: Conceptualization, Luis Gézero; Formal analysis, Luis Gézero and Carlos Antunes; Investigation, Luis Gézero; Methodology, Luis Gézero; Supervision, Carlos Antunes; Writing—original draft, Luis Gézero; Writing—review & editing, Luis Gézero and Carlos Antunes. Funding: This research received no external funding. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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