sensors

Article Feasibility of Mobile Scanning towards Operational Accurate Road Rut Depth Measurements

Aimad El Issaoui 1,*,†, Ziyi Feng 1,†, Matti Lehtomäki 1, Eric Hyyppä 1 , Hannu Hyyppä 2, Harri Kaartinen 1,3 , Antero Kukko 1,2 and Juha Hyyppä 1,2

1 Department of and , Finnish Geospatial Research Institute FGI, The National Land Survey of Finland, Geodeetinrinne 2, 02430 Masala, Finland; ziyi.feng@nls.fi (Z.F.); matti.lehtomaki@nls.fi (M.L.); [email protected] (E.H.); harri.kaartinen@nls.fi (H.K.); antero.kukko@nls.fi (A.K.); Juha.Hyyppa@nls.fi (J.H.) 2 Department of Built Environment, Aalto University, 02150 Espoo, Finland; hannu.hyyppa@aalto.fi 3 Department of Geography and Geology, University of Turku, 20500 Turku, Finland * Correspondence: aimad.elissaoui@nls.fi; Tel.: +358-503-135-042 † These authors contribute equally to this manuscript.

Abstract: This paper studied the applicability of the Roamer-R4DW mobile (MLS) system for road rut depth measurement. The MLS system was developed by the Finnish Geospatial Research Institute (FGI), and consists of two mobile laser scanners and a Global Navigation Satellite System (GNSS)-inertial measurement unit (IMU) . In the study, a fully automatic algorithm was developed to calculate and analyze the rut depths, and verified in 64 reference pavement plots (1.0 m × 3.5 m). We showed that terrestrial laser scanning (TLS) data is an adequate reference for MLS-based rutting studies. The MLS-derived rut depths based on 64 plots resulted   in 1.4 mm random error, which can be considered adequate precision for operational rutting depth measurements. Such data, also covering the area outside the pavement, would be ideal for multiple Citation: El Issaoui, A.; Feng, Z.; road environment applications since the same data can also be used in applications, from high- Lehtomäki, M.; Hyyppä, E.; Hyyppä, definition maps to autonomous car navigation and digitalization of street environments over time H.; Kaartinen, H.; Kukko, A.; Hyyppä, and in space. J. Feasibility of Mobile Laser Scanning towards Operational Accurate Road Rut Depth Measurements. Sensors Keywords: road rut depth; road mapping; road maintenance; laser scanning; point cloud; MLS; 2021, 21, 1180. https://doi.org/ TLS; photogrammetry 10.3390/s21041180

Academic Editor: Daniele Cocco Received: 9 December 2020 1. Introduction Accepted: 3 February 2021 Road network maintenance takes an extensive share of public expenditure in many Published: 8 February 2021 countries. In the US alone, the estimated countrywide road maintenance backlog is $420 billion [1]; the corresponding value in Finland is €2.5 billion [2]. The common causes Publisher’s Note: MDPI stays neutral of road distress include overloading, frost, use of studded tires, driving speeds, the thick- with regard to jurisdictional claims in ness of surfacing, traffic volume, the type of surfacing material, improper or poor road published maps and institutional affil- surface drainage, lack of proper road maintenance, and improper design. Road distresses iations. disturb traffic flow and safety, and cause an increase in fuel and service costs, time delays with increased pollution, and other trouble for road users. Early identification of road distress is essential, because it provides invaluable infor- mation about the development of damage due to weathering and wear, and also offers an Copyright: © 2021 by the authors. early warning for detecting deeper structural problems due to heavy traffic in combination Licensee MDPI, Basel, Switzerland. with climate effects such as increased winter rain, accelerated freeze-thaw cycles and soft- This article is an open access article ening road foundation due to excessive water runoff. Thus, improved methodologies to distributed under the terms and allow faster and objective/reliable pavement condition data for informed and optimized conditions of the Creative Commons pavement maintenance have potentially enormous economic and environmental benefits. Attribution (CC BY) license (https:// Proper, timely, and selective road maintenance extends the lifespan of the pavement, re- creativecommons.org/licenses/by/ duces the cost of road maintenance, lessens vehicle damage and accidents, and minimizes 4.0/).

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sustained traffic disturbance. An automated, accurate and robust distress detection system is essential to quantify the quality of road surfaces and assist in optimizing the mainte- nance of the road network. The automatic detection system should be able to detect early pavement degradations, such as transverse and longitudinal cracks, potholes, rutting, road fretting, road deformation, and standing water, for minimized maintenance and timely and informed renovations. State-of-the-art automated pavement distress detection methods are discussed in multiple reviews, such as [3–6]. In the past two decades, many research groups have been developing pavement distress detection and recognition algorithms, using 2D passive imaging systems (e.g., [5,7]). Over time, increasing attention has been drawn to the devel- opment of active laser-based 3D data acquisition systems for road distress mapping [8–12]. Despite this fact, there are only a few published papers on measuring road rutting using mobile laser scanner (MLS). For example, MLS has been studied for off-road driving ca- pabilities in robotics [13] as an assisting means of navigation. Zhang et al. [14] performed experimental tests for road distress, and briefly mentioned the possibility of rut analysis. Gézero and Antunes [15] applied ten manually-measured road cross-sections, showing that it is possible to measure road rut depths with better accuracy than the nominal 5 mm precision of the MLS system used. In the current operational road inspection, human raters travel all over the road measuring its distress elements, but these surveys are too laborious, slow, costly, and unsafe to perform at the scale of the whole network even if prioritized based on road class or traffic load, and they are prone to subjective errors. For example, manual rut depth measurement is performed by placing a straight edge across a rut and the distance between the straight edge and the rut bottom is measured [16] as applied also in Gézero and Antunes [15]. Quantitative analysis of road rut depths is for the most part missing from the scientific literature due to lack of accurate and extensive field reference. Therefore, in the previous rut depth studies, reference has been very limited. Since the phenomena under our scrutiny is affected by road surface roughness (grain size of the gravel used and wear of bitumen) and laser ranging accuracy, statistical in-depth analysis are missing. This has led to the situation that road administrations are mainly using old-fashioned profilometers for rutting measurement in their operations. Profilometer laser systems typically include a fairly limited number of laser detectors (e.g., 13 or 17) installed on a bar perpendicular to the direction of the road [17–19], as shown in Figure1, which further illustrates the operating principle of such a laser profilometer for rutting measurements. The shortcoming of such a special rut measuring system includes a low capability in finding the actual maximum left and right ruts due to limited point spacing across the lane. As a result, despite high range accuracy, such systems tend to underestimate the rut depths [15]. Another shortcoming is that such systems are incapable of measuring any road distress other than ruts. While sparse sampling does not permit detection of other surface defects, it biases individual measurements, in effect leading to false rut depth estimation. Even today, such profilometer systems are considered as de facto reference for new sensors, shown recently by Virtala et al. [19]. Sensors 2021, 21, x FOR PEER REVIEW 3 of 20 Sensors 2021, 21, 1180 3 of 20

Figure 1. Measurement principle of laser profilometer for rutting measurements. The measurement Figure 1. Measurement principle of laser profilometer for rutting measurements. The measure- area is determined by the Finnish standard in the way that laser beams 3–7 should locate at the left ment area is determined by the Finnish standard in the way that laser beams 3–7 should locate at rut. Such a system can cover a 3.2-m-wide area of the pavement, with point spacing of 11–30 cm the left rut. Such a system can cover a 3.2-m-wide area of the pavement, with point spacing of 11– across the road [20]. 30 cm across the road [20]. Additionally, there are no international standards for rut depth definition and calcula- tionAdditionally, [21]. In many countries,there are studdedno international tires cause st rutting,andards and for yearly rut depth rutting definition measurements and calcu- lationare needed [21]. In to optimizemany countries, road maintenance studded frequencies. tires cause In rutting, Finland, and pavements yearly arerutting updated measure- mentswhen are rutting needed depth to is optimize over 15 mm, road when maintena safety ofnce the frequencies. road is suffering In Fi ornland, when correction pavements are updatedbecomes when topical. rutting Main depth roads withis over high 15 traffic mm, flowswhen are safety paved of everythe road 2–5 years,is suffering whereas or when correctionsuburban andbecomes residential topical. streets Main can roads have 30–40with high year updatingtraffic flows cycles. are All paved roads every are classi- 2–5 years, whereasfied into suburban quality classes and residential based on rut streets depth, can traffic have speed 30–40 and year volume. updating These cycles. classes areAll roads determined with 1 mm rut depth intervals. Rut depths are provided with 100 or 1000 m are classified into quality classes based on rut depth, traffic speed and volume. These clas- averages, and in future with 10 m averages. It can be seen that rut depths should be sesmeasured are determined with 1 mm with precision 1 mm atrut 10 depth m averages, interv providingals. Rut depths submillimeter are provided accuracy with on 100 or 1000100 m averagesaverages, [22 and,23]. in future with 10 m averages. It can be seen that rut depths should be measuredIn our study, with we1 mm incorporate precision several at 10 innovative m averages, elements. providing We will submillimeter show that carefully accuracy on 100conducted m averages terrestrial [22,23]. laser scanning (TLS) measurements can be used to serve as reference dataIn for our rutting study, studies. we incorporate To verify several the accuracy innovative of the elements. TLS data, We three will validation show that areas carefully 2 conductedwith approximate terrestrial sizes laser of 2.4scanning m (a 1-m (TLS) wide meas rectangleurements across can the be lane) used were to serve measured as reference databy afor stereo-photogrammetric rutting studies. To verify technique, the accuracy which offersof the higherTLS data, accuracy. three validation Besides, a totalareas with of 64 one-meter-wide pavement plots across the lane are utilized for the rut depth study, approximate sizes of 2.4 m2 (a 1-m wide rectangle across the lane) were measured by a which are large enough to investigate the feasibility of MLS data for rut depth. Opera- stereo-photogrammetrictionally, road rut depth measurement technique, results which at offers 10 m intervals higher willaccuracy. be requested Besides, in the a neartotal of 64 one-meter-widefuture [2] and we pavement will show plots that across MLS can the provide lane are the utilized precision for needed the rut indepth operational study, which arenationwide large enough rut measurements. to investigate We the based feasibility our measurements of MLS data on for relatively rut depth. standard Operationally, but roadhigh-end rut depth MLS technologymeasurement since results it provides at 10 multiplem intervals use ofwill road be environmentrequested in the near future [2]data and in we applications will show beyond that ruttingMLS can measurements provide the including precision navigation, needed trafficin operational noise mod- nation- wideeling rut and measurements. mitigation, nearby We citybased 3D our modeling, measurem andents in the on production relatively of standard high-definition but high-end MLS(HD) technology maps for the since needs it of provides autonomous multiple cars, to use be discussedof road environment in Section 4.3 of surveying this paper. data in applications2. Materials beyond and Methods rutting measurements including navigation, traffic noise modeling and2.1. mitigation, Test Site nearby city , and in the production of high-definition (HD) maps Thefor the survey needs area of was autonomous located (60◦ 09cars,04600 toN, be 24 ◦discussed3202100 E) in in the Section municipality 4.3 of ofthis Kirkkon- paper. ummi, Southern Finland, where a 3-km-long section of a two-lane regional road was se- 2.lected Materials as a test and road. Methods The speed limit in the area is between 40 and 50 km/h. This section 2.1.of theTest road Site was selected because of the condition of the pavement, with a varied state of rut offering a good living laboratory for comparative measurement system analysis and computationalThe survey methodology. area was located The road (60°09 pavement′46″ N, 24°32 at the′21 site″ exhibitsE) in the different municipality properties of Kirkko- nummi,such as newSouthern and old Finland, asphalt, differentwhere a depths 3-km-long for ruts, section and various of a typestwo-lane and sizesregional of cracks road was selectedand potholes. as a test road. The speed limit in the area is between 40 and 50 km/h. This section of the road was selected because of the condition of the pavement, with a varied state of rut offering a good living laboratory for comparative measurement system analysis and computational methodology. The road pavement at the site exhibits different properties such as new and old asphalt, different depths for ruts, and various types and sizes of cracks and potholes.

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2.2.2.2. ExperimentExperiment DescriptionDescription TheThe road road section section was was signaled signaled by by painting painting white white hourglass hourglass shaped shaped signal signal patterns patterns on on thethe road road surface surface at at the the edge edge of of the the carriageway carriageway (Figure (Figure2 )2) about about every every 50 50 m, m, on on opposing opposing sidessides ofof thethe road.road. Sixty-twoSixty-two signalssignals werewere paintedpainted perper lane,lane, totalingtotaling 124124 signalssignals altogether.altogether. Real-timeReal-time kinematickinematic (RTK)(RTK) GlobalGlobal NavigationNavigation SatelliteSatellite SystemSystem(GNSS) (GNSS)measurements measurements werewere performed performed for for each each signal signal center center to to serve serve as as reference reference points points for for georeferencing georeferencing and and validationvalidation of of MLS MLS data, data, using using the the Topcon Topcon HIPER HIPER HR RTKHR GNSSRTK GNSS system system (Topcon (Topcon Positioning Posi- Systemstioning Systems Inc., Livermore, Inc., Livermore, CA, USA). CA, The USA). receiver The wasreceiver set to was take set five to measurementstake five measure- per signalments to per compute signal to the compute signal position. the signal The positi purposeon. The of thepurpose signals of wasthe signals to allow was alignment to allow betweenalignment the between point cloud the point datasets cloud collected datasets co withllected the with different the different instruments, instruments, enabling ena- a comparativebling a comparative analysis. analysis.

FigureFigure 2. 2.Ground Ground targettarget paintedpainted onon thethe pavement.pavement. TheThe locationlocation for the target was measured to the center between the two triangles. center between the two triangles.

BecauseBecause thisthis studystudy focusedfocused onon evaluatingevaluating thethe accuracyaccuracy ofof thetheMLS MLSsystem systemin in road road pavementpavement rut rut depth depth derivation, derivation, thethe MLSMLS datadata hadhad to to be be comparedcompared with with other,other, assumedly assumedly moremore accurate,accurate, measurementmeasurement methods.methods. TheThe purposepurpose ofof thethe TLSTLS measurementsmeasurements waswas toto serveserve asas reference reference data data for for MLS MLS measurements measurements;; the thepurpose purpose of the of photogrammetric the photogrammetric meas- measurementsurements was wasto verify to verify the accuracy the accuracy of the of TLS the TLSdata. data. SinceSince TLSTLS and photogrammetric photogrammetric measurements measurements were were static, static, the the evaluation evaluation of the of theTLS TLSinstrument instrument was waslimited limited to selected to selected study study plot areas. plot areas. The painted The painted signals signals served served as indica- as indicatorstors for the for test the plots, test which plots, whichwere defined were defined as one-meter as one-meter long and long 3.5-m and (width 3.5-m of (width one driv- of oneing drivinglane) wide lane) rectangular wide rectangular sections sections around aroundthe signals the signalsfor each for lane. each As lane. a result, As a in result, total in64 total TLS 64plots TLS (1.0 plots m (1.0× 3.5 m m)× were3.5 m) scanned were scanned and used and in used this instudy this for study the for analysis. the analysis. Meas- Measurementsurements by photogrammetric by photogrammetric methods methods were were performed performed to validate to validate the TLS the data TLS dataon three on threeof the of pavement the pavement plots plotscovering covering an approximate an approximate area areaof 2.4 of m 2.42 each. m2 each.

2.3. Data Acquisition 2.3.1. MLS Data Acquisition

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2.3. Data Acquisition 2.3.1. MLS Data Acquisition TheThe MLSMLS data were were collected collected in in June June 2018 2018 using using the theFGI FGI Roamer-R4DW Roamer-R4DW mobile mobile map- mappingping system system developed developed at the at Finnish the Finnish Geospati Geospatialal Research Research Institute Institute (Figure (Figure 3). The3). system The systemprovides provides kinematic kinematic 3D laser 3D scanning laser scanning measurements, measurements, and panoramic and panoramic imagery, imagery, at high res- at higholution, resolution, enabling enabling mapping mapping and modeling and modeling for road asset for road management. asset management. Roamer-R4DW Roamer- con- R4DWsists of consists two profiling of two profilingscanners scanners(the first (theis used first in is usedthe experiment in the experiment in this paper), in this paper), a posi- ationing positioning system system mounted mounted on a modular on a modular aluminum aluminum truss trussstructure structure for versatility for versatility and a andhigh asensor high sensorelevation elevation for enhanced for enhanced visibility visibility behind behindstreet-side street-side objects. objects.The two The 2D twoscanners 2D scannersmounted mounted on Roamer-R4DW on Roamer-R4DW were Riegl were VUX-1HA Riegl VUX-1HA and Riegl miniVUX-1UAV and Riegl miniVUX-1UAV (RIEGL La- (RIEGLser Measurement Laser Measurement Systems GmbH, Systems Horn, GmbH, Austria) Horn, (referred Austria) to as (referred VUX and to miniVUX as VUX in and the miniVUXfollowing), in operating the following), at two operating distinctive at wavelengths, two distinctive 1550 wavelengths, and 905 nm, 1550 respectively. and 905 nm,Cor- respectively.respondingly, Correspondingly, the beam divergences the beam were divergences 0.5 mrad and were 0.5 0.5 × 1.6 mrad mrad, and while 0.5 × the1.6 ranging mrad, whileaccuracy the rangingspecifications accuracy were specifications 5 mm and 15 were mm 5 for mm 3 andmm 15and mm 10 formm 3 precision, mm and 10 respec- mm precision,tively. respectively.

FigureFigure 3. 3.Roamer-R4DW Roamer-R4DW system system is is a a vehicle-mounted vehicle-mounted mobile mobile laser laser scanning scanning (MLS) (MLS) system system for for road road environment mapping. The unit offers unique dual-wavelength sampling of objects. In the environment mapping. The unit offers unique dual-wavelength sampling of objects. In the image image on the right, the Global Navigation Satellite System (GNSS) antenna is on top, with the iner- on the right, the Global Navigation Satellite System (GNSS) antenna is on top, with the inertial tial measurement unit (IMU) and VUX-1HA and miniVUX-1UAV scanners back-to-back to pro- measurementvide cross-track unit scanning (IMU) andover VUX-1HA the road surfaces. and miniVUX-1UAV The system could scanners also be back-to-back fitted with a topanoramic provide cross-trackcamera for scanning georeferenced over the images. road surfaces. The system could also be fitted with a panoramic camera for georeferenced images. The positioning subsystem consists of a NovAtel ISA-100C inertial measurement unit The positioning subsystem consists of a NovAtel ISA-100C inertial measurement (IMU) and a Pwrpak7 global navigation satellite system (GNSS) receiver to obtain the po- unit (IMU) and a Pwrpak7 global navigation satellite system (GNSS) receiver to obtain sition and orientation of the sensors as a function of time. The IMU output data rate was the position and orientation of the sensors as a function of time. The IMU output data 200 Hz, and GNSS range observations were recorded at 5 Hz. The trajectory solution is rate was 200 Hz, and GNSS range observations were recorded at 5 Hz. The trajectory typically computed in multi-pass differential post-processing to obtain the best accuracy solution is typically computed in multi-pass differential post-processing to obtain the best possible at the given GNSS constellation during the survey and the environment, specifi- accuracy possible at the given GNSS constellation during the survey and the environment, cally in terms of GNSS visibility. specifically in terms of GNSS visibility. The test area was driven once in both directions for MLS data calibration, but only The test area was driven once in both directions for MLS data calibration, but only the the data collected on the eastbound lane was used in this study. The average driving speed data collected on the eastbound lane was used in this study. The average driving speed duringduring thethe measurementsmeasurements was 40 40 km/h. km/h. The The scan scan settings settings used used were were 250 250and and100 LPS 100 (lines LPS (linesper second), per second), and 1017 and 1017and 100 and kHz 100 kHzPRF PRF(pulse (pulse repetition repetition frequency) frequency) for the for theVUX VUX and andminiVUX, miniVUX, respectively. respectively. At Atthe the given given speed, speed, this this resulted resulted in in about about 44 mmmm andand 111111 mm mm profileprofile spacings spacings for for the the respective respective scanner scanner data data (i.e., (i.e., ~22 ~22 and and ~9 ~9 lines lines per per each each 1 1 m m wide wide validationvalidation plot). plot). Point Point spacing spacing along along the the profile profile was was 4.3 4.3 mm mm immediately immediately below below the the VUX VUX scannerscanner at at a a minimum minimum distance distance of of about about 2.9 2.9 m m from from the the road road surface, surface, which which corresponded corresponded to theto the actual actual laser laser beam beam spot spot size atsize the at same the same distance. distance. The general The general point point density density on the on road the surfaceroad surface was approximately was approximately 5000 points/m 5000 points/m2 in the2 middlein the middle of the lane of the immediately lane immediately behind behind the measurement vehicle. For miniVUX at 2.7 m above the road surface, the corre- sponding point spacing was 17 mm, and the density was about 500 points/m2. Beam size

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the measurement vehicle. For miniVUX at 2.7 m above the road surface, the corresponding point spacing was 17 mm, and the density was about 500 points/m2. Beam size was not specifiedwas not specified for short ranges,for short but ranges, was expected but was expect to be similared to be to similar that of to VUX, that althoughof VUX, although slightly ellipticalslightly elliptical in shape. in However, shape. However, miniVUX miniVUX data was data not used was innot this used study. in this study.

2.3.2.2.3.2. TLS TLS and and Photogrammetric Photogrammetric Measurements Measurements TLSTLS measurements measurements were were performed performed using using the the FARO FARO Focus Focus S 350 S 350 (FARO (FARO Technologies, Technolo- Inc.,gies, LakeInc., Lake Mary, Mary, FL, USA). FL, USA). The The scanner scanner uses uses the the phase-shift phase-shift principle principle for for measuring measuring distances.distances. Its Its measurement measurement speed speed is is up up to to 976,000 976,000 points/second. points/second. It It has has a a ranging ranging accuracy accuracy ◦ ofof± ± 1 mm, andand itit usesuses 15501550 nmnm wavelength.wavelength. TheThe fieldfield of of view view (FOV) (FOV) for for the the scanner scanner is is 360 360° ◦ inin the the horizontal horizontal axis, axis, and and 300 300°in in the the vertical vertical axis. axis. For For this this study, study, scanning scanning parameters parameters werewere set set to to provideprovide aa pointpoint spacingspacing of 7.7 mm in in both both vertical vertical and and horizontal horizontal directions directions at ata adistance distance of of 10 10 m m from from the the scanner, scanner, resulting in 2.3 mmmm pointpoint spacingspacing onon thethe plot plot road road surface.surface. TheThe measurementmeasurement timetime for for a a single single scan scan was was approximately approximately three three minutes. minutes. The The scannerscanner was was mounted mounted on on the the roof roof rack rack of of the the car car so so that that the the blind blind spot spot of of the the scanner scanner was was pointingpointing inin thethe driving driving direction, direction, allowingallowing fullfull visibilityvisibility ofof the the road road surface surface below below the the scannerscanner (see (see Figure Figure4 A).4A). During During the the TLS TLS measurement, measurement, the the vehicle vehicle was was stationary stationary in in the the centercenter ofof thethe lane,lane, placingplacing the scanner about 2.8 2.8 m m above above the the plot plot (Figure (Figure 4B).4B). The The aim aim of ofthis this setup setup was was to to get get the the scanner scanner as as close close as as possible to the plotplot areaarea soso thatthat the the point point densitydensity remained remained asas high high as as possible possible and and to to ensure ensure that that the the whole whole plot plot was was fully fully visible visible for the scanning. The measurement was then repeated for each plot. The point density for the scanning. The measurement was then repeated2 for each plot. The point density for forthe the measured measured plots plots was was about about 150,000 150,000 points/m points/m2. Stationary. Stationary TLS TLS measurements measurements were were per- performedformed at night at night between between 11 PM 11 PM and and 5 AM, 5 AM, when when the traffic the traffic flow flow was wasminimal, minimal, and there and there was no heavy vehicle traffic. This was to ensure that passing vehicles did not cause was no heavy vehicle traffic. This was to ensure that passing vehicles did not cause the the measuring system to move, and measurements could be carried out with minimum measuring system to move, and measurements could be carried out with minimum dis- disturbance to the public. turbance to the public.

FigureFigure 4. 4.( A(A)) MeasurementMeasurement systemsystem forfor TLS.TLS. (B) TLS point cloud cloud from from one one measurement. measurement. (C (C) )Photo- Pho- grammetric measurement system. togrammetric measurement system.

PhotogrammetricPhotogrammetric measurement measurement was was conducted conducte withd with a custom-built a custom-built and automaticallyand automati- operatedcally operated stereo stereo camera camera system system (Figure (Figur4C). Thee 4C). system The system was built was around built around Nikon D850Nikon camerasD850 cameras equipped equipped with Sigma with Art Sigma 50 mm Art 1.4 50 Gmm prime 1.4 lenses.G prime The lenses. cameras The were cameras mounted were onmounted a remotely on a controlledremotely controlled and electronically and electronically operated cameraoperated rig. camera The averagerig. The groundaverage samplingground sampling distance distance (GSD) of (GSD) the three of the plots three varied plots betweenvaried between 0.079 and 0.079 0.100 and mm.0.100 Themm. meanThe mean reprojection reprojection error variederror varied between between 0.090 and0.090 0.116 and pixels.0.116 pixels. All the All image the image blocks blocks were processedwere processed without without 3D control 3D control points. points. The scale The of scale the of blocks the blocks was determined was determined by utilizing by uti- eightlizing scale eight bars scale in bars each in block.each block. The The sigma sigma of the of the scale scale varied varied between between 0.014 0.014 mm mm and and 0.0210.021 mm. mm. 3D 3D point point densities densities on on the the test test plots plots varied varied between between 163 163 and and 230 230 points/mm points/mm22..

2.4.2.4. MLS MLS Data Data Pre-Processing Pre-Processing TheThe pre-processingpre-processing ofof the MLS data data had had three three steps: steps: (1) (1) trajectory trajectory computation; computation; (2) (2)MLS MLS system system calibration; calibration; and and (3) (3) point point cloud cloud georeferencing. georeferencing. The trajectory, i.e., the measurement path of the MLS, was computed using the No- vAtel Waypoint Inertial Explorer (version 8.80) (NovAtel Inc, Calgary, AB, Canada). For the differential GNSS, we used a virtual GNSS base station generated at the site from the

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The trajectory, i.e., the measurement path of the MLS, was computed using the No- Trimnet service (Geotrim Oy, Vantaa, Finland). The 1 Hz virtual base station data were vAtel Waypoint Inertial Explorer (version 8.80) (NovAtel Inc, Calgary, AB, Canada). For interpolated to meet the 5 Hz records of the Roamer-R4DW positioning system. A 15- the differential GNSS, we used a virtual GNSS base station generated at the site from degree elevation angle was used to reduce multipath effects in the GNSS signals, and the the Trimnet service (Geotrim Oy, Vantaa, Finland). The 1 Hz virtual base station data static initialization method was used for the IMU. The final trajectory was computed in a were interpolated to meet the 5 Hz records of the Roamer-R4DW positioning system. A multi-pass process with three forward and reverse computations, and the solutions were 15-degree elevation angle was used to reduce multipath effects in the GNSS signals, and combined and smoothed for the final result. the static initialization method was used for the IMU. The final trajectory was computed in The trajectory data were associated with the raw laser scanning data (18 leap seconds a multi-pass process with three forward and reverse computations, and the solutions were combinedwere also andapplied smoothed to match for thethe finaltime result.systems), and initial system internal bore-sight pa- rametersThe trajectory(three translations data were and associated rotations with between the raw the laser system scanning IMU and data each (18 leapscanner) sec- ondswere wereapplied. also The applied initial to point match cloud the time was systems),then generated and initial using system RiProcess internal software. bore-sight After parametersthis step, we (three ran a translations scan alignment and rotationstool in th betweene RiProcess the to system improve IMU the and initial each bore-sight scanner) wererotations applied. for mounting, The initial pointbut the cloud translations was then were generated considered using as RiProcess known parameters. software. After Ro- thisbust step, distance we ran weighted a scan alignmentestimation toolwas inused the to RiProcess solve the to parameter improve thevalues initial for bore-sightplanar fea- rotationstures automatically for mounting, extracted but the translationsfrom the point were cloud considered data and as knownmatched parameters. at locations Robust with distancedata from weighted multiple estimation visits. After was solving used tothe solve fine-tuned the parameter orientation values bore-sight for planar parameters, features automaticallywe generated the extracted final point from cloud the point for rut cloud study data method and development matched at locations and rut depth with dataanal- fromysis. multiple visits. After solving the fine-tuned orientation bore-sight parameters, we generatedThe trajectory the final pointaccuracy cloud was for estimated rut study in method the post-processing development andsoftware rut depth by computing analysis. the mean,The trajectory standard accuracy deviation, was and estimated the root inmean the post-processingsquare (RMS) insoftware the 3D position by computing and the theattitude mean, (square standard root deviation, of the mean and thevalue root of meanthe squared square (RMS)observed in thevalues, 3D position e.g., differences and the attitudein position (square and attitude root of thebetween mean the value forward of the and squared reverse observed trajectory values, solutions e.g., to differences their com- inbined position and smoothed and attitude solution) between over the the forward timespan and of the reverse data. trajectoryThe estimated solutions position to theirmean combinedaccuracy was and 4.5 smoothed mm with solution) 1.2 mm over standard the timespan deviation. of theThe data. corresponding The estimated RMS position was 4.6 meanmm. accuracyThe average was attitude 4.5 mm withaccuracies 1.2 mm were standard −0.0711, deviation. −0.0687, The and corresponding −0.3139 arcminutes RMS was for 4.6Roll, mm. Pitch, The and average Yaw, attitude respectively. accuracies The werecorresponding−0.0711, − standard0.0687, and deviations−0.3139 were arcminutes 0.0584, for0.0286, Roll, and Pitch, 0.2193 and Yaw,arcminutes, respectively. and the The RMS corresponding values 0.0920, standard 0.0744, deviations and 0.3829 were arcminutes 0.0584, 0.0286,for Roll, and Pitch, 0.2193 and arcminutes, Yaw. The Yaw/Heading and the RMS an valuesgle uncertainty 0.0920, 0.0744, dominates and 0.3829 the solution, arcminutes but forthe Roll, effect Pitch, of this and at Yaw. a range The of Yaw/Heading 10 m from the angle scanner uncertainty (Yaw RMS) dominates results the in solution,1.1 mm point but thedisplacement, effect of this and at athe range maximum of 10 m absolute from the uncertainty scanner (Yaw (0.8179) RMS) yields results a 2.4 in mm 1.1 mm spatial point er- displacement,ror. and the maximum absolute uncertainty (0.8179) yields a 2.4 mm spatial error. TheThe bore-sightbore-sight calibration resulted resulted in in 7800 7800 planar planar pair pair matches matches and, and, eventually, eventually, a 10.2 a 10.2mm mmerror error (standard (standard deviation) deviation) in the in theestimation. estimation. The Thevalues values applied applied to the to final the finaldata datageoreferencing georeferencing were were −0.03501,−0.03501, −0.03877,−0.03877, and −0.18758 and −0.18758 for Roll, for Pitch, Roll, and Pitch, Yaw, and respec- Yaw, respectively.tively. The plot The of plot theof histogra the histogramm of the ofresiduals the residuals (Figure (Figure 5) shows5) shows that the that majority the majority of the ofobservations the observations were werewithin within 30 mm 30 around mm around the me thean mean (note (notethe logarithmic the logarithmic scale scaleof the of plot), the plot),and the and orientation the orientation of the of observations the observations was well was distributed well distributed for a forreliable a reliable solution. solution.

Figure 5. Histogram of residuals andand orientationorientation chartchart ofof thethe bore-sightbore-sight calibration calibration result result show show good accuracygood accuracy and reliability and reliability of the of solution. the solution.

TheThe pre-processed pre-processed MLS MLS data data were were compared compared against against RTK RTK measurements measurements at the at targetsthe tar- ongets the on road, the road, clearly clearly visible visible in the in reflectance the reflectance data fromdata thefrom scanners, the scanners, and the and study the study con- cludedconcluded that that the MLSthe MLS positioning positioning system system was sufficientlywas sufficiently accurate accurate for georeferencing. for georeferencing. The RTKThe measurementsRTK measurements were were used toused confirm to confirm the success the success of the of georeferencing the georeferencing with the with MLS the system.MLS system. Subsequently, Subsequently, the data the measured data measured by the other by the instruments other instruments for the study for werethe study geo- referencedwere georeferenced with the MLS with data: the theMLS TLS data: data the were TLS georeferenced data were georeferenced in CloudCompare in CloudCom- (version 2.10.2,pare (version http://www.cloudcompare.org/ 2.10.2, http://www.cloudcompare.org/), (accessed on 15 using January the 2021)), georeferenced using the MLS georefer- data,

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enced MLS data, and the photogrammetric data were aligned with the georeferenced TLS dataand the using photogrammetric the same software. data were aligned with the georeferenced TLS data using the sameTest software. plots were created in Bentley MicroStation (v.10.00.00.25) by cutting the data from the roadTest surfaceplots were into created one-meter in Bentley wide MicroStation slices (Figure (v.10.00.00.25)6) according by to cutting the MLS the scan data profiles. Thefrom scan the profileroad surface pattern into of one-meter the pavement wide sl seenices at(Figure the top 6) ofaccording Figure6 to was the formedMLS scan when the scannerprofiles. mirrorThe scan rotated profile atpattern high of speed the paveme (each mirrornt seen rotationat the top creates of Figure one 6 was scan formed profile) while thewhen car the was scanner moving mirror forward. rotated at The high scan speed plane (each was mirror slightly rotation tilted creates to aone 15-degree scan pro- nominal angle,file) while as canthe car be seenwas moving in Figure forward.3. The The rotation scan plane speed was of slightly the scanner tilted to and a 15-degree driving speed determinednominal angle, the as space can be between seen in Figure two scanning 3. The rotation profiles. speed The of number the scanner ofscan and driving profiles within thespeed plots determined therefore the varied space between between two 19 scanning and 22. profiles. An illustration The number of theof scan scan profiles profiles from Plotwithin 2 can the beplots seen therefore in Figure varied6, where between the 19 MLS and point 22. An cloud illustration contains of the 22 scanscan profilesprofiles for the from Plot 2 can be seen in Figure 6, where the MLS point cloud contains 22 scan profiles particular plot. for the particular plot.

Figure 6. MLS (above) and TLS (below) point clouds from the plot area (Plot 2). Here, the scanner Figure 6. MLS (above) and TLS (below) point clouds from the plot area (Plot 2). Here, the scanner was located on the right lane in both cases. The right lane was therefore the studied plot area. was located on the right lane in both cases. The right lane was therefore the studied plot area. 2.5. TLS Preprocessing and TLS Accuracy as Reference 2.5. TLSTo evaluate Preprocessing the accuracy and TLS of Accuracy the TLS measurement, as Reference the photogrammetric and TLS data Towere evaluate aligned the using accuracy CloudCompare’s of the TLS regi measurement,stration , the followed photogrammetric by the use of and the TLS data wereCloud-2-Cloud aligned using (C2C) CloudCompare’s distance comparison registration . C2C is tools, a method followed in which by thedistances use of be- the Cloud- 2-Cloudtween predetermined (C2C) distance reference comparison point clouds tool. and C2C corresponding is a method point in which clouds distances are calcu- between lated. The method can be used to detect changes between point clouds, and it can also be predetermined reference point clouds and corresponding point clouds are calculated. The used to evaluate accuracy when the method is combined with CloudCompare’s Local Sta- method can be used to detect changes between point clouds, and it can also be used to tistical Test (LST) tool. Here, the C2C tool calculates distances between two point clouds evaluatefrom the same accuracy area, whenafter which the method the LST istool combined draws a histogram with CloudCompare’s of the distances Localbetween Statistical Testeach (LST) point tool.pair and Here, calculates the C2C a Gaussian tool calculates distribution, distances providing between the twomean point distance clouds and from the samestandard area, deviation after which for each the plot. LST tool draws a histogram of the distances between each point pair andThe RMS calculates value for a GaussianTLS and MLS distribution, data alignment providing (3D distances the mean between distance the two and da- standard deviationtasets) for foreach each plot plot. was between 4 and 7 mm, depending on the road environment; georeferencingThe RMS was value usually for TLS more and accurate MLS wh dataen alignmentthere were also (3D corresponding distances between points the two datasets)from objects for above each the plot pavement, was between such as 4 andstreetlamps, 7 mm, dependingfences, and road on the signs. road TLS environment; and georeferencingphotogrammetric was datasets usually were more aligned accurate using the when same there method were as TLS also and corresponding MLS. Here, points fromthe RMS objects value above for registration the pavement, was around such 0.5 as mm streetlamps, for all the three fences, validation and road plots. signs. TLS and photogrammetricThe TLS accuracy datasets was wereevaluated aligned using using photogrammetric the same method data as and TLS by and using MLS. the Here, the cloud-to-cloud (C2C) distance tool in CloudCompare. The mean absolute C2C distances RMS value for registration was around 0.5 mm for all the three validation plots. between the TLS and photogrammetric point cloud were 0.85 mm (±0.47 mm, standard deviation)The TLS for accuracyPlot 1, 0.82 was mm evaluated (±0.50 mm, using standard photogrammetric deviation) for dataPlot and2, and by 0.72 using mm the cloud- to-cloud(±0.39 mm, (C2C) standard distance deviation) tool in for CloudCompare. Plot 3 (Figure 7). The Thus, mean better absolute than 0.5 C2C mm distances precision between thefor TLS was and confirmed. photogrammetric point cloud were 0.85 mm (±0.47 mm, standard deviation) for Plot 1, 0.82 mm (±0.50 mm, standard deviation) for Plot 2, and 0.72 mm (±0.39 mm, standard deviation) for Plot 3 (Figure7). Thus, better than 0.5 mm precision for TLS was confirmed.

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Figure 7. Distances between TLS and photogrammetric point cloud points. The y-axis represents Figure 7. Distances between between TLS TLS and and photogra photogrammetricmmetric point point cloud cloud points. points. The The y-axisy-axis represents represents the number of corresponding points, and the x-axis represents the absolute distance (in millime- thethe numbernumber ofof correspondingcorresponding points,points, andand thethe xx-axis-axis representsrepresents the the absolute absolute distance distance (in (in millimeters) millime- ters) between corresponding points. (A) (Plot 1): Cloud-to-cloud absolute distance for 390,000 betweenters) between corresponding corresponding points. points. (A) (Plot (A) 1): (Plot Cloud-to-cloud 1): Cloud-to-cloud absolute absolute distance distance for 390,000 for 390,000 points (road points (road surface of 2.4 m2). (B) (Plot 2): C2C absolute distance for 390,000 points (road surface points (road surface2 of 2.4 m2). (B) (Plot 2): C2C absolute distance for 390,000 points (road surface2 surface of2 2.4 m ). (B) (Plot 2): C2C absolute distance for 390,000 points (road surface2 of 2.4 m ). of 2.4 m2 ). (C) (Plot 3): C2C absolute distance for 330,000 points (road surface of 2.2 m2 ). (ofC )2.4 (Plot m ). 3): (C C2C) (Plot absolute 3): C2C distance absolute for distance 330,000 for points 330,000 (road points surface (road of 2.2surface m2). of 2.2 m ). The TLS scan pattern was much denser than the MLS point cloud (see Figures 6 and The TLSTLS scanscan patternpattern waswas muchmuch denser denser than than the the MLS MLS point point cloud cloud (see (see Figures Figures6 and 6 and8 8 for reference) and, as the 3D scan was stationary, the scan pattern on the ground in gen- for8 for reference) reference) and, and, as as the the 3D 3D scan scan was was stationary, stationary, the the scan scan pattern pattern on on the the ground ground in generalin gen- eral differed from that of the MLS. The normally vertical rotation axis of the TLS scanner differederal differed from from that ofthat the of MLS. the MLS. The normallyThe normally vertical vertical rotation rotation axis ofaxis the of TLS the scannerTLS scanner was was tilted 75 degrees backward, and while the scanner rotated across the lane, the scan- tiltedwas tilted 75 degrees 75 degrees backward, backward, and whileand while the scannerthe scanner rotated rotated across across the lane,the lane, the scanningthe scan- ning mirror cast scan profiles roughly oriented along the longitudinal axis of the road. mirrorning mirror cast scan cast profilesscan profiles roughly roughly oriented oriented along thealong longitudinal the longitudinal axis of axis the road.of the Given road. Given the scan settings and the approximate 2.8 m distance to the road surface, the aver- theGiven scan the settings scan settings and the and approximate the approximate 2.8 m distance 2.8 m distance to the road to the surface, road thesurface, average the pointaver- age point spacing within the plot was approximately 2.3 mm. spacingage point within spacing the within plot was the approximately plot was approximately 2.3 mm. 2.3 mm.

Figure 8. A piece of road surface from the MLS (red dots) and TLS (blue dots) data. Figure 8. A piece of road surface from thethe MLSMLS (red(red dots)dots) andand TLSTLS (blue(blue dots)dots) data.data.

ToTo generate generate a aa high-accuracy high-accuracy rut rut rut depth depth depth refe refe reference,rence,rence, down-sampling down-sampling down-sampling of of the ofthe theTLS TLS TLS data data data was was wasperformedperformed performed to to generate generate to generate road road roadprofiles profiles profiles at at the the at lo lo thecationscations locations of of the the of profiles profiles the profiles generated generated generated by by the the by MLS. MLS. the MLS.TheThe down-sampling down-sampling The down-sampling was was conducted wasconducted conducted by by averaging averaging by averaging the the neighboring theneighboring neighboring TLS TLS TLSdata data data around around around the the theMLSMLS MLS data.data. data. MoreMore More specifically,specifically, specifically, atat at thethe the positionposition position ofof of each each MLS MLS point, point,point, thethe surroundingsurrounding TLS TLSTLS pointspoints werewere were selectedselected selected withinwithin within aa a horizontalhorizontal horizontal distancedistance distance ofof of 55 5 mmmm mm (black(black (black circlecircle circle inin in FigureFigure Figure8 8).). 8). The The The z z z coordinatescoordinates ofof of thethe the down-sampled down-sampled down-sampled TLS TLS TLS points points points were were were the the the average average average elevation elevation elevation values values values within within within the neighborhood,thethe neighborhood, neighborhood, and and theand thehorizontal the horizontal horizontal coordinates coordina coordinates weretes were were equal equal equal to thoseto to those those of theof of the correspondingthe correspond- correspond- MLSinging MLS MLS data. data. data. In thisIn In this this way, way, way, the the the rut rut rut depth depth depth estimation esti estimationmation with with with TLS TLS TLS data data data and and and MLS MLS MLS datadata data cancan can bebe be performedperformed atat at exactly exactly exactly same same same locations, locations, locations, which which which help help help avoid avoid avoid possible possible possible variation variation variation errors errors errors introduced intro- intro- byducedduced location. by by location. location. The down-sampling The The down-sampling down-sampling matches matche matche TLS datass TLS TLS with data data MLS with with data MLS MLS to guarantee data data to to guarantee guarantee accurate TLSaccurateaccurate reference TLS TLS reference (Figurereference9). (Figure (Figure 9). 9).

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Figure 9. A piece of road surface from MLS (red dots)dots) and down sampled TLSTLS (blue(blue dots)dots) data.data.

2.6. Applied Signal Processing and Statistical Methods A digital low-pass low-pass filter, filter, which which only only allows allows a signal a signal with with a frequency a frequency of less of less than than the presetthe preset cut-off cut-off frequency frequency to pass to pass[24,25], [24 ,was25], a waspplied applied to reduce to reduce data noise, data noise, therefore therefore elim- inatingeliminating short-term short-term fluctuation fluctuation in the in the ruts. ruts. Lo Low-passw-pass filters filters can can be be designed designed with with various algorithms, andand inin our our study study a a finite finite impulse impulse response response filter filter with with a Hamming a Hamming window window was applied [26], in which the two most important factors were the filter order and the cut-off was applied [26], in which the two most important factors were the filter order and the frequency. Similar filters were applied to both the MLS and the down-sampled TLS data, cut-off frequency. Similar filters were applied to both the MLS and the down-sampled while the filter order, which determined the filter window length, was 25 for the MLS data, TLS data, while the filter order, which determined the filter window length, was 25 for and 15 for the TLS data. the MLS data, and 15 for the TLS data. In addition, some statistical tools were used to assess the performance of the MLS rut In addition, some statistical tools were used to assess the performance of the MLS rut depth analysis. The bias, random error, and root-mean-square error (RMSE) of a variable x depth analysis. The bias, random error, and root-mean-square error (RMSE) of a variable are evaluated using the following equations: 𝑥 are evaluated using the following equations: 1 N biasbias= = ∑ ((𝑥xˆ −−𝑥x ),), (1)(1) N∑i=1 i i

r random error = 1 ∑ N (𝑒 −bias)2, (2) random error = (e𝑖 − bias) , (2) N − 1 ∑i=1 i r 1 N RMSERMSE= = ∑((𝑥xˆ−−𝑥x ))2,, (3)(3) N∑i=1 i i

where N𝑁is is the the number number of of observations, observations,xˆi is𝑥 the is the observation, observation, and xandi is the𝑥 is reference the reference value. Variablevalue. Variableei is the 𝑒 difference is the difference between between the observation the observation and reference and reference value. value. The corresponding relative bias ( (biasbiasrelrel)) andand RMSERMSE (RMSE(RMSErelrel)) areare defineddefined asas follows: bias =bias ∗ 100%, (4) bias rel= ̅ ∗ 100%, (4) rel x RMSE = ∗ 100%, (5) rel RMSE̅ RMSErel = ∗ 100%, (5) where 𝑥̅ is the mean reference value, which isx defined as where x is the mean reference value, which is defined as 𝑥̅ = ∑ 𝑥 , (6) 1 N x = x , (6) N ∑i=1 i 3. Computational Algorithms 3. ComputationalIn this section, Algorithms the computational methods for the rut depth and crossfall calculation are described.In this section, Figure the 10 computational briefly presents methods the process for the for rut obtaining depth and the crossfall rut depth calculation and the crossfall,are described. while Figurethe details 10 briefly of each presents process the block process are explained for obtaining in the the following rut depth sections. and the crossfall, while the details of each process block are explained in the following sections.

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Figure 10. The process of rut depth and crossfall calculation. FigureFigure 10. 10. TheThe process process of of rut rut depth depth and and crossfall crossfall calculation. calculation.

3.1.3.1.3.1. Rut Rut Rut Depth Depth Depth Estimation Estimation Estimation ToTo Toguarantee guarantee guarantee the the the accuracy accuracy accuracy of ofthe of the the rut rut rutdepth depth depth and and and crossfall crossfall crossfall estimation, estimation, estimation, the the the points points points of ofeach of each each profileprofileprofile were were were transformed transformed transformed into into into a newa a new new local local local scan-profile-specific scan-profile-specific scan-profile-specific 2D 2D 2Dcoordinate coordinate coordinate system. system. system. In In In moremoremore detail, detail, detail, the the thehorizontal horizontal horizontal axis axis axis corresponded corresponded corresponded to tothe to the the horizontal horizontal horizontal distance distance distance along along along the the the scan scan scan profileprofileprofile with with with respect respect respect to tothe to the the first first first point point point on on onthe the the scan scan scan profile. profile. profile. The The The vertical vertical vertical axis axis axis coincided coincided coincided with with with 𝑧 thethethe original original original z axis.𝑧 axis. axis. Figure Figure Figure 11 11 11illustrates illustrates illustrates one one one filteredfiltered filtered (see(see (see SectionSection Section 2.6 2.6) )2.6) scan scan scan profile profile profile of of the ofthe MLS the MLSMLSand and referenceand reference reference data data data in in the inthe new the new new local local local scan-profile-specific scan-profile-specific scan-profile-specific coordinate coordinate coordinate system. system. system.

FigureFigure 11. 11.ComparisonComparison of MLS of MLS and and reference reference data data for forone one scan scan profile. profile. Figure 11. Comparison of MLS and reference data for one scan profile. In the Nordic countries, rut depths are estimated using the wire method [20,27]. The In Inthe the Nordic Nordic countries, countries, rut rut depths depths are are es timatedestimated using using the the wire wire method method [20,27]. [20,27]. The The wirewire method method determines determines the therut rutdepth depth as th ase the maximum maximum distance distance between between a tensed a tensed wire wire wireand amethod road surface determines measurement the rut depth point onas th a profilee maximum (see, e.g.,distance Figure between1). a tensed wire andand a road a road surface surface measurement measurement point point on on a profile a profile (see, (see, e.g., e.g., Figure Figure 1). 1). ForFor each each plot, plot, rut rutdepths depths were were estimated estimated from from each each scan scan profile profile independently, independently, and and the rutFor depthseach plot, were rut then depths averaged were estimated over all the from scan each profiles scan profile in the plot,independently, resulting in and the thethe rut rut depths depths were were then then averaged averaged over over all all th eth scane scan profiles profiles in inthe the plot, plot, resulting resulting in inthe the finalfinal rut rutdepths depths of the of the plot. plot. Each Each scan scan profil profilee was was a cross a cross section section of the of the whole whole lane, lane, thus thus finalcontaining rut depths two of ruts the in plot. the leftEach and scan right profil partse was respectively a cross section (Figure of 12 the). Thewhole depths lane, of thus the

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containing two ruts in the left and right parts respectively (Figure 12). The depths of the leftcontaining and right two ruts, ruts as inwell the as left the and maximum right parts rut, respectively were determined (Figure in 12).accordance The depths with of the the standardsleftleft andand right right of the ruts, ruts, Nordic as as well well countries as as the the maximum [20,27].maximum rut, rut, were were determined determined in in accordance accordance with with the the standardsstandards of of the the Nordic Nordic countries countries [ 20[20,27].,27].

Figure 12. TLS point cloud from test plot that illustrates left and right ruts (rainbow colors). Below is a side view that shows one TLS profile extracted from the plot. FigureFigure 12.12.TLS TLS pointpoint cloud cloud from from test test plot plot that that illustrates illustrate lefts left and and right right ruts ruts (rainbow (rainbow colors). colors). Below Below is is a side view that shows one TLS profile extracted from the plot. a side view that shows one TLS profile extracted from the plot. Figure 13 presents how the rut depths were estimated in one scan profile. For each rut, anFigureFigure ideal 13 road13 presents presents virtual how howline thewithoutthe rutrut depths depthsrutting were were was estimated representedestimated in in oneby one a scan linescan passing profile. profile. Forthrough For each each startrut,rut, anandan idealideal end roadpointsroad virtual virtual of the line linerut without (blackwithout solid rutting rutting line was wasand represented representeddash line in by Figureby a a line line 13). passing passing The selection through through ofstartstart the and andstart end end and points points end points of of the the rutof rut the (black (black rut solidis solid described line line and and below. dash dash line All line inpoints Figurein Figure between 13). 13). The Thethe selection rutselection start of andtheof the startend start points and and end were end points pointsselected, of the of rutandthe is rutthe described is perpen describeddicular below. below. Alldistances points All points from between betweeneach the selected rut the start rut point andstart toendand the pointsend virtual points were line selected,were were selected, calculated. and the and perpendicular The the maxiperpenmumdicular distances distance distances from was eachused from selectedas each a rut selected pointdepth to esti-point the mate.virtualto the virtual line were line calculated. were calculated. The maximum The maxi distancemum distance was used was as aused rut depthas a rut estimate. depth esti- mate.

FigureFigure 13. 13. LeftLeft and and right right rut rut depth depth calculation calculation for for one one scan scan profile profile in in MLS MLS data. data. Figure 13. Left and right rut depth calculation for one scan profile in MLS data.

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To find the start and end points of the ruts, a convex hull of the road data for each profile was computed. The vertices making up the convex hull (green stars in Figure 13) were first classified into upper and lower hull points, and then the upper hull points were further assigned into left, middle, and right groups, according to their locations. More specifically, a least squares fitting line for the whole profile was generated (orange dash dotted line in Figure 13), and all the vertices located above the fitting line were selected. The selected vertices were then assigned into the left, middle, and right groups based on cluster center position and using k-means clustering. The vertex groups acted as candidates for the start and end points of the ruts. It was assumed that the start and end points of the ruts corresponded to the local minima of the absolute value of the tangent slope along the profile. We sought three local minima, one from each of the left, middle, and right groups (red square, diamond, and circle in Figure 13), which are referred to as the left, middle, and right edge points, respectively, in the following. The left edge point was the start point of the left rut and the right edge point was the end point of the right rut. The middle edge point was both the end point of the left rut and start point of the right rut. The tangent slope for point (xi, yi), where i ∈ Iprof = {1, ··· , n}, where Iprof is the index set of all points on the profile and n is the number of points on the profile, was estimated using the following formula:

yi − yi−1 mi = (7) xi − xi−1

Let Ileft, Imiddle, and Iright denote the index sets of the points in the left, middle, and right vertex groups, that is, Ileft, Imiddle, Imiddle ⊂ Iprof. The indices of the left, middle, and right edge points, denoted by ileft, imiddle, and iright, respectively, were retrieved using the following equations: i = argmin {|m |} (8) left i i∈Ileft i i = argmin {|m |} (9) middle i i∈Imiddle i i = argmin {|m |} (10) right i i∈Iright i In a real situation, the road geometric shape varies in distinct files, and the points around the peaks are sometimes not contained in the data due to data segmentation, which leads to an issue that the slope of the tangent at the edge point is found not to be the smallest. Consequently, before calculating the rut depth, the start and end points of the rut were verified to avoid errors in the selection of edge points. In other words, the other non-selected convex hull points in the left group were checked as to whether they were below the line composed by the start and end points of the left rut. If not, the start point was changed to the neighboring point, and the rest of the points in the instance were checked again with the newly assigned start and end points. The same verification was also performed for the middle and right rut point groups. When conducting the rut depth study, one issue that needed consideration was presence of cracks in the pavement. In some cases, the road surface pavement not only had ruts, but also cracks (or other such damage in general) like the one on the right rut shown in Figure 14. Using the implemented rut depth calculation algorithm, the rut depth for the right rut was observed as B, which was obviously affected by the presence of a crack, while the rut depth determined by A was the actual rut depth. As this paper focuses on rutting, only plots with small amounts of cracks were adopted for the analysis of the performance and robustness of the rut depth estimation method. The crack detection was performed in all the plots automatically using a method developed for the purpose, though we will talk more about crack detection algorithms in a subsequent paper. Sensors 2021, 21, x FOR PEER REVIEW 14 of 20 SensorsSensors 20212021,, 2121,, 1180x FOR PEER REVIEW 14 ofof 2020

Figure 14. Rut and crack of one scan profile profile in MLS data.

Besides the plots spoiled with cracks, ther theree were also plots where the pavement had no obvious ruts, i.e., smaller in depth thanthan thethe detectiondetection capabilitycapability ofof thethe MLSMLS data.data. AsAs this paperpaper focusesfocuses on on the the rut rut depth depth measurement measurement accuracy, accuracy, these these good good plots plots were excludedwere ex- cludedafter they after had they been had identified. been identified. Consequently, Conseq a totaluently, of 34a total out of of 64 34 plots out wasof 64 adopted plots was for adoptedthe rut analysis for the rut in this analysis study. in As this the study. left and As the right left ruts and were right treated ruts were separately, treated andseparately, the rut anddepths the were rut depths averaged were over averaged the profiles over of the each prof plot,ileswe of hadeach a plot, total we of 68had rut a depthtotal of samples 68 rut depthfrom the samples 34 plots. from the 34 plots. 3.2. Crossfall 3.2. Crossfall Crossfall is an important geometric road surface safety indicator. It is defined as a Crossfall is an important geometric road surface safety indicator. It is defined as a transverse slope along a horizontal distance [20]. In normal situations, the elevation of transverse slope along a horizontal distance [20]. In normal situations, the elevation of the the road surface is planned to be highest at the middle, and the slope drains towards the road surface is planned to be highest at the middle, and the slope drains towards the edges. The road slope should be neither too small nor too large; the former slows the edges. The road slope should be neither too small nor too large; the former slows the rain- rainwater run-off from the road surface, while the latter may result in high heavy vehicle water run-off from the road surface, while the latter may result in high heavy vehicle roll roll vibration. In Finland, the crossfall design is ±15%. vibration. In Finland, the crossfall design is ±15%. Different measurement methods are used for crossfall [28]. In Finland, this is calcu- Different measurement methods are used for crossfall [28]. In Finland, this is calcu- lated based on linear regression [20]. For a group of 17 measurement points, inherently lated based on linear regression [20]. For a group of 17 measurement points, inherently from the pavement survey system, a regression line is fitted, based on the least square from the pavement survey system, a regression line is fitted, based on the least square method (line (line AC AC in in Figure Figure 15). 15). The The line line is isthen then compared compared with with the the horizontal horizontal line, line, and and the methodthe lateral (line slope AC isin calculated.Figure 15). The In detail, line is for then any compared point (C) with on the the regressionhorizontal line,line, theand per- the lateral slope is calculated. In detail, for any point (C) on the regression line, the perpen- dicularpendicular distance distance from from the point the point to the tohorizontal the horizontal line is called line is Rise called (|BC|), Rise (|BC|),and the distance and the diculardistance distance from the from start the point point (A) to ofthe the horizontal fitting line line (AC) is called to the Rise cross (|BC|), point and (B), the where distance the from the start point (A) of the fitting line (AC) to the cross point (B), where the rise per- fromrise perpendicular the start point interacts (A) of the with fitting horizontal line (AC) line isto calledthe cross Run point (|AB|). (B), Thewhere crossfall the rise is thenper- pendicular interacts with horizontal line is called Run (|AB|). The crossfall is then calcu- pendicularcalculated andinteracts expressed with ashorizontal a percentage: line is called Run (|AB|). The crossfall is then calcu- lated and expressed as a percentage: riserise crossfall = rise∗ 100%, (11) 𝑐𝑟𝑜𝑠𝑠𝑓𝑎𝑙𝑙run = ∗ 100%, (11) run

Figure 15. Crossfall measurement method.

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When the crossfall was measured using MLS and TLS data, a regression line was When the crossfall was measured using MLS and TLS data, a regression line was fitted Whento each the profile crossfall using was the measuredleast square usings method. MLS andOne TLSexample data, using a regression MLS data line is pre- was fitted to each profile using the least squares method. One example using MLS data is pre- sentedfitted toin eachFigure profile 16. Then using the the slope least of squares the fitting method. line was One calculated example and using converted MLS data into is sented in Figure 16. Then the slope of the fitting line was calculated and converted into percentagespresented in according Figure 16 .to Then Equation the slope (11). of Simila the fittingr to the line rut was depth calculated estimation, and converted crossfall val- into percentages according to Equation (11). Similar to the rut depth estimation, crossfall val- uespercentages were averaged according over to all Equation the profiles (11). for Similar each toplot. the However, rut depth estimation,there was only crossfall one valuescross- ues were averaged over all the profiles for each plot. However, there was only one cross- fallwere measurement, averaged over in allcontrast the profiles to the fortwo each ruts plot. in each However, plot. Therefore, there was 34 only crossfall one crossfall values fall measurement, in contrast to the two ruts in each plot. Therefore, 34 crossfall values weremeasurement, acquired in in total contrast from to 34 the plots. two ruts in each plot. Therefore, 34 crossfall values were wereacquired acquired in total in fromtotal from 34 plots. 34 plots.

Figure 16. Crossfall estimation for one scan profile in MLS data. FigureFigure 16. CrossfallCrossfall estimation estimation for for one scan profile profile in MLS data. 4. Results and Discussion 4.4. Results Results and and Discussion Discussion 4.1.4.1. Rut Rut Depth Depth Analysis Analysis 4.1. Rut Depth Analysis FigureFigure 1717 presentspresents the the accuracy accuracy of of the the rut rut depth estimates. The The rut rut depths depths ranged ranged Figure 17 presents the accuracy of the rut depth estimates. The rut depths ranged fromfrom 4.7 4.7 mm mm to to 26.2 26.2 mm, mm, and and for for most most rut rut samples samples the the residuals residuals were were small—on small—on average average from 4.7 mm to 26.2 mm, and for most rut samples the residuals were small—on average 0.660.66 mm. mm. 0.66 mm.

FigureFigure 17. 17. RutRut depth depth estimation estimation results. results. Figure 17. Rut depth estimation results. FigureFigure 18 18 demonstratesdemonstrates the the bias bias and and random random errors errors inside inside each each rut, rut, calculated calculated from from Figure 18 demonstrates the bias and random errors inside each rut, calculated from thethe profiles profiles of of the the plot. plot. The The ra randomndom errors errors ranged ranged from from 0.28 0.28 mm mm to to 2 2 mm. mm. In In addition, addition, the the thebiases profiles from of all the the plot. 34 plots The wererandom between errors− ranged1.6 mm from and 0.28 2.7 mm.mm to Bias 2 mm. is mainly In addition, caused the by

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biasesbiases from from all all the the 34 34 plots plots were were between between − −1.61.6 mm mm and and 2.7 2.7 mm. mm. Bias Bias is is mainly mainly caused caused by by thethethe variability variability variability of of of the the the road road road surface surface surface (grain (grain (grain size size size,, ,small small small differences differences differences in in in georeferencing) georeferencing) georeferencing) and and and how how how biasbiasbias can can can be be be decreased decreased decreased should should should be be be dealt dealt dealt with with with in in future future studies. studies. For For For the the the 68 68 68 sample sample ruts, ruts, the the averageaverageaverage bias bias bias of of of the the the rut rut rut depth depth depth estimation estimation estimation was was was 0.66 0.66 0.66 mm, mm, mm, with with with a a a1.4 1.4 1.4 mm mm mm random random random error, error, error, and and thethethe RMSE RMSE RMSE was was was 1.5 1.5 1.5 mm. mm. mm. This This This proves proves proves that that that th th theee rut rut detection detection and and depth depth measurement measurement with with thethethe MLS MLS MLS data data data point point point density, density, density, 5 5 5mm mm mm ranging ranging ranging accuracy accuracy accuracy and and and 3 3 3mm mm mm precision precision precision specification specification specification was was was sufficientlysufficientlysufficiently accurate accurate accurate for for for th th theee road road road rutting rutting measurement. measurement.

FigureFigureFigure 18. 18. 18. Bias BiasBias and and and random random random error error error of of of the the the rut rut rut depth depth depth estimation. estimation. estimation.

FigureFigure 19 19 presents presents the the relative relative bias bias and and RMSE RMSE for for the the individual individual ruts. ruts. The The biasbias andand Figure 19 presents the relative bias and RMSE for the individual ruts. The biasrel and thethe RMSERMSE overover all all the the plots plots were were 5.0% 5.0% and and 11.3%, 11.3%, respectively. respectively. The The highest highest biasbias andand the RMSErel over all the plots were 5.0% and 11.3%, respectively. The highest biasreland RMSERMSE occurredoccurred at at the the same same rut (in thethe redredrectangle rectangle marked marked with with ‘Outliers’ ‘Outliers’ in inFigure Figure 19 ), RMSErel occurred at the same rut (in the red rectangle marked with ‘Outliers’ in Figure 19),19),which which which were were were 51.2% 51.2% 51.2% and and and 54.5%, 54.5%, 54.5%, respectively, respective respectively,ly, and and and thethe the corresponding corresponding reference referencereference rut rut depth depth waswaswas only only only 4.8 4.8 4.8 mm. mm. mm. However, However, However, at at at the the the 44th 44th 44th rut rut rut (in (in (in the the red red rectangle rectangle marked marked with with ‘Good’ ‘Good’ in in FigureFigureFigure 19), 19),19), the the the reference reference reference rut rut rut depth depth depth was was was 4.9 4.9 4.9 mm, mm, mm, but but but the the the relative relative relative bias bias bias and and and RMSE RMSE RMSE were were were 13.8% 13.8% 13.8% andandand 19.4%, 19.4%, 19.4%, respectively, respectively, respectively, which which were were much much better better than than the the outliers. outliers. The The relative relative bias bias and and RMSE are not important when the measured rut depth is less than 10 mm. In Finland, RMSERMSE are are not not important important when when the the measured measured ru rut tdepth depth is is less less than than 10 10 mm. mm. In In Finland, Finland, maintenance is targeted when rut depth exceeds 15–20 mm. maintenancemaintenance is is targeted targeted when when rut rut depth depth exceeds exceeds 15–20 15–20 mm. mm.

Figure 19. Individual and overall relative bias and root-mean-square error (RMSE) of all the ruts. FigureFigure 19. 19. Individual Individual and and overall overall relative relative bias bias and and root-mean-square root-mean-square e errorrror (RMSE) (RMSE) of of all all the the ruts. ruts.

4.2.4.2. Crossfall Crossfall Analysis Analysis

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4.2. Crossfall Analysis As mentioned above, the elevation of the road surface is usually designed to be the highestAs at mentionedthe middle, above, and the the pavement elevation ofsurface the road drains surface towards is usually the edges designed (Figure to be 16). the However,highest atwhen the middle, pavement and settlement the pavement happens surface, the drains elevation towards of the edgesroad surface (Figure 16is ). changed,However, leading when to pavement crossfall settlement with distinct happens, angles. the We elevation therefore of assumed the road surfacethat the is crossfall changed, wasleading zero when to crossfall the elevation with distinct of the angles. road surface We therefore remained assumed the same that along the crossfall the horizontal was zero axiswhen from the the elevation middle ofposition the road of surfacethe road remained to its edge. the We same also along assumed the horizontal that the crossfall axis from the middle position of the road to its edge. We also assumed that the crossfall was a was a positive value when the elevation was lowest in the middle of the road and rose to positive value when the elevation was lowest in the middle of the road and rose to the the edge. Otherwise, the crossfall was a negative value, which fulfilled the design purpose. edge. Otherwise, the crossfall was a negative value, which fulfilled the design purpose. As expected, the calculated crossfalls of all the profiles within each plot rectangle As expected, the calculated crossfalls of all the profiles within each plot rectangle were were similar. They were therefore averaged as the final crossfall estimation for each par- similar. They were therefore averaged as the final crossfall estimation for each particular ticular plot. The mean crossfall of all plots calculated from both the MLS and reference plot. The mean crossfall of all plots calculated from both the MLS and reference data are data are presented in Figure 20. The crossfalls measured from the MLS data matched well presented in Figure 20. The crossfalls measured from the MLS data matched well with with the reference. The maximum and minimum errors were 0.02% and −0.12%, respec- the reference. The maximum and minimum errors were 0.02% and −0.12%, respectively. tively. Moreover, the crossfall bias was −0.0153%, and the random error was 0.0257%. Moreover, the crossfall bias was −0.0153%, and the random error was 0.0257%.

FigureFigure 20. 20. CrossfallCrossfall estimation estimation results results from from MLS MLS (red (red dashed dashed starred starred line) and reference (blue(bluedashed dashedcircle line).circle line). 4.3. Discussion 4.3. Discussion Rutting is the most significant distress caused to asphalt pavement in the Nordic Rutting is the most significant distress caused to asphalt pavement in the Nordic countries because of the use of studded tires in the winter season. Rutting can significantly countries because of the use of studded tires in the winter season. Rutting can significantly deteriorate road safety since rainwater may fill ruts, leading to a loss of wheel grip and deteriorate road safety since rainwater may fill ruts, leading to a loss of wheel grip and vehicle traction. Maintenance operations to remove ruts should, therefore, be timely. vehicle traction. Maintenance operations to remove ruts should, therefore, be timely. Ac- According to Virtala et al. [2], the rutting rate during winter is 0.5–1.3 mm/year on average, cording to Virtala et al. [2], the rutting rate during winter is 0.5–1.3 mm/year on average, depending on the traffic volume class. Similarly, excessive compacted snow on the road dependingsurface could on the lead traffic to centimeters volume class. deep Simila temporaryrly, excessive ice ruts withcompacted similar snow effects. on the road surfaceCurrently, could lead the to mostcentimeters commonly deep used temporary standard ice in ruts rutting with measurements similar effects. relies on laser systemsCurrently, with the a discrete most commonly number ofused laser standard detectors in rutting installed measurements on a vehicle-mounted relies on laser bar systemsperpendicular with a discrete to the directionnumber of of laser the road.detectors From installed such discrete on a vehicle-mounted measurements, bar the per- most pendicularcommon ruttingto the direction features of calculated the road. areFrom the such maximum discrete rut, measurements, the slope, the the left most and com- right monruts, rutting the distance features between calculated ruts, are the the ridge, maximum and the rut, cross-sectional the slope, the area left and of ruts. right In ruts, addition, the distanceVirtala etbetween al. [2] proposed ruts, the ratioridge, indicators and the cross- such assectional the ratio area of theof ruts. left rut In toaddition, the right Virtala rut, the etratio al. [2] of proposed the maximum ratio rutindicators to the ridge, such and as the the ratio ratio of of the the left rut andrut to the the ridge right to rut, the area.the ratio Such offeatures the maximum could be rut used, to the e.g., ridge, in change-based and the ratio rutting of the studies.rut and Preciselythe ridge georeferencedto the area. Such MLS featuresdata provide could be good used, possibilities e.g., in change-based for future studiesrutting onstudies. change-based Precisely ruttinggeoreferenced development MLS dataand provide evolution good of otherpossibilities deterioration for future of paved studies surfaces. on change-based rutting development and evolution of other deterioration of paved surfaces.

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There are multiple error sources regarding the measurements. Due to the actual roughness of the road surface, correct elevation level is non-trivial to determine. Therefore, in the current process using a profilometer, there was a bias found in measurements [15], allegedly because not enough samples were taken. Another error source is the laser ranging accuracy. When using an MLS system, the major error source is the laser ranging error, which potentially causes both bias and random errors. Since there are hundreds of samples from the road cross-section, it is possible to calibrate the bias provided that there is an accurate reference to be used. Since rutting measurements are conducted annually, the key parameter is precision (the variation within a repeated observation). Further averaging at 10 m or 100 m intervals reduces the obtained random errors. At best, 100 m statistics reduces the random errors obtained for one-meter-plots shown in the paper by 90%, if error sources are independent. In our study, the bias was 0.66 mm, while the random error and RMSE were 1.4 mm and 1.5 mm, respectively, showing that sub-millimeter accuracies can be obtained with 100 m averages. On the other hand, using MLS, Gézero and Antunes [15] reported rutting RMSE of 3.2, 5.6, 7.9, and 8.3 mm, with different computational strategies. There are also high-end pavement measurement systems under development allowing the measurement of thousands of points in each profile with high ranging accuracy (at best, submillimeter level), but they are still very expensive, cover only the road surface and therefore do not allow multipurpose use of the data. Such systems are provided, e.g., by Pavemetrics (Québec, QC, Canada) and Fraunhofer Institute (Munich, Germany). Currently, there are multiple needs to map roads and the road environment. In Finland alone, measurements for multiple services and geospatial information systems are performed on the same roads separately. The national Digiroad covers the center lines of the roads and streets with key attribute information. Ruts are measured with dedicated service cars, equipped with profilometers. Other distresses are monitored separately by human recognition. The road environment is increasingly being mapped using MLS for navigation, traffic noise modeling and mitigation, nearby city 3D modeling, and other applications. MLS can even be used to produce high-definition (HD) maps for the needs of operating autonomous cars in the future. In many cases, HD maps consist of the point clouds of the environment, captured with autonomous vehicles or high-end mobile mapping systems. Autonomous positioning is performed using matching algorithms, such as variants of iterative closest point techniques [29–32]. To decrease the costs of such road and road environment surveys, and increase the multiple use of road environment surveying data, it would be beneficial to be able to conduct all imaginable road maintenance related measurements with a single mobile laser scanning (MLS) survey.

5. Conclusions To decrease the costs of road and road environment surveys, and increase the multiple use of road environment surveying data, it would be beneficial to be able to conduct all road related measurements with a single MLS survey. In this paper, the pavement rut depth and road slope measurement capability of an MLS system was investigated using terrestrial laser scanning (TLS) measurements as a reference. To verify the accuracy of TLS data, the TLS data were analyzed with geometric models obtained with stereophotogrammetry, resulting in standard deviations less than 0.5 mm for the verification plots. The MLS and TLS data were collected in a short time interval, and in total 34 one-meter-long road plots were qualified for evaluation in the end. Using the implemented fully automatic rut analysis, we found that the bias and random errors were 0.66 mm and 1.4 mm for the rut depth estimation using Roamer-R4DW MLS (based on Riegl VUX-1HA). The mean error of the crossfall measurements of the road surface was −0.0153%, with a standard deviation of 0.0257%. Sensors 2021, 21, 1180 19 of 20

The results proved that rut depth and crossfall slope measurements using MLS are highly accurate and feasible for operational application in many countries especially in busy roads where maintenance cycles are short. This offers the potential to develop a mobile road surface management system supporting various road environment applications with a high level of automation, and the possibility to use commercial off-the-shelf (COTS) sensors for road asset inventories.

Author Contributions: A.E.I. contributed to the field test preparations, GNSS and TLS data collection, data pre-processing, data quality analysis and writing. Z.F. developed the method and performed rut analysis and writing. M.L. assisted with rut analysis and writing. E.H. contributed to the rut analysis computational code. H.K. and A.K. were responsible for the study design, undertook the MLS and TLS data collection, pre-processing of the MLS data and contributed to writing. J.H. was the PI of the project, assisting with data analysis and paper writing. H.H. was the Co-PI of the project at Aalto University, with expertise in Road Engineering, and acted as the advisor for the application. J.H., A.K. and H.K. acted jointly as Senior Authors of the paper. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the Academy of Finland (decisions 323750, 293389, 314312 and 337656). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Acknowledgments: The Academy of Finland supported this study through the “Road Distress Mapping Combining Expertise of Sensors and Point Cloud Processing, Surveying and Road Engi- neering” project (decision 323750) and the Strategic Research Council “Competence-Based Growth Through Integrated Disruptive Technologies of 3D Digitalization, Robotics, Geospatial Information and Image Processing/Computing—Point Cloud Ecosystem” project (decisions 293389 and 314312) under Academy of Finland flagship project UNITE—Forest-Human-Machine Interplay (337656). Conflicts of Interest: The authors declare no conflict of interest.

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