International Journal of Geo-Information

Article Utilizing Airborne LiDAR and UAV Photogrammetry Techniques in Local Geoid Model Determination and Validation

Serdar Erol * , Emrah Özögel, Ramazan Alper Kuçak and Bihter Erol Geomatics Engineering Department, Civil Engineering Faculty, Istanbul Technical University, 34469 Maslak, Istanbul, Turkey; [email protected] (E.Ö.); [email protected] (R.A.K.); [email protected] (B.E.) * Correspondence: [email protected]; Tel.: +90-212-285-3826



Received: 24 July 2020; Accepted: 30 August 2020; Published: 2 September 2020


Abstract: This investigation evaluates the performance of digital terrain models (DTMs) generated in different vertical datums by aerial LiDAR and unmanned aerial vehicle (UAV) photogrammetry techniques, for the determination and validation of local geoid models. Many engineering projects require the point heights referring to a physical surface, i.e., geoid, rather than an ellipsoid. When a high-accuracy local geoid model is available in the study area, the physical heights are practically obtained with the transformation of global navigation satellite system (GNSS) ellipsoidal heights of the points. Besides the commonly used geodetic methods, this study introduces a novel approach for the determination and validation of the local geoid surface models using photogrammetry. The numeric tests were carried out in the Bergama region, in the west of Turkey. Using direct georeferenced airborne LiDAR and indirect georeferenced UAV photogrammetry-derived point clouds, DTMs were generated in ellipsoidal and geoidal vertical datums, respectively. After this, the local geoid models were calculated as differences between the generated DTMs. Generated local geoid models in the grid and pointwise formats were tested and compared with the regional gravimetric geoid model (TG03) and a high-resolution global geoid model (EIGEN6C4), respectively. In conclusion, the applied approach provided sufficient performance for modeling and validating the geoid heights with centimeter-level accuracy.

Keywords: airborne LIDAR; UAV photogrammetry; georeferencing; digital terrain model; local geoid; vertical datum

1. Introduction Digital elevation models (DEM) provide information on the topographic surface elevation with respect to a reference datum. Hence a digital representation of the topography can be generated using these models [1]. As a generic term, DEM is used for both the digital terrain model (DTM) and the digital surface model (DSM). DTM means the elevation of the bare surface of the topography without man-made structures, vegetation and other surface features, whereas DSM includes the elevations of all these ground cover objects [2,3]. Depending on this definition, the application areas of DSM and DTM may be different. Accordingly, while a DSM is more useful for landscape modeling, city modeling, flight-simulation and various visualization applications, a DTM is required for deriving different geomorphological attributes, modeling water flow, drainage networks, gravity field and geoid modeling, etc. [2–4]. Various factors including data acquisition technique, terrain character, topographical slope, landscape cover, computation strategy affect the accuracy of generated DEM. The quality of a DEM can be measured by the ability of the height information produced from DEM to match the bare surface of the topography [5]. The uncertainties naturally occur in DEM generation because of the mentioned observational and computational error factors. These uncertainties eventually

ISPRS Int. J. Geo-Inf. 2020, 9, 528; doi:10.3390/ijgi9090528 www.mdpi.com/journal/ijgi ISPRS Int. J. Geo-Inf. 2020, 9, 528 2 of 26 affect the outcome quality and analysis precision in DEM applications [5]. Therefore, it is critical to choose and employ an appropriate digital elevation model according to required height accuracy in an application. Various methods can be applied for quality assessments of the DEM data in a study area prior to the application. The data from a broad range of measurement techniques such as terrestrial surveying, airborne photogrammetric imagery, airborne laser scanning (LiDAR), interferometric synthetic aperture radar (InSAR) are commonly used for generating DEMs today. Among these techniques, airborne LiDAR is rather effective and reliable for generating a high-quality DEM with dense resolution in a typical study area. Besides the favorable aspects of airborne-LiDAR versus the terrestrial surveying and photogrammetry in DEM generation that makes this technique almost a standard practice in spatial data applications, certain points regarding the processing of raw LiDAR data requires special attention and makes this technique demanding [6]. Although aerial LiDAR measurement from a manned platform, e.g., an airplane leads the DEM production techniques in large areas today, it is rather costly for low-budget applications in the smaller areas. However, in a result of progress in drone technologies, a cost-effective alternative of this technique for mapping the topography in small areas, unmanned aerial vehicle (UAV) photogrammetry is in use for a decade [7]. Studies have shown that UAV photogrammetry is an applicable alternative with measurement effectiveness and sufficient precision in DEM generation [7,8]. Height information and geomorphological parameters obtained from digital elevation models by airborne laser scanning and photogrammetric techniques are used in wide a range of applications. These applications include creation of topographic/cartographic maps, orthorectification of aerial imagery, landform analyses, land use mapping, hydrological studies and climate research, among others. In the vast majority of the mentioned applications, digital elevation models are used. However, in physical geodesy, the DTMs are employed for either calculating or validating another physical surface, which is formed under the attraction effect of the topographical masses and called the geoid [9]. The geoid is an equipotential surface of the Earth gravity field that approximates to mean ocean level [9]. In the practical meaning of geoid for geodetic and surveying applications, its surface constitutes a datum (reference surface) for physical heights (H) of points on topography. In many engineering and surveying projects, the required physical heights of the points referring to the geoid are usually obtained through a transformation of GNSS (global navigation satellite system) ellipsoidal heights (hGNSS) with geoid height (Nmodel)-derived from a local geoid model based on a basic relation H = h N [9]. The methods are various for calculating the geoid model that yields the N GNSS − model model parameter to be used in this transformation [10]. The two most commonly used methods in calculating the geoid model are gravimetric and geometric (GNSS/leveling) approaches. Gravimetric approach bases on the solution of the defined geodetic boundary value problem and employs mainly terrestrial gravity observations for calculating a country-scale to continental-scale geoid model. The geometric approach is rarely applied as a rather practical and quick solution to yield a height transformation model, so-called “local geoid model”, in quite small areas in absence of high-accuracy gravimetric geoid model [11]. In the later, discrete control points with collocated GNSS and levelling data, homogeneously distributed on the topography are employed. Usually, a local geoid model is calculated with a suitable surface interpolation algorithm. In both approaches, the geoid model either in the form of an analytical equation or in the raster model as regularly sampled grid nodes is derived with centimeter-level accuracy. After calculating the geoid model, independent datasets, e.g., GNSS/leveling data, astrogeodetic deflections of vertical, are required in order to assess the accuracy of calculated geoid models [12]. The purpose of this study is to investigate the performance of aerial laser-scanner and UAV photogrammetry techniques in determination and testing local geoid models as an alternative to the conventional geoid modeling methods. The tests were carried out for the Bergama region in an area of approximately 156 km2, located in the west of Turkey. Here, the DTMs of the area, referring to the ellipsoid and geoid surfaces, were generated using point clouds by aerial LiDAR and UAV ISPRS Int. J. Geo-Inf. 2020, 9, 528 3 of 26 photogrammetry techniques [7,13]. The aerial LiDAR measurements were provided by the general directorate of mapping [13]. The point heights of the dataset were obtained in the ITRF (International Terrestrial Reference Frame) datum in the ellipsoidal height system. The UAV photogrammetric measurements were carried out by the General Directorate of geographic information systems of Turkey. In georeferencing the UAV aerial photographs, the ground control points having 2D coordinates in ITRF and Helmert orthometric heights in regional vertical datum (Turkey national vertical control network datum—TUDKA99) were employed. Due to this process, the generated DTM by UAV photogrammetry referred to TUDKA99 datum. Thus, having two types of heights for the points on topography, namely are the ellipsoidal heights and orthometric heights from the DTMs allowed the modeling of the local geoid surface as a result of the differences of the DTMs. In numeric assessments, the DTMs were generated from the aerial LiDAR and UAV photogrammetry point clouds using the progressive densification filter with adaptive triangulated irregular network (ATIN) algorithm (using Envi LiDAR software) and morphologic filter (using Global Mapper software), separately in order to choose the best performing algorithm for obtaining higher DTM accuracy. The performances of the applied filter algorithms in DTM generation were compared and discussed though the local geoid models’ accuracies that were calculated by using the produced DTMs from each filter algorithms. Local geoid surface models, obtained from the DTM couples in the result of two filtering methods, were generated in two forms as grid data as well as pointwise data at approximately 250 selected control points on the topography. Hence the obtained geoidal heights (N) from the calculated local geoid models were compared with the geoid heights obtained from the regional Turkey Geoid 2003 (TG03) and a high-resolution global geoid model (EIGEN6C4), respectively, at the grid nodes and the discrete control points [14,15]. In the result of these comparisons, the usability of the DTMs, generated with photogrammetric techniques, for deriving and validating the local geoid models as an alternative to the GNSS/Levelling approach was discussed. In the content of this article, the study area and used point cloud data as well as the regional and global geoid models, used in comparisons, are introduced in Section2. The same section includes a brief definition of the applied methodologies for blunder detection and removal, DTM generation from the point clouds data, local geoid surface modeling and comparisons. In Section3, statistics of two local geoid surface models derived using the DTM-couples generated with tested filter algorithms are given and discussed. The comparison results of the local geoid surface models in grids and pointwise formats, separately, with the regional and global geoid models, are also provided under Section3. This section is closed with a discussion part on the strengths and drawbacks of the introduced technique in local geoid model determination and validation from a broad perspective of the applications in the light of the obtained results. Section4 summarizes the drawn conclusions and suggestions for further studies.

2. Materials and Methods

2.1. Test Site The study was carried out in the Bergama test site, which covers an area of 156 km2 in the west of Turkey (see map in Figure1). In the area, the landscape pattern is heterogeneous and includes forests, urban and rural areas and surface water sources. In the entire area, the topography is rather hilly with a moderate slope from site-to-site. ISPRS Int. J. Geo-Inf. 2020, 9, x FOR PEER REVIEW 4 of 26 ISPRS Int. J. Geo-Inf. 2020, 9, 528 4 of 26

Figure 1. TestTest site site location location and and topography topography using ( top) Google Google Earth Earth image image and and ( (bottom)) SRTM SRTM DTM. 2.2. Airborne LiDAR Data 2.2. Airborne LiDAR Data Airborne LiDAR technique is one of the most efficient remote-sensing methods used in Airborne LiDAR technique is one of the most efficient remote-sensing methods used in terrain terrain mapping since the last decade, and it provides an accuracy almost equivalent to the mapping since the last decade, and it provides an accuracy almost equivalent to the conventional conventional terrestrial techniques in DTM generation [16]. This technique bases on laser distance terrestrial techniques in DTM generation [16]. This technique bases on laser distance measurements measurements integrated with GNSS/IMU (IMU-Inertial Measurement Unit) data from the aircraft integrated with GNSS/IMU (IMU-Inertial Measurement Unit) data from the aircraft platform (see platform (see Figure2)[ 17]. After an almost automatic data capturing and processing procedure, Figure 2) [17]. After an almost automatic data capturing and processing procedure, the three- the three-dimensional (3D) coordinates of all measured points are obtained, and then digital terrain dimensional (3D) coordinates of all measured points are obtained, and then digital terrain models models and/or digital surface models are produced. Briefly, processing the airborne laser scanning data and/or digital surface models are produced. Briefly, processing the airborne laser scanning data typically includes a few steps with preparation, GNSS data evaluation, system calibration, calculation typically includes a few steps with preparation, GNSS data evaluation, system calibration, calculation of the coordinates of all laser points in a geodetic coordinate system, filtering and classification of the of the coordinates of all laser points in a geodetic coordinate system, filtering and classification of the laser points. Accordingly, the GNSS data recorded during the flight are first checked, and then the flight laser points. Accordingly, the GNSS data recorded during the flight are first checked, and then the track is calculated with relative positioning employing the double differences of kinematic observations. flight track is calculated with relative positioning employing the double differences of kinematic System calibration bases on evaluations of the corresponding measurements in swath overlap and observations. System calibration bases on evaluations of the corresponding measurements in swath chosen control points on the ground, i.e., corners of parking lots or other specific constitutions having overlap and chosen control points on the ground, i.e., corners of parking lots or other specific even profiles that are measured with terrestrial surveying techniques or GNSS. Following the control constitutions having even profiles that are measured with terrestrial surveying techniques or GNSS. and calibration processes, the three-dimensional coordinates of reflected laser spots covering the area Following the control and calibration processes, the three-dimensional coordinates of reflected laser flown over are calculated. These preliminarily calculated 3D coordinates of the laser-scanned spots, spots covering the area flown over are calculated. These preliminarily calculated 3D coordinates of constitute the point cloud, include the elevations of vegetation, man-made objects as well as bare the laser-scanned spots, constitute the point cloud, include the elevations of vegetation, man-made topography surface points. objects as well as bare topography surface points.

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ISPRS Int. J. Geo-Inf. 2020, 9, x FOR PEER REVIEW T 5 of 26 e = e e e The position vector, xp xb yb zb r p y ρ θ , of the observed scanned spot p can be principally expressedThe position as a function vector, of 𝑥 the = ( estimated𝑥 𝑦 𝑧 𝑟 GPS𝑝 𝑦/INS 𝜌 𝜃) , (INS-Inertialof the observed Navigation scanned System) spot 𝑝 trajectory can be  T e = e e e (seeprincipally Figure2 ),expressed parameterized as a function with the GPSof the/INS esti positionmated GPS/INSxb xb y(INS-Inertialb zb and orientation Navigation parameters System) T (rolltrajectory (r), pitch (see (Figurep) and yaw2), parameterized (y)) (r p y) , respectively,with the GPS/INS having position the observed 𝑥 = ( range,𝑥 𝑦 𝑧ρ)and and the orientation encoding angle,parametersθ, of (roll the laser (𝑟), pitch beam (𝑝 as) and they yaw are ( shown𝑦)) (𝑟 in𝑝 Figure)𝑦 , respectively,2. The observation having the equation observed in range, the e -frame𝜌 and (Earth-centered,the encoding angle, Earth-fixed 𝜃, of the (ECEF) laser beam frame, as realized they are by shown ITRF) in is Figure as follows 2. The [18 observation]: equation in the e-frame (Earth-centered, Earth-fixed (ECEF) frame, realized by ITRF) is as follows [18]:      0    0  xe (t) = xe (t) + Re (ϕ(t), λ(t))R`(r(t), p(t), y(t))Rb(ω, ϕ, κ)xs + ρ(t) sin θ(t)  (1) 𝑥p(𝑡) =𝑥b(𝑡) +𝑅`𝜑(𝑡), (𝑡)𝑅b ℓ𝑟(𝑡),𝑝(𝑡),𝑦(𝑡)𝑅s (𝜔, 𝜑,) 𝜅 b𝑥 +𝜌(𝑡) sin 𝜃(𝑡) ℓ   ( )  (1) coscosθ t 𝜃(𝑡) in thethe equationequation ((t𝑡)) symbolizesymbolize aa quantity,quantity, whichwhich variesvariesby by time. time. Here,Here, thethe trajectory-dependenttrajectory-dependent e ( ) ` ℓ ( ) ( ) parameters ofof positionposition x𝑥bt(𝑡)and and attitude attitudeR b𝑅, which, which is parameterizedis parameterized by threeby three Euler Euler angles anglesr t ,𝑟p(𝑡t),, b y𝑝(t𝑡)),, range𝑦(𝑡), ρrange(t) and 𝜌( the𝑡) and encoder the encoder angle θ( anglet) are considered𝜃(𝑡) are considered as measurements. as measurements. The lever-arm The xlever-arms and the b bore-sight𝑥 and theR bore-sights are assumed 𝑅 are tobe assumed constant tothat be constant are obtained that are from obtained calibration from process, calibration and process, the rotation and e ( ) ( ) Rthe` trotationcomes as𝑅ℓ a𝑡 function comes as of geographica function of position geographic according position to theaccording reference to ellipsoidthe reference and providesellipsoid transformationand provides transformation from local geodetic from local (`-frame) geodetic to global (ℓ-frame) geodetic to global system geodetic (e-frame). system (𝑒-frame). In the result of Equation (1), the 3D coordinatescoordinates of the finalfinal laser point cloud in the e-frame may be required to transformtransform to a nationalnational datumdatum (n-frame).-frame). Consequently, it may be necessary to apply mapping projection to 3D geodetic coordinates (m-frame; mapping frame where the coordinates are expressed in a grid (i.e., east-, north-) coordinate system in used geodetic datum) datum) according according to to users’ users’ requirements. InIn certain certain applications, applications, the the laser laser point point cloud cloud heights, heights, which arewhich defined are indefined the ellipsoidal in the heightellipsoidal system height are system required are to required be transformed to be transf intoormed a physical into a height physical system height referring system toreferring the geoid to surfacethe geoid (v -frame).surface ( Afterv-frame). transformation After transformation of point heights of point to heights the national to the vertical national datum vertical (from datume/n-frame (from toe/nv-frame-frame), to thev-frame), projection the projection coordinates coordinates using a suitable using mapa suitable projection, map projection, e.g., UTM, e.g., TM, UTM, are generated TM, are (generatedm-frame). (m Depending-frame). Depending on the software, on the software, the transformation the transformation from e-frame from e to-framen-frame to n-frame and v-frame, and v- mayframe, not may beapplicable. not be applicable. In such cases,In such the cases, necessary the datumnecessary transformation datum transfor of pointmation cloud of point coordinates cloud iscoordinates applied externally. is applied On externally. the other hand,On the most other these hand, laser most scanner these data laser processing scanner software data processing offer the outputsoftware option offer forthe theoutput projection optioncoordinates for the projection with a coordinates map projection with selection a map projection [19]. selection [19].

(a) (b)

Figure 2. (a) Airborne LiDAR system in airplane [[20]20] and (b) observationobservation geometry of airborne laser scanning: ss—sensor—sensor frame, frame, defined defined by by principle principle axes axes of oflaser laser scanner, scanner, b—bodyb—body frame, frame, realized realized by the by thetriad triad of accelerometers of accelerometers in INS, in INS, e—earth-centerede—earth-centered earth-fixed earth-fixed (ECEF) (ECEF) frame, frame, realized realized by byITRF ITRF [18]. [18 It]. Itshould should be be noticed noticed that that the the defined defined frames frames in in the the system system are are right-handed right-handed Cartesian Cartesian systems. systems.

Figure 3 illustrates a sequential relation (transformations) among the “global frame” and other intermediate frames that are required for generating point cloud coordinates from the airborne laser scanning data according to users’ requirements [18,19].

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Figure3 illustrates a sequential relation (transformations) among the “global frame” and other intermediate frames that are required for generating point cloud coordinates from the airborne laser

ISPRSscanning Int. J. dataGeo-Inf. according 2020, 9, x FOR to users’ PEER REVIEW requirements [18,19]. 6 of 26

Figure 3. TransformationTransformation between intermediate coordi coordinatenate systems (right-handed) in generating point cloud coordinates by airborneairborne laser scanning data: s—sensor frame, defined defined by principle axes of laser scanner, b—body frame, realized by the triad of accelerometers in INS, ee—earth-centered earth-fixedearth-fixed (ECEF)(ECEF) frame, frame, i.e., i.e., ITRF, ITRF,`—Local ℓ—Local geodetic geodetic coordinate coordinate system, system,n—national n—national coordinate coordinate datum, datum,v—national v—national vertical vertical datum, mdatum,—map m projection—map projection grid coordinate grid coordinate system [system7]. [7].

As a standard data format, the point cloud data are archived and distributed in in “LAS” “LAS” format. format. Depending on the purpose in mapping, the laser spots in a point cloud are classified classified in order to generate the digital terrain, surface,surface, andand/or/or canopy models. In this process, an appropriate filteringfiltering algorithm is used [[16].16]. In the quality of the 3D coordinates of the po pointint cloud data, data, various various error error sources sources interfere. interfere. Mainly imperfections in the sensors and their assemb assemblyly cause observational errors and thus decrease the accuracyaccuracy of of generated generated models models [18 [18].]. Among Among the the observed observed quantities, quantities, the accuracy the accuracy of the laser-scannerof the laser- scannerrange (ρ rangein Figure (𝜌 2inb) Figure mainly 2b) depends mainly on depends the precision on the of time-of-flightprecision of time-of-flight measurements. measurements. Accordingly, Accordingly,the determination the determination accuracy of the accuracy range isof reportedthe range as is 2 reported cm in average as 2 cm [21 in]. average The GNSS [21]. positioning The GNSS positioningaccuracy that accuracy depends that on depends the precision on the of precision GNSS receivers of GNSS as receivers well as the as well GNSS as processingthe GNSS processing strategies, strategies,and the precision and the ofprecision used IMU of used sensors, IMU play sensors, a significant play a significant role in 3D role coordinate in 3D coordinate accuracy accuracy of the laser of thescanning laser scanning points. The points. coordinate The coor accuraciesdinate accuracies of reference of reference GNSS stations GNSS onstations the ground, on the whichground, are which used arein relative used in positioning, relative positioning, the distance the of distance these points of th toese the points study to area, the asstudy well area, as the as flight well altitude as the flight affect altitudethe 3D position affect the accuracy 3D position of derived accuracy point cloud.of deri Furtherved point information cloud. Further on the errorinformation budget andon the accuracy error budgetassessment and ofaccuracy DEM generation assessment with of DEM airborne generation laser scanning with airborne technique laser can scanning be found technique in [18] and can [21 be]. Afterfound calculating in [18] and the [21]. 3D After coordinates calculating of the the laser 3D coordinates spots as a point of the cloud laser dataset, spots as the a qualitypoint cloud of secondary dataset, products,the quality i.e., of secondary DSMs, DTMs, products, DCMs i.e., (digital DSMs, canopy DTMs, models), DCMs (digital are also canopy affected models), by the are performance also affected of byapplied the performance filtering algorithm. of applied Higher filtering the reliability algorithm. in outlier Higher removal the reliability and classification in outlier inremoval the filtering and process,classification the higher in the thefiltering quality process, of the generatedthe higher products.the quality Süleymano˘gluand of the generated products. Soycan [22 Süleymano] providesğ anlu andassessment Soycan of[22] various provides filtering an assessment algorithms of used vari forous DTM filtering generation algorithms from used the airborne for DTM LiDAR generation point fromcloud, the with airborne a case study LiDAR in Bergamapoint cloud, territory. with Süleymano˘gluanda case study in Bergama Soycan [territory.22] tested Süleymano six commonlyğlu usedand Soycanfiltering [22] algorithms tested andsix commonly compared themused infiltering four test algorithms areas having and di ffcomparederent landscape them andin four topographical test areas patterns.having different In conclusion, landscape the and iterative topographical polynomial patterns. fitting In (IPF) conclusion, algorithm the was iterative suggested polynomial for the fitting areas (IPF)having algorithm a smooth was landscape, suggested urbanized for the areas to a certainhaving extenta smooth and landscape, agricultural urbanized patterns. to However, a certain extent rather andthan agricultural IPF, the evaluation patterns. threshold However, with rather an expand than windowIPF, the (ETEW)evaluation filter threshold algorithm with was reportedan expand as windowthe best performing(ETEW) filter filter algorithm method inwas steep reported areas withas th densee best vegetationperforming and filter infrastructure method in steep [22]. areas with Indense literature, vegetation it is possibleand infrastructure to find many [22]. studies on the assessment of DTM accuracy depending on variousIn literature, factors it includingis possible GNSS to find data many processing studies on approach, the assessment position of accuracyDTM accuracy and the depending number onof referencevarious factors stations, includ filteringing GNSS algorithm data processing for blunder approach, detection po ofsition point accuracy cloud data,and the interpolation number of referenceand classification stations, algorithmsfiltering algorithm in DTM for generating, blunder etc.detection [23–25 of]. point Although cloud it data, changes interpolation depending and on classificationthe conditions algorithms related to in the DTM aerial generating, laser scanning etc. [23–25]. experiment, Although the verticalit changes accuracy depending by airborne on the conditionslaser scanning related systems to the in aerial open areaslaser scanning is reported experiment, as approximately the vertical 0.15 accuracy m root means by airborne square errorlaser (RMSE)scanning [25 systems,26]. However, in open withareas appropriate is reported planningas approximately of the measurements, 0.15 m root means using precisesquare measurementerror (RMSE) [25,26].equipment However, and rigorous with appropriate data processing planning strategies, of the the measurements, accuracies of theusing DTMs precise obtained measurement from the equipmentLiDAR techniques and rigorous can be data further processing improved strategies [27]. , the accuracies of the DTMs obtained from the LiDAR techniques can be further improved [27]. In this study, airborne LiDAR data were collected using Optech Pegasus HA-500 mounted on a Beechcraft B200 aircraft in a test flight. The measurements were organized and conducted by the general directorate of mapping [13]. Parameters of the laser sensor and flight technical data are summarized in Table 1. Airborne laser scanning measurements were carried out and completed between October 23–November 6, 2014. The flight plan was prepared using flight planner software FMS planner 4.7.3 [13]. The flight altitude was planned as 1200 m, average point density was at least

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In this study, airborne LiDAR data were collected using Optech Pegasus HA-500 mounted on a Beechcraft B200 aircraft in a test flight. The measurements were organized and conducted by the general directorate of mapping [13]. Parameters of the laser sensor and flight technical data are summarized in Table1. Airborne laser scanning measurements were carried out and completed between October 23–November 6, 2014. The flight plan was prepared using flight planner software FMS planner 4.7.3 [13]. The flight altitude was planned as 1200 m, average point density was at least 2 8 points per m and the flight included 32 strips with an overlap of 25%. The scan width was 35◦, and the scan line spacing was 580 m. The recorded GNSS/IMU data during the flight was processed by the general directorate of mapping using POSPac MMS (Position and Orientation System Postprocessing Package (POSPac) Mobile Mapping Suite (MMS)) software [28]. The collected GNSS/IMU data were processed and adjusted referring the two CORS-TR (continuously operating reference stations—Turkey) network stations’, AYVL (Ayvalık, latitude 39◦18041.04”N and longitude 26◦41009.96”E) and KIKA (Kırka˘gaç, latitude 39◦06021.24”N and longitude 27◦40019.92”E), which are in 65 km and 45 km distances, respectively, from the test site. During the postprocesses, RINEX (receiver independent exchange format) data of CORS-TR stations in 1-second sampling interval were employed [13]. General directorate of mapping preprocessed the airborne laser scanning data using LMS (LIDAR Mapping Suite) software by OPTECH, the producer company of the used laser scanning sensor. In the tests of the produced point cloud data, 51 ground points that separated as 26 control and 25 test points, were used. In the result of the preliminary tests, carried out using control points in the area, the obtained vertical accuracy by means of RMSE is reported as 0.07 m [13]. The resulting unclassified point data were delivered by ± general directorate of mapping with their universal transversal mercator (UTM) projection coordinates (grid zone 35S) and ellipsoidal heights (h) in ITRF datum.

Table 1. Technical specifications of Optech Pegasus HA-500 laser sensor and flight data.

Laser Scanner Sensor 1 Pulse repetition rate (kHz) 100–500 Laser wavelength (nm) 1064 Scan width (FOV) (deg) 0◦–75◦ Scan frequency (Hz) 0–140 Sensor scan product (maximum) 800 Vertical target separation distance (m) <0.7 Horizontal accuracy 2 (1σ) 1/5 500 x altitude Elevation accuracy 2 (1σ) (cm) 5–20 ≤ Flight Data Flight altitude (m) 1200 Groundspeed (knot) 150 Scan Pattern Scan line spacing (m) 580 Scan width (deg) 35 ± ◦ Average density (point m 2) 8 − ≤ Number of columns 32 Overlap 25% Vertical accuracy (RMSE) (cm) 7 ± 1 The technical specifications are obtained from Optech Pegasus HA-500 [29]. 2 Dependent on selected operational parameters using nominal field of view (FOV) of up to 40◦in standard conditions with 24-km visibility.

2.3. UAV Photogrammetry Data In this study, a second DTM generated from the point cloud data of the General Directorate of geographic information systems was employed. As different from the first dataset, this second point cloud data were obtained with the aerial photographs from the unmanned aerial vehicle using ISPRS Int. J. Geo-Inf. 2020, 9, 528 8 of 26 indirect georeferencing. The horizontal coordinates of the ground control points, which were used for indirect georeferencing the point cloud, were obtained with GNSS measurements in ITRF datum. The orthometric heights of the ground control points were obtained through the leveling measurements in TUDKA99 datum. As depending on the ground control points and the indirect georeferencing of the aerial photographs, the point cloud data were generated in physical height system referring to the geoid (v-frame). Having the orthometric heights of the point cloud spots and consequently generating a second DTM in regional vertical datum was crucial for calculating the geoid heights as the difference between the two DTMs. Aerial photogrammetry is a conventional approach widely used for 3D and 2D mapping the land parts by evaluating the photographs taken from an aerial vehicle. Similar to the aerial LiDAR technique, the photogrammetric approach is also commonly used for DTM generation in many applications. Emerging the light–weight unmanned aerial vehicles being equipped with GNSS-IMU devices and starting their use in aerial photogrammetry has significantly increased the use of this technique especially in small budget projects and applications. The fundamental theory of photogrammetric map production bases on a single image and stereo image pairs orientation. Although the fundamental outline of the theory has remained the same, the developing technologies with sensors integration opportunities led the modernization in mathematical models and calculation algorithms [30–32]. In the modernization manner, the “structure from motion” (SfM) algorithm resolves the 3D structure employing a series of overlapping, offset images as in the stereoscopic photogrammetry. Although this algorithm follows the same basic tenets in principle, it has fundamental differences from conventional photogrammetry by means of the solution strategy. In SfM, the camera locations, the geometry of the scene, orientation parameters are solved automatically without requiring a network of ground control points with known 3D coordinates. Instead, the listed parameters are solved simultaneously using iterative bundle adjustment having high redundancy based on a set of featured points, which are automatically extracted from the multiple overlapping images [32,33]. The development of the SfM algorithm dates back to the 1990s and bases on computer vision technology and automatic feature-matching algorithms [32]. It has been popularized through a number of cloud-processing software, which employ the SfM algorithm for generating point-cloud data for various purposes [32,34]. The advantages provided by the SfM algorithm led improvements in the quality of terrain products derived from aerial photogrammetry with UAVs [35]. Figure4 describes the relations between object point ( A), image frame (i), UAV frame (u) and geodetic coordinate system shown as the global frame (g). Based on the described observational geometry, generating DEM grids with UAV imagery bases on a number of operational steps that involve the cooperation of different sensors including magnetic compass, barometer, CMOS camera, dual-frequency GNSS, IMU with gyroscope and accelerometer. Figure5 shows the workflow of the process for generating the georeferenced sparse point-cloud and finally DEM through the photogrammetric method. Accordingly, after planning and carrying out the fieldwork procedures, a sparse 3D model from triangulating correspondences between multiple images in the scene is obtained with employing the SfM algorithm. Then the 3D positions of the points, which were matched with feature tracking, are recovered with the help of georeferencing. In the final section, an optimization-based procedure is applied for calculating and triangulating a dense mesh-grid data. Resulting 3D point-cloud is filtered for removing blundered points and finally, the dense point-cloud data are interpolated in order to obtain a surface model in mesh-grid form. There are two main approaches for georeferencing the image data [36]. One of them is the indirect approach in aerial photogrammetry applications using UAVs. In this method, the image data are georeferenced indirectly using ground control points (GCP) having known coordinates that are visible on images. For indirect georeferencing, the aerial vehicle is not necessarily to be equipped with position and orientation instruments and this is assumed as an advantage. Accordingly, indirect georeferencing provides accurate positioning results in required geodetic datum depending on the accuracy and ISPRS Int. J. Geo-Inf. 2020, 9, 528 9 of 26 reference datum of the used ground control points’ coordinates. The indirect georeferencing process is formulated in Equation (2). g = g ( ) + g( ) i ( ) roA roi t sA Ri t ria t (2) g where roA represents the ground coordinates vector of the object point (A) in geodetic coordinate g ( ) g( ) system (g-frame), roi t is coordinates vector of camera sensors at the time (t) in g-frame, Ri t is the i ( ) rotationISPRS Int. matrixJ. Geo-Inf. of 2020i-frame, 9, x FOR to g PEER-frame, REVIEWsA is scale factor, ria t represents the object coordinates vector 9 of in26 i-frame (see Figure4). measuredOn the using other a hand, GNSS the set second and an approach INS unit is mount the directed georeferencing.on the aircraft body. This approach This method uses onboardrequires sensorsaccurate for sensors image time georeferencing. synchronizat Inion this and approach, misalignment the exterior calibration. orientation is typically measured using a GNSSISPRSDirect setInt. J. andgeoreferencing Geo-Inf. an 2020 INS, 9 unit, x FOR for mounted PEER obtaining REVIEW on the grou aircraftnd coordinates body. This of method the object requires point accurate (A) in sensorsthe 9 of geodetic 26 time synchronizationcoordinate system and (g misalignment-frame), relies calibration.on the Equation (3). Using this equation in the direct approach measured using a GNSS set and an INS unit mounted on the aircraft body. This method requires Direct georeferencing for obtaining ground coordinates of the object𝑠 𝑟 point (A) in the geodetic requiresaccurate a priorisensors knowledge time synchronizat of a nuionmber and misalignmentof systematic calibration. parameters ( , ) stated in the equation coordinate[37]. Direct system georeferencing (g-frame), for relies obtaining on the grou Equationnd coordinates (3). Using of the this object equation point ( inA) thein the direct geodetic approach requires a priori knowledge of a number of systematic parameters (s , ru ) stated in the equation [37]. coordinate system (g-frame),𝑟 relies=𝑟 on(𝑡 )the+𝑅 Equation(𝑡)𝑠 𝑅(3).( 𝑡Using)𝑟 (𝑡 this) +𝑟 equationA , ui in the direct approach (3) requires a priori knowledge of a number of systematic parameters (𝑠 , 𝑟 ) stated in the equation where 𝑟 (𝑡) is coordinates vectorg = ofg ( GNSS-IMU) + g( ) sensorsu( ) i at( )the+ timeu (𝑡) of exposure, 𝑅(𝑡) is the [37]. roA rou t Ru t sA Ri t ria t rui , (3) rotation matrix of u-frame to g-frame, 𝑅 (𝑡) is the rotation matrix from of i-frame to u-frame, 𝑟(𝑡) g 𝑟 =𝑟(𝑡) +𝑅 (𝑡)𝑠 𝑅 (𝑡)𝑟(𝑡) +𝑟 , g (3) whereis the objectr (t) coordinatesis coordinates vector vector in of𝑖-frame, GNSS-IMU 𝑟 is sensors the position at the timevector (t) of of camera exposure, projectionR (t) is thecenter rotation in u- ou u ( ) ( ) matrixframewhere (see of u𝑟 Figure-frame𝑡 is 4).coordinates to Theg-frame, 𝑟 lever-armvectorRu(t) ofis GNSS-IMU theand rotation𝑅 boresight sensors matrix at parameters the from time of (i𝑡-frame )in of 𝑢exposure,-frame to u-frame, are 𝑅 constant.𝑡 risi (thet) is the i ia rotation matrix of u-frame to g-frame,u 𝑅 (𝑡) is the rotation matrix from of i-frame to u-frame, 𝑟(𝑡) object coordinates vector in i-frame, rui is the position vector of camera projection center in u-frame is the object coordinatesu vector in 𝑖-frame,u 𝑟 is the position vector of camera projection center in u- (see Figure4). The rui lever-arm and Ri boresight parameters in u-frame are constant. frame (see Figure 4). The 𝑟 lever-arm and 𝑅 boresight parameters in 𝑢-frame are constant.

Figure 4. Observation geometry in mapping with unmanned aerial vehicle (UAV) photogrammetry FigureFigure 4. Observation 4. Observation geometry geometry in in mapping mapping with with unmanned[38]. unmanned aerialaerial vehicle (UAV) (UAV) photogrammetry photogrammetry [38]. [38].

FigureFigure 5. 5.Workflow Workflow forfor generating point-cl point-cloudoud using using UAV UAV photogrammetry photogrammetry [35]. [35]. Figure 5. Workflow for generating point-cloud using UAV photogrammetry [35]. In each step of the 3D point cloud generation process in UAV photogrammetry, different factors includingIn each inputstep of data, the image 3D point quality, cloud GNSS generation position processaccuracy, in employed UAV photogramme processing parameterstry, different affect factors includingthe final input DEM data, accuracy. image Considering quality, GNSS the experimentposition accuracy,al results employed on accuracy processing assessments parameters of DEMs affect the generatedfinal DEM by accuracy.UAV photogrammetry Considering imagery, the experiment it is seen thatal results ∼5–6 cm on vertical accuracy accuracy assessments in RMSE ofcan DEMs generatedbe obtained by UAV in bare photogrammetry areas with moderate imagery, topography it is seen[39]. that ∼5–6 cm vertical accuracy in RMSE can be obtainedFollowing in bare the areas described with methodology moderate topography and indirect [39]. georeferencing procedure, 3D coordinates of theFollowing point cloud the were described derived methodology using UAV photogrammetry and indirect georeferencing by the General Directorateprocedure, of 3D geographic coordinates of ∼ the informationpoint cloud systems were derived of Turkey. using The UAV vertical photogrammetry accuracy of the point by the cloud General data wereDirectorate reported of as geographic 5–6 ∼ information systems of Turkey. The vertical accuracy of the point cloud data were reported as 5–6

ISPRS Int. J. Geo-Inf. 2020, 9, 528 10 of 26

In each step of the 3D point cloud generation process in UAV photogrammetry, different factors including input data, image quality, GNSS position accuracy, employed processing parameters affect the final DEM accuracy. Considering the experimental results on accuracy assessments of DEMs generated by UAV photogrammetry imagery, it is seen that ~5–6 cm vertical accuracy in RMSE can be obtained in bare areas with moderate topography [39]. ISPRSFollowing Int. J. Geo-Inf. the 2020 described, 9, x FOR PEER methodology REVIEW and indirect georeferencing procedure, 3D coordinates 10 of of26 the point cloud were derived using UAV photogrammetry by the General Directorate of geographic cminformation by the data systems provider of Turkey. institution. The vertical The accuracydataset was of the provided point cloud with data their were universal reported transversal as ~5–6 cm mercatorby the data (UTM) provider projection institution. coordinates The dataset (grid was zone provided 35S) in ITRF with theirdatum universal and orthometric transversal heights mercator (𝐻) (UTM)in Turkey projection national coordinates vertical control (grid network zone 35S) (TUDKA99) in ITRF datum datum. and The orthometric density of heights the provided (H) in Turkey point cloudnational was vertical 450 points control per networkm2. (TUDKA99) datum. The density of the provided point cloud was 450 points per m2. 2.4. DTM Generation from Point Cloud Data for Modeling Local Geoid Surface 2.4. DTM Generation from Point Cloud Data for Modeling Local Geoid Surface In the tests, the local geoid surface was derived from the differences between two DTMs, that were generatedIn the with tests, point the local cloud geoid data surface by aerial was derivedlaser scanning from the (𝐷𝑇𝑀 differences𝐈) (Section between 2.2) twoand DTMs,UAV photogrammetricthat were generated imagery with point(𝐷𝑇𝑀𝐈𝐈 cloud) (Section data 2.3), by aerialrespectively. laser scanning The point(DTM heights,I) (Section obtained 2.2 from) and 𝐷𝑇𝑀 UAV𝐈 photogrammetricare the geometrically imagery meaningful (DTMII ellipsoidal) (Section 2.3 heights), respectively. (ℎ) in ITRF The datum point heights,and refer obtained to GRS80 from referenceDTMI ellipsoid,are the geometrically whereas the meaningful 𝐷𝑇𝑀𝐈𝐈 provided ellipsoidal us the heights physically (h) inITRF meaningful datum andorthometric refer to GRS80 heights reference ( 𝐻 ) in regionalellipsoid, height whereas datum the DTM TUDKA99.II provided Hence us the the physically local geoid meaningful heights orthometric ( 𝑁 ) were heights generated (H) infrom regional the differencesheight datum of TUDKA99.ℎ and 𝐻 as Hence𝑁=ℎ−𝐻 the local in meter geoid (see heights Figure (N )6 werefor the generated definition from of geoid the di heightfferences 𝑁 ofat ah topographyand H as N =point).h H in meter (see Figure6 for the definition of geoid height N at a topography point). −

Figure 6. Geoid height ( 𝑁N)) definition definition as as difference difference between the ellipsoidal height ((hℎ) and orthometric height ( 𝐻H)) of of a a topography topography point point [9]. [9].

With following the described procedure, based on differences of DTM and DTM , the local geoid With following the described procedure, based on differences of 𝐷𝑇𝑀I𝐈 and 𝐷𝑇𝑀II𝐈𝐈, the local geoid models in in grids grids and and pointwise pointwise formats formats were were generate generated.d. Numeric Numeric tests carried tests carried out using out the using grid the models grid aimedmodels to aimed evaluate to evaluate the performance the performance of the produced of the produced models along models the along entire the area entire which area involves which involves various variousland cover land types. cover On types. the other On thehand, other the hand, pointwise the pointwise local geoid local models geoid were models calculated were calculated at the manually at the selectedmanually points selected at the points bare attopogr the bareaphy. topography. Thus, the numeric Thus, the tests numeric with the tests local with geoid the local models geoid in pointwise models in pointwiseformat were format expected were to expected provide to more provide realistic more realisticand reliable and reliableresults regarding results regarding the performance the performance of the suggestedof the suggested geoid modeling geoid modeling methodology. methodology. The distribu The distributiontion of the manually of the manually selected selected 250-geoid 250-geoid control pointscontrol in points the study in the area study is areashown is shownin Figure in Figure7. As 7will. As be will explained be explained in detail in detail below, below, the numeric the numeric tests carriedtests carried out with out the with local the geoid local geoidmodels models in gridwise in gridwise format formatalso show also the show asse thessment assessment results of results the two of differentthe two diclassificationfferent classification methodologies methodologies used in DTM used ingeneration. DTM generation. Accordingly, Accordingly, the two DTM the two couples DTM generatedcouples generated using both using progressive both progressive densification densification and morphologic and morphologic filter algorithms, filter algorithms, respectively, respectively, were wereused in used deriving in deriving the two the gridwise two gridwise local geoid local geoidmodels. models. The obtained The obtained geoidal geoidal heights heights from each from DTM each couple were investigated through their basic statistics in the following. Both filter algorithms, as their theories are mentioned in the following, were implemented with separate software.

ISPRS Int. J. Geo-Inf. 2020, 9, 528 11 of 26

DTM couple were investigated through their basic statistics in the following. Both filter algorithms, ISPRSas their Int. theoriesJ. Geo-Inf. are2020 mentioned, 9, x FOR PEER in REVIEW the following, were implemented with separate software. 11 of 26

Figure 7. Manually selected Geoid control points scattered on the study area. Color bar shows the orthometric heights of the points in meters.

After obtaining the point cloud data from the data provider institutions, in the first first step of the processes, the data were filteredfiltered and the DTMs were generated accordingly. The original point cloud by aerial LiDAR measurements was given to us in divideddivided tiles. However, the second point cloud obtained fromfrom UAVUAV photogrammetric photogrammetric imagery imagery covered covered the entirethe entire area andarea providedand provided as a single as a datasetsingle datasetfor the wholefor the area. whole Since area. the Since study the area study is ratherarea is largerather and large therefore and therefore processing processing dense point dense clouds point cloudsas a whole as a requireswhole requires high-capacity high-capacity computer computer processors processors and lengthy and lengthy processing processing time, we time, divided we the UAV point cloud data into 1 km 1 km subareas at first for the filtering process. Thereafter, divided the UAV point cloud data into× 1 km × 1 km subareas at first for the filtering process. Thereafter,the piecewise the DTMspiecewise generated DTMs generated as separate as tiles separate were tiles connected were connected in order toin constituteorder to constitute the DTM the of DTMthe whole of the area. whole The area. gaps, The which gaps, werewhich at were the tileat the boundaries, tile boundaries, were interpolatedwere interpolated from from the DTM the DTM data datain neighboring in neighboring map map sheets. sheets. However, However, since since it wasit was recognized recognized that that the the interpolation interpolation processprocess was unsuccessful for providing smooth and seamless tran transitionsition along along the the tile tile boundaries of of the the DTMs, the computation strategy was altered and the DTMs were generated using the point cloud data as a whole, after blunder removal and denoising the partitionedpartitioned point cloud data. As mentioned above, above, the generation generation of of DTMs DTMs was was carried carried out out using using two two different different filtering filtering approaches approaches in classification. in classification. In differentIn different stages stages of ofthe the point point cloud cloud data data proces processingsing and and then then the the DTM generating: CloudCompare, Envi LiDAR, Global Global Mapper Mapper GIS GIS software software were were used used [40–42]. [40–42 ].In In calculating calculating local local geoid geoid models models both both in in gridwise and pointwise formats by subtracting the orthometric heights of the DTM from the gridwise and pointwise formats by subtracting the orthometric heights of the 𝐷𝑇𝑀𝐈𝐈II from the ellipsoidal heights of the DTM , the Surfer software by Golden Software company was employed [43]. ellipsoidal heights of the 𝐷𝑇𝑀𝐈I, the Surfer software by Golden Software company was employed [43]. We selectedselected 250 geoid control points on bare topography with homogeneous distribution over the area for generating the pointwise version of the local geoidgeoid model. While determinin determiningg the locations of these scattered points set, we paid special attention to include the characteristic points of the topography that can be be assumed assumed to to be be remained remained unchanged, unchanged, and and thus thus to tobe bemeasured measured during during both both the aerial the aerial LiDAR LiDAR and UAVand UAV photogrammetry photogrammetry campaigns campaigns (Figure (Figure 7). 7In). Inthis this way, way, we we aimed aimed to to use use the the topographic points,points, which are common in both datasets and hence to elim eliminateinate the effect effect of possible environmental changes within a short time-lag time-lag between between the the airb airborneorne and and UAV UAV flights flights in in the the results. results. In the filteringfiltering step of the point-clouds, the noisenoise and blunders in the point clouds were cleaned using statistical statistical outlier outlier removal removal (SOR) (SOR) filter filter algorith algorithmm in CloudCompare in CloudCompare software software [44]. [SOR44]. filter SOR has filter a ratherhas arather simple simple computation computation algorithm algorithm that bases that on bases stochastic on stochastic analysis analysis of all points of all pointsin the inpoint the cloud point andcloud removes and removes the points, the points, which whichdo not do satisfy not satisfy the assigned the assigned threshold threshold as the ascriterion, the criterion, from the from point the pointcloud [45]. cloud In [ 45filtering,]. In filtering, for each forpoint each in the point point in thecloud, point the cloud,spatial thedistance spatial to a distance number to of aneighboring number of pointsneighboring are calculated. points are The calculated. average of the The calculated average ofdistances the calculated is taken distancesinto account. is taken The distribution into account. of the differences between the calculated distances from their average is assumed as Gaussian. Then any point having a distance difference, which does not fit the distribution is removed as a blunder. Therefore, the distance between a points-couple constituted based on the assigned number of points for defining the neighborhood boundaries (let us say 𝑘 points around the point in question) cannot exceed

𝑑. in meter that:

ISPRS Int. J. Geo-Inf. 2020, 9, 528 12 of 26

The distribution of the differences between the calculated distances from their average is assumed as Gaussian. Then any point having a distance difference, which does not fit the distribution is removed as a blunder. Therefore, the distance between a points-couple constituted based on the assigned number ISPRSof points Int. J. forGeo-Inf. defining 2020, 9, the x FOR neighborhood PEER REVIEW boundaries (let us say k points around the point in question) 12 of 26 cannot exceed dmax. in meter that: d𝑑max. ==𝜇+𝑛×𝜎µ + n σ (4)(4) . × where µ𝜇is is average average distance, distance,n = 𝑛1,2,3 = 1,2,3 is a multiplieris a multiplier constant constant that is th selectedat is selected depending depending on the required on the requiredinterval ofinterval confidence, of confidence,σ is the standard 𝜎 is the deviation standard ofdeviation the distances. of the Hence,distances. the Hence, points whichthe points are fartherwhich arethan fartherdmax. are than removed. 𝑑. are In removed. the process, In thethe definitionprocess, the of kdefinition, the number of 𝑘 of, the points number in the of neighborhood points in the neighborhoodand n, the multiplier and 𝑛, the of standardmultiplier deviation, of standard are deviation, critical parameters are critical thatparameters determine that thedetermine number the of numberpoints, deletedof points, from deleted the dataset. from the Hence, dataset. the Hence, success the of success the filtering of the process.filtering process. In the study, In the in study, a result in aof result a trial-and-error-based of a trial-and-error-based approach, approach, we determined we determined and used asandk =used6 and asn 𝑘= =1, 6 with and concerning 𝑛 = 1, with to concerningreach the required to reach accuracythe required from accuracy the generated from th DTMse generated according DTMs to according our purpose. to our After purpose. removing After removingthe blunders the blunders with applying with applying distance-based distance-based statistical statistical outlier outlier removal removal filter, wefilter, ran we a SOR-likeran a SOR-like filter filteralgorithm algorithm for further for further denoising denoising of the of point the cloudpoint cl dataoud in data order in toorder obtain to obtain higher higher accuracy accuracy DTM data DTM in dataresult in [ 46result]. The [46]. formulation The formulation of the denoisingof the denoisin algorithm,g algorithm, which waswhich applied was applied after distance-based after distance-based outlier outlierdetection detection filter, isfilter, similar is similar to the SORto the filter. SOR Asfilter. diff Aserent different from thefrom first the step, first thestep, denoising the denoising filter takesfilter takesthe height the height differences differences among among the points the points into account into account instead instead of the distancesof the distances and remove and remove the points the pointshaving having the height the height difference differenc exceedinge exceeding the threshold the threshold value (valuehmax. =(ℎµ.+ n=𝜇+𝑛.𝜎.σ, where, µwhereis the average𝜇 is the averagevalue of value height of di heightfferences, differences,n is multiplier 𝑛 is multiplier constant, constant,σ is the standard 𝜎 is the deviationstandard ofdeviation height diofff erenceheight differencefrom their from average their value). average In applying value). In the applying denoising the filter, denoising the number filter, ofthe points number in the of neighborhoodpoints in the neighborhoodwas chosen 6 andwas thechosen multiplier 6 and the constant multiplier was 1constant too. was 1 too. After removing the the blunders and and denoising denoising the the data, data, the the number number of of points in in the point cloud decreased. As As an an example, example, in in the the point point cloud cloud de derivedrived from from UAV UAV photogrammetric photogrammetric imagery, imagery, while the number of points was 23,175,329 in the original data dataset,set, it reduced to 18,231,092 after filtering. filtering. Thus, Thus, 21% of all points were removed with filtering.filtering. Afte Afterr the stochastic-based filtering, filtering, which was carried out automatically using using SOR SOR and denoising filters filters in CloudCompare software modules, the remained points in in both both point point cloud cloud datasets datasets were were also also visua visuallylly detected detected once onceagain again and a andfew more a few points, more points,which werewhich suspected were suspected to be outliers, to be outliers, were removed were removed manually manually using the using same the software. same software. The point The cloud point in viewcloud of in the view vertical of the section vertical before section (a) and before after (a) (b and) the afterautomatic (b) the and automatic manual (c) and cleaning manual processes (c) cleaning are shownprocesses in Figure are shown 8 [46]. in This Figure visualization8[ 46]. This gives visualization an idea of the gives success an idea of the of applied the success filters of and the the applied need forfilters manual and theintervention need for manualafter automatic intervention cleaning after of automatic the data. cleaning of the data.

(a) (b)

Figure 8. Cont.

ISPRS Int. J. Geo-Inf. 2020, 9, 528 13 of 26 ISPRSISPRS Int.Int. J.J. Geo-Inf.Geo-Inf. 2020,, 9,, xx FORFOR PEERPEER REVIEWREVIEW 13 13 ofof 2626

((c))

Figure 8. Point cloud in view of vertical section. (a) Before (legend on figure shows the SOR filter Figure 8. Point cloud in view of vertical section. (a)) BeforeBefore (legend(legend onon figurefigure showsshows thethe SORSOR filterfilter parameters used as k = 6 and n = 1); (b) after the automatic filtering; (c) manual cleaning processes. parameters used as 𝑘 = = 66 andand 𝑛 == 1);1); ((b)) afterafter thethe automaticautomatic filtering;filtering; (c)(c) manual cleaning processes. Following the filtering and denoising processes of the point clouds, the DTMs from aerial LiDAR Following the filtering and denoising processes of the point clouds, the DTMs from aerial LiDAR and UAV photogrammetry point clouds were generated separately in raster (*.geotiff) format. In this and UAV photogrammetry point clouds were generated separately in raster (*.geotiff) format. In this stage, the DTM generation process was carried out through different filter algorithms and obtained stage, the DTM generation process was carried out throughthrough differentdifferent filterfilter algorithmsalgorithms andand obtainedobtained results were assessed in order to clarify the difference between the applied algorithms by means results were assessed in order to clarify the difference between the applied algorithms by means of of calculated geoid heights [40,47]. As was mentioned above, in the piecewise generation of the calculated geoid heights [40,47]. As was mentioned above, in the piecewise generation of the DTMs, DTMs, the artifacts occurred along the tile boundaries on the DTM pattern (see Figure9). Because of thethe artifactsartifacts occurredoccurred alongalong thethe tiletile boundariesboundaries onon thethe DTMDTM patternpattern (see(see FigureFigure 9).9). BecauseBecause ofof thesethese these artifacts, in a second trial, the piecewise point cloud datasets were combined after filtering and artifacts, in a second trial, the piecewise point cloud datasets were combined after filtering and denoising processes and then the DTMs were generated using point clouds as a whole in the study denoising processes and then the DTMs were generated using point clouds as a whole in the study area. In order to optimize the computational time and computer processor usage, the point densities of area. In order to optimize the computational time and computer processor usage, the point densities the point clouds were partly decreased [46]. of the point clouds were partly decreased [46].

Figure 9. DigitalDigital terrainterrain modelmodel (DTM)(DTM) generatedgenerated usingusing partitionedpartitioned pointpoint cloudsclouds andand combinedcombined usingusing Global Mapper software, artifact of interpolation process alongalong thethe tiletile boundariesboundaries areare recognized.recognized.

InIn thethe classification classificationclassification forfor DTM DTM generation,generation, first,first, first, th thethe progressive densification densification filter filter with adaptive triangulatedtriangulated irregularirregular irregular networknetwork network (ATIN)(ATIN) (ATIN) algorithmalgorithm waswas was appliedapplied applied usingusing using EnviEnvi Envi LiDARLiDAR LiDAR softwaresoftware software [22].[22]. [22]. Following the generation generation of of DTMs DTMs from from both both ae aerialrial LiDAR LiDAR and and UAV UAV photogrammetry point clouds using Envi LiDAR software, the same production was repeated with morphologic filter by using Global Mapper software [22,40].

ISPRS Int. J. Geo-Inf. 2020, 9, 528 14 of 26 using Envi LiDAR software, the same production was repeated with morphologic filter by using Global ISPRS Int. J. Geo-Inf. 2020, 9, x FOR PEER REVIEW 14 of 26 Mapper software [22,40]. Basically,Basically, inin thethe progressive progressive densification densification filter filter with with the ATINthe ATIN algorithm, algorithm, the study the areastudy is dividedarea is dividedinto subareas into subareas and the minimumand the minimum elevation elevation is locally is determined. locally determined. The points The with points minimum with minimum elevation elevationare assumed are assumed to be ground to be surface ground points surface (bare points topography (bare topography surface). surface). Then triangulated Then triangulated irregular irregularnetwork (TIN)network isgenerated (TIN) is generated using the Delaunayusing the triangulationDelaunay triangulation method. Considering method. Considering the distance the of distancea point (butof a exceptpoint (but the seedexcept point) the inseed a Delaunaypoint) in cella Delaunay to the TIN cell surface to the (TIN∆h) andsurface the widest(∆ℎ) and of the the three angles (αi) with the TIN surface (see Figure 10), it is decided whether to keep or remove the point widest of the three angles (𝛼) with the TIN surface (see Figure 10), it is decided whether to keep or (pc). In order to make this decision, the distance and angle at the point in question are compared with remove the point (𝑝). In order to make this decision, the distance and angle at the point in question arepredefined compared threshold with predefined values. If the threshold compared values. values areIf the smaller compared than the values threshold are values,smaller the than point the is thresholdassumed asvalues, the ground the point point. is assumed This filtering as the algorithm ground point. is an iterativeThis filtering process algorithm and each is timean iterative when a processpoint is removedand each fromtime the when ground a point points is dataset,removed the from TIN isthe regenerated, ground points and thedataset, process the continues TIN is regenerated,until all points and are the classified process ascontinues ground oruntil object all points detail are [48]. classified as ground or object detail [48].

FigureFigure 10. 10. DefinitionDefinition of of height height difference difference (∆ℎ (∆)h )and and the the angles angles (𝛼 (α) iused) used as asmeasures measures to todetermine determine if

theif the point point (𝑝 (p) cin) inquestion question is isa aground ground point point in in adaptive adaptive triangulated triangulated irregular irregular network network (ATIN) (ATIN) algorithmalgorithm [48]. [48].

BesideBeside of of the the progressive progressive densification, densification, the the morpho morphologiclogic filter filter that that we we a appliedpplied in in DTM DTM generation generation withwith Global Global Mapper Mapper software, software, is is also also mentioned mentioned in in four four filtering filtering algorithm algorithm categories categories given given in in [48]. [48]. MorphologicMorphologic filtering filtering algorithm algorithm bases bases on on mathematic mathematicalal morphology morphology principles principles and andmainly mainly uses usestwo two operations, erosion ( ) and dilation ( ). According to the sequential use of these operators, operations, erosion (⊖) and dilation (⊕). According⊕ to the sequential use of these operators, closing (erosion-dilation)closing (erosion-dilation) and opening and opening (dilation-erosion) (dilation-erosion) operations operations are areapplied. applied. In Inthe the progressive morphologicmorphologic filtering filtering algorithm, algorithm, the the points points having having minimum minimum height height values values in a inwindow a window are chosen are chosen and anand approximate an approximate surface surface as geometric as geometric locations locations of th ofese these points points is determined. is determined. Secondary Secondary surfaces surfaces are generatedare generated by carrying by carrying out an out opening an opening operation operation to th toe initially the initially described described surface. surface. The Thetwo twosurfaces surfaces are are compared considering a threshold value (∆hmax.) and the points below the threshold value are compared considering a threshold value ( ∆ℎ. ) and the points below the threshold value are categorizedcategorized as as ground ground points. points. Not Not only only the the height height difference difference threshold threshold value, value, but also but alsothe window the window size selectionsize selection is also is critical also critical to achieving to achieving good results good resultsin a morphologic in a morphologic filter. The filter. size Theof the size selected of the window selected canwindow be enlarged can be according enlarged according to the size to of the the size largest of the ob largestject in the object workspace in the workspace in order to in detect order and to detect filter theand non-ground filter the non-ground objects effectively objects e ff[49].ectively In practice [49]. In, practice,along the along filtering the filteringprocess, process,the window the window size is increasedsize is increased gradually. gradually. Because Because the morphologic the morphologic filter wi filterth fixed with window fixed window size is size capable is capable to detect to detect and removeand remove the measurements the measurements for the for buildings the buildings and trees and from trees the from point the cloud point data, cloud however, data, however, it is difficult it is todi ffidetectcult toall detect non-ground all non-ground objects objectshaving havingvarious various sizes. Increasing sizes. Increasing the window the window size is size a solution is a solution for increasingfor increasing the effectiveness the effectiveness of the of filter. the filter.The ground The ground points pointsare differentiated are differentiated by comparing by comparing the points’ the valuepoints’ with value the withthreshold. the threshold. The height The difference height threshold difference can threshold be determined can be determinedconsidering the considering slope of topographythe slope of in topography a study area. in Assuming a study area. the slope Assuming as constant, the slope the relation as constant, between the the relation maximum between height the difference (𝑑ℎ(), ) for the terrain (𝑡), window size (𝑤 ) at 𝑘 iteration and terrain slope (𝑠) is formulated as:

𝑑ℎ(), 𝑠= (𝑤 −𝑤) (5) 2

ISPRS Int. J. Geo-Inf. 2020, 9, 528 15 of 26

th maximum height difference (dhmax(t),k) for the terrain (t), window size (wk) at k iteration and terrain slope (s) is formulated as: dhmax(t),k s = (5) (wk wk 1) −2 − and accordingly, the height difference threshold dhT,k is:   dh0, i f wk 3  ≤ dh =  s(w w )c + dh , i f w > 3 (6) T,k  k k 1 0 k  − − dhmax, i f dhT,k > dhmax where dh0 is the initial height difference threshold, s is the slope, c is the cell size and dhmax is the maximum height difference threshold [49]. Applying the addressed classification filters, the DEMs (DTMI and DTMII) with 1-m grid resolution covering the entire study area were generated from aerial LiDAR and UAV photogrammetry point cloud data, respectively, using Envi LiDAR (the progressive densification filter with ATIN algorithm) and Global Mapper software (progressive morphologic filtering algorithm). In the results, Global Mapper software was found more successful in extracting and removing the artificial objects in order to obtain the DTMs. The superior accuracy of DTMs, generated with the Global Mapper Software and the morphologic filter is clear in the statistics from the local geoid model test results (please see in Section3).

2.5. Regional Geoid Models Used in Validations Geoid models can be determined using one of a few methods given in the literature and available to the users either as an analytical function or as a raster form [10]. In geodetic applications the geoid height parameters (N) obtained from a suitable geoid model are used for various purposes including the transformation of GNSS ellipsoidal heights to the physical heights that are in the regional vertical datum, calculating corrections and reductions of the terrestrial observations to a reference surface, inspecting the Earth’s interior, observing and predicting Earth-mass transfer, etc. As depending on the required accuracy of height information, an appropriate geoid model is chosen and used in computations. In many engineering projects, geodetic infrastructure establishment studies and large scale mapping applications, the required geoid model accuracy is lower than 5 cm, whereas in studies such as in geographic information system establishment, archeological surveys, forest applications, a geoid model with decimeter or sub-decimeter level accuracy may satisfy the required vertical accuracy [50]. Parallel to the advances in GNSS techniques and their use in mapping and surveying applications, many countries serve the high-accuracy regional geoid model to the practitioners and surveyors as part of their national geodetic infrastructure in order to support and increase the efficiency of satellite-based positioning techniques in geodetic and surveying applications [51,52]. In Turkey where the study area is located in the west of the country (Figure1), the accuracy of the most recent publicly available regional geoid model (Turkey Geoid 2003– TG03) is ~ 8.0 cm. This accuracy is not sufficient for the large scale maps and spatial data production studies and most of the engineering projects [14]. TG03 is one of the geoid models that was used in this study. It was compared with the derived geoid models from generated DTMs in gridwise and pointwise formats, respectively. The TG03 model was calculated by the general directorate of mapping and released to the civilian users as the most recent official regional geoid model of Turkey in 3 arc-minute resolution grid data. This model was calculated using the remove-compute-restore (RCR) method with the least-squares-collocation (LSC). The used data included the terrestrial gravity observations distributed over the country having ~7–8 mGal accuracy and ~30 arc-second spatial resolution in modified Potsdam gravity datum [53,54]. In addition, the marine gravity data derived from satellite altimetry products by ERS1, ERS2, and TOPEX/POSEIDON satellite observations at the surrounding seas were employed ISPRS Int. J. Geo-Inf. 2020, 9, 528 16 of 26 to complete the land gravity dataset in computations. EGM96 with harmonic expansion degree `max. = 360◦ was used as a reference geopotential model for TG03 [55]. In order to consider the high-frequency contribution of the topographic masses in the model, the DTM data having 450-m spatial resolution grids on land and dense bathymetry data in shoreline areas were employed [53]. Involving a number of GNSS/leveling data sparsely distributed over the country in computations, the geoid heights by TG03 model fitted to the ITRF96 coordinate datum and the regional vertical datum of Turkey (TUDKA99). The geoid height values at the scattered geoid control points (see in Figure7) were interpolated from the TG03 grid nodes using the inverse distance weighting method and compared with calculated geoid heights derived from the local geoid models by DTMs differences [56]. Since the TG03 model has already been served as grid-data, the comparison results of the local geoid models in grid form with the TG03 model were easily generated at grid nodes and visualized as “geoid height difference surfaces” in Section3. In certain applications where decimeter level geoid model accuracy is sufficient, global geopotential models (N N ) may provide the required accuracy. Global geopotential models are released ≈ GGM as spherical harmonic expansion equations with coefficients up to certain degree/order (d/o). The accuracies of these global models were significantly improved since 2000 with data contribution of Earth gravity field satellite missions, namely CHAMP, GRACE, GOCE and recently GRACE-FO [57]. Equation (7) provides the mathematical formulation of the geoid height value by means of spherical harmonic expansion coefficients [9].

` ` GM Xmaxa` X  N = ∆C cosmλ + S sinmλ P ( cosθ) (7) GGM rγ r `m `m `m `=2 m=0 where (θ, λ, r) are co-latitude, longitude and geocentric radius of the computation point, respectively; a is the major axis radius of the reference ellipsoid; GM is the product of the gravitational constant and the mass of the Earth; ∆C`m and S`m are the fully normalized spherical harmonic coefficients, related to the normal potential of the reference ellipsoid from a specific degree of ` and order m, P`m( cosθ) are the fully normalized associated Legendre functions. The global geopotential models with their spherical harmonic coefficients are obtained from a number of international data centers. The International Center for Global Earth Models (ICGEM) serves an almost complete list of the geopotential models, which were released since 1966 [15]. In numeric tests of this study, one of the high-resolution geopotential models, EIGEN6C4 (`max.=2194) (EIGEN=”European improved gravity model of the earth by new techniques”), was evaluated and compared with the local geoid model derived from the photogrammetric techniques [58]. The spatial resolution of the model corresponding to its maximum expansion degree is ~9 km. In the maximum expansion degree, its reported accuracy by means of RMSE of geoid height differences in Turkey is ~12 cm [57]. In the numeric tests of the study, EIGEN6C4 (with d/o of 2194) was employed and the geoid heights (Equation (7)) from the model were calculated both at the geoid control points (Figure7) as well as at the grid nodes for surface-based comparisons. In calculation with the geopotential model, ICGEM calculation service was used [15]. The calculated geoid heights referenced to the ITRF datum (GRS80 reference ellipsoid), in order that they were comparable with the local geoid models by the photogrammetric techniques. After calculating the geoid models, another critical process is validating their accuracy using independent data and appropriate method before releasing these models to the users. Independent high-accuracy ground datasets are required to evaluate their external accuracy. In this purpose high-accuracy GNSS/leveling data, astrogeodetic deflections of vertical values, as well as sea-level observations at tide-gauge stations (for validations along the coastline) are commonly used [12]. However, local geoid data derived from the photogrammetric techniques have not been employed for either determination or validation of the geoid models so far. In this manner, the numeric tests, which were carried out for clarifying the usability of the DTMs derived from the photogrammetric techniques ISPRS Int. J. Geo-Inf. 2020, 9, 528 17 of 26 in geoid modeling and validations make an original contribution to the geoid determination studies. The following chapter discusses the obtained results from the numeric tests of local geoids by aerial LiDAR and UAV photogrammetry DTMs.

3. Results and Discussion

3.1. Local Geoid Model Accuracy Evaluation According to DEM Generation Strategy In the first part of the numeric tests, the DTMs from point clouds were generated for local geoid model determination. In their generation, two different filtering algorithms were used in the classification. One of the algorithms was the progressive densification filter with the ATIN algorithm, applied using Envi LiDAR software [47]. The other was the progressive morphologic filtering algorithm applied using Global Mapper GIS software [40]. In results, the two DTMs by aerial LiDAR data were in hand for obtaining the ellipsoidal heights of the terrain points. On the other hand, the two DTMs by UAV photogrammetric imagery were for providing the orthometric heights of the same points in TUDKA99ISPRS Int. J. datum.Geo-Inf. 2020 Accordingly,, 9, x FOR PEER two REVIEW local geoid surface models were generated using the DTM-couples 17 of 26 (N = h HDTM ) by Envi LiDAR and Global Mapper outputs, respectively. DTMI − II algorithmFigure applied11 shows using the calculatedGlobal Mapper local geoid GIS software surfaces [40]. using In DTMs results, generated the two byDTMs Envi by LiDAR aerial (a) LiDAR and Globaldata were Mapper in hand (b), for respectively. obtaining Tablethe ellipsoidal2 gives the heights statistics of the of theterrain calculated points. localOn the geoid other heights hand, atthe grid two nodesDTMs (1-m by UAV spatial photogrammetric resolution) along imagery with the were whole for test providing site. However, the orthometric considering heights the geoid of the model same surfacespoints in in TUDKA99 Figure 11 and datum. their Accord maximum,ingly, minimum two local values geoid insurface Table2 mo, itdels was concludedwere generated that the using geoid the models,DTM-couples derived (𝑁=ℎ from two −𝐻 different) by software, Envi LiDAR included and blunders.Global Mapper Thus, outputs, blunder respectively. detection with one sigmaFigure (1-σ) test 11 shows was applied the calculated and the local geoid geoid height surfac values,es using which DTMs deviate generated from the by meanEnvi LiDAR geoid height(a) and valueGlobal in Mapper the area (b), more respectively. than 1-σ (corresponds Table 2 gives to the keep statis thetics points of the having calculated geoid heightlocal geoid values heights within at 68% grid confidencenodes (1-m interval), spatial resolution) were removed along from with each the dataset.whole test The site. geoid However, height surfaces considering after the geoid 1-σ test model and theirsurfaces statistics in Figure are given 11 and in their Figure ma 12ximum, and Table minimum3, respectively. values in Table 2, it was concluded that the geoid models,When derived the obtained from two statistics different in Tables software,2 and 3incl areuded compared, blunders. it is Thus, seen that blun removingder detection the blunders with one usingsigma 1- (1-σ test𝜎) test succeeded was applied and theand two the localgeoid geoid height model values surfaces, which by deviate Envi LiDARfrom the and mean Global geoid Mapper height arevalue closer in the to eacharea othermore now.than 1- However,𝜎 (corresponds comparing to keep the the statistics points of ha twoving geoid geoid model height surfaces values within in Table 68%3, theconfidence distribution interval), of geoid were heights removed by from means each of theirdataset. standard The geoid deviations height surfaces differs withafter ~4.1the 1- cm𝜎 test that and is actuallytheir statistics significant are given for local in Figure geoid 12 modeling and Table purposes 3, respectively. in geodetic applications.

(a) (b)

Figure 11. Before removing blunders with 1-σ test: Local geoid surfaces using DTMs generated by Figure 11. Before removing blunders with 1-𝜎 test: Local geoid surfaces using DTMs generated by (a) (a) Envi LiDAR and (b) Global Mapper. Envi LiDAR and (b) Global Mapper. Table 2. Statistics of calculated geoid heights from models using Envi LiDAR and Global Mapper softwareTable 2. over Statistics the whole of calculated test site (m).geoid heights from models using Envi LiDAR and Global Mapper software over the whole test site (m). Geoid Model by Minimum Maximum Mean Std. Deviation Geoid Model by Minimum Maximum Mean Std. Deviation Envi LiDAR 26.099 48.610 38.506 0.481 EnviGlobal LiDAR Mapper 26.0995.925 48.61050.567 38.507 38.506 0.291 0.481 Global Mapper −5.925− 50.567 38.507 0.291

When the obtained statistics in Tables 2 and 3 are compared, it is seen that removing the blunders using 1-𝜎 test succeeded and the two local geoid model surfaces by Envi LiDAR and Global Mapper are closer to each other now. However, comparing the statistics of two geoid model surfaces in Table 3, the distribution of geoid heights by means of their standard deviations differs with ∼4.1 cm that is actually significant for local geoid modeling purposes in geodetic applications. In the last row of Table 3, the statistics of geoid heights derived at scattered geoid control points that their distribution is seen in Figure 7, are given. The geoid heights at these geoid control points were calculated with interpolation from the local geoid surface model by the Global Mapper grid-wise solution.

ISPRS Int. J. Geo-Inf. 2020, 9, 528 18 of 26 ISPRS Int. J. Geo-Inf. 2020, 9, x FOR PEER REVIEW 18 of 26

(a) (b)

(c)

Figure 12. After removing blunders with 1-σ test: The gridwise local geoid surfaces generated using Figure 12. After removing blunders with 1-𝜎 test: The gridwise local geoid surfaces generated using DTMs by (a) Envi LiDAR and (b) Global Mapper and (c) the pointwise local geoid surface (interpolated DTMs by (a) Envi LiDAR and (b) Global Mapper and (c) the pointwise local geoid surface from Global Mapper grid-wise geoid model in geoid control points and gridded by Surfer software (interpolated from Global Mapper grid-wise geoid model in geoid control points and gridded by Kriging approach). Surfer software Kriging approach). Table 3. After removing blunders with 1-σ test: the statistics of calculated geoid heights from models Tableusing 3. Envi After LiDAR removing and Global blunders Mapper with 1- software𝜎 test: the over statistics the whole of calculated test site and geoid point-wise heights geoidfrom models heights usinginterpolated Envi LiDAR from Globaland Global Mapper Mapper grid-wise software solution over the (m). whole test site and point-wise geoid heights interpolated from Global Mapper grid-wise solution (m). Geoid Model by Minimum Maximum Mean Std. Deviation GeoidEnvi Model LiDAR by Minimum 38.029 Maxi38.979mum 38.552Mean Std.0.143 Deviation EnviGlobal LiDAR Mapper 38.029 38.215 38.97938.798 38.533 38.552 0.102 0.143 Globalpoint-wise Mapper 38.215 38.424 38.79838.691 38.572 38.533 0.055 0.102 point-wise 38.424 38.691 38.572 0.055 In the last row of Table3, the statistics of geoid heights derived at scattered geoid control pointsIn thatFigure their 12c, distribution the pointwise is seen local in Figure geoid7 ,surfac are given.e is shown. The geoid This heights surface at thesewas generated geoid control by interpolatingpoints werecalculated the geoid withheight interpolation values at the from scattered the local geoid geoid control surface points model given by the in Global Figure Mapper 7. In calculatinggrid-wise solution. the surface model, the geostatistical Kriging algorithm in Surfer software was applied. FromIn this Figure figure, 12 thec, thechange pointwise amount local and geoid slope surfacedirection is of shown. the local This geoid surface surface was are generated recognized. by Thisinterpolating pattern of the the geoid local height geoid values surface at the derived scattered from geoid photogrammetric control points given approaches in Figure 7was. In calculatingcompared withthe surfacethe regional model, geoid the model geostatistical (TG03) Kriging(the TG03 algorithm geoid model in Surfer surface software is shown was in Figure applied. 13a) From and thisthe globalfigure, geoid the change model amount (EIGEN6C4) and slope (global direction geoid of mode the locall surface geoid in surface Figure are 13b). recognized. Compared This Figures pattern 12 of andthe local13, it geoidis seen surface that all derivedthree geoid from surface photogrammetric models have approachesthe same characteristic was compared trend, with but the in regionalvarying levelsgeoid of model details. (TG03) Because (the TG03 the local geoid geoid model surface surface is ismore shown detailed in Figure (Figure 13a) and12c) theand global the compared geoid model to local(EIGEN6C4) geoid, the (global regional geoid geoid model surface surface is smoother in Figure 13(Figureb). Compared 13a) and Figuresthe global 12 andgeoid 13 ,model it is seen surface that allis naturallythree geoid the surface least detailed models havesurface the model same characteristic(Figure 13b) trend,in the butconsidered in varying area. levels Since of details.this figure Because was generated as depending on rather dense data points, the smooth character of the local geoid surface can hardly be recognized in Figure 12c. When Figure 7, Figure 12c and Figure 13a,b are considered

ISPRS Int. J. Geo-Inf. 2020, 9, 528 19 of 26 the local geoid surface is more detailed (Figure 12c) and the compared to local geoid, the regional geoid surface is smoother (Figure 13a) and the global geoid model surface is naturally the least detailed surface model (Figure 13b) in the considered area. Since this figure was generated as depending on rather dense data points, the smooth character of the local geoid surface can hardly be recognized in ISPRS Int. J. Geo-Inf. 2020, 9, x FOR PEER REVIEW 19 of 26 Figure 12c. When Figures7, 12c and 13a,b are considered together, it is confirmed that the descending together,trend of the it is geoid confirmed surface that from the north descending to south tren followsd of thethe topographicgeoid surface heights from shownnorth to in south Figure follows7 with thechanging topographic colors ofheights the point shown symbols. in Figure 7 with changing colors of the point symbols.

(a) (b)

Figure 13. GeoidGeoid model model surfaces, surfaces, used used in in validation validation of of local local geoid geoid models generated with Photogrammetric methods. ( (aa)) Regional Regional geoid geoid model model (TG03) (TG03) surface; surface; ( (b)) global geopotential model (EIGEN6C4) surface.

3.2. Comparisons Comparisons of Local Geoid Models by the PhotogrammetricPhotogrammetric Techniques withwith RegionalRegional andand GlobalGlobalGeoids GeoidsIn the second part of the numeric tests, the local geoid models generated using the photogrammetric techniquesIn the weresecond compared part of withthe regionalnumeric geoidtests, model,the local TG03 geoid and models a global generated geopotential using model, the photogrammetricEIGEN6C4 (`max. = techniques2194), and statisticswere compared obtained fromwith these regional comparisons geoid clarifymodel, the TG03 fitting and performance a global of the compared models each other. Erol et al. [54] tests the TG03 model using high-accuracy geopotential model, EIGEN6C4 (ℓ. = 2194), and statistics obtained from these comparisons clarify theGNSS fitting/leveling performance data in of a the larger compared area very models close each to ourother. test Erol site et al. and [54] reports tests the external TG03 model accuracy using of high-accuracyTG03 ~8.0 cm inGNSS/leveling terms of RMSE data of in geoid a larger height area di ffveryerences close at to GNSS our /levelingtest site and benchmarks. reports external Erol et accuracyal. [57] validates of TG03 a∼8.0 high cm resolution in terms of geopotential RMSE of geoid model, height EGM2008 differences (`max at. =GNSS/leveling2194) [59], using benchmarks. the same GNSS/leveling dataset in the area close to the Bergama test site and reports its external accuracy as Erol et al. [57] validates a high resolution geopotential model, EGM2008 (ℓ. = 2194) [59], using the ~12.0same cmGNSS/leveling by means of dataset RMSE. in Although the area theclose external to the Bergama accuracy test of the site EIGEN6C4 and reports has its not external been published accuracy asin this∼12.0 article cm by [57 means], in its of preparation, RMSE. Although this geopotential the external model accuracy having of equalthe EIGEN6C4 expansion has degree not/ orderbeen publishedwith EGM2008 in this has article been validated [57], in its as well.preparation, In the unpublished this geopotential results, model it has beenhaving seen equal that EIGEN6C4expansion degree/orderrevealed almost with the EGM2008 same accuracy has been with validated EGM2008. as well. The reasonsIn the unpublished for these two results, global it models has been having seen thatsimilar EIGEN6C4 accuracies revealed is that the almost spherical the same harmonic accuracy expansion with EGM2008. degrees of The both reasons geopotential for these models two areglobal the modelssame and having almost similar datasetsaccuracies were is usedthat inthe their spherical calculations. harmonic As a conclusion expansion of degrees this, we assumedof both geopotentialthe external accuracymodels are of EIGEN6C4the same and model almost as ~12.0 simila cmr datasets in the test were site used in this in study their ascalculations. well. As a conclusionThe accuracy of this, we ofthe assumed ellipsoidal the exte heightsrnal accuracy obtained of from EIGEN6C4 the aerial model LiDAR as ∼ point12.0 cm cloud in the is reported test site inas this 7.0 study cm in as [13 well.]. Regarding the personal communication with the data provider of the UAV photogrammetricThe accuracy imagery of the ellipsoidal point cloud, heights the accuracy obtained of from the orthometric the aerial LiDAR heights point obtained cloud from is reported the UAV asphotogrammetry 7.0 cm in [13]. point Regarding cloud isthe ~5–6 personal cm. According communication to known with accuracies the data of theprovider data, weof estimatedthe UAV the accuracy of geoid heights generated using local geoid models with error propagation principles: photogrammetricq imagery point cloud, the accuracy of the orthometric heights obtained from the = 2 + 2 ∼ UAVσN photogrammetryσh σH = ~9.2 cm.point In thiscloud case, is the5–6 local cm. geoidAccording models to calculatedknown accuracies in this study of the are data, assumed we estimatedcomparable the with accuracy TG03 of and geoid EIGEN6C4 heights generated models by using means local of geoid accuracy models and with have error the capability propagation for ∼ principles:validating these𝜎 =𝜎 regional +𝜎 and = global9.2 cm. models. In this case, the local geoid models calculated in this study are assumedFigure comparable 14 shows the with diff erenceTG03 betweenand EIGEN6C4 the generated models local by geoids means from of twoaccuracy software and and have regional the capabilitygeoid (TG03) for modelvalidating surfaces. these In regional Figure 14 anda TG03 global model models. surface is compared with the Envi LiDAR local Figure 14 shows the difference between the generated local geoids from two software and regional geoid (TG03) model surfaces. In Figure 14a TG03 model surface is compared with the Envi LiDAR local geoid surface and in (b) it is compared with the Global Mapper local geoid surface. Comparing the geoid height differences maps and considering the distribution of the differences over the area, we can say that the local geoid surface calculated with Global Mapper software fits the TG03 model surface better. This result is confirmed by the fitting statistics given in Table 4. The mean values of differences show that the local geoid surfaces do not include a systematic shift from TG03 and their datums are

ISPRS Int. J. Geo-Inf. 2020, 9, 528 20 of 26 geoid surface and in (b) it is compared with the Global Mapper local geoid surface. Comparing the geoid height differences maps and considering the distribution of the differences over the area, we can say that the local geoid surface calculated with Global Mapper software fits the TG03 model surface better. This result is confirmed by the fitting statistics given in Table4. The mean values of di fferences showISPRS that Int. the J. Geo-Inf. local 2020 geoid, 9, x surfacesFOR PEER REVIEW do not include a systematic shift from TG03 and their datums 20 of 26 are quiteISPRS compatible. Int. J. Geo-Inf. The 2020 last, 9, x FOR row PEER of Table REVIEW4 shows the statistics of interpolated geoid height di 20ff oferences 26 quite compatible. The last row of Table 4 shows the statistics of interpolated geoid height differences between the local geoid model (Global Mapper grid-wise model) and TG03 at the selected control quitebetween compatible. the local Thegeoid last model row of (Global Table 4Mapper shows thegrid statistics-wise model) of interpolated and TG03 geoid at the height selected differences control points. Comparing with the results obtained from the grid-wise local geoid model (having 9.8 cm betweenpoints. Comparing the local geoid with modelthe results (Global obtained Mapper from grid the-wise grid-wise model) local and geoidTG03 atmodel the selected(having control9.8 cm standardstandardpoints. deviation Comparing deviation and andwith -1.0 -1.0 thecm cm results mean valuesobtained values for for fromgeoi geoidd the height heightgrid-wise differences di fflocalerences of geoid Global of model Global mapper (having mapper solution 9.8 solutionandcm andTG03),standard it it wasdeviation was seen seen that and that the -1.0 thepoint-wise cm point-wise mean values local localgeoid for geoi geoid modeld height model solution differences solution has a better of has Global fit a betterwith mapper the fit regional with solution the geoid and regional geoidmodelTG03), model TG03it was TG03 (with seen (with that4.6 cm the 4.6 standard point-wise cm standard deviation local deviation geoid and model −5.9 and cm solution mean5.9 cmvalues). has mean a better values). fit with the regional geoid − model TG03 (with 4.6 cm standard deviation and −5.9 cm mean values).

(a) (b) (a) (b) FigureFigure 14. 14.Diff Differenceserences between between calculated calculated locallocal geoids and and TG03 TG03 regional regional geoid geoid surfaces surfaces with with (a) Envi (a) Envi LiDAR;FigureLiDAR; (b) 14. Global(b )Differences Global Mapper. Mapper. between calculated local geoids and TG03 regional geoid surfaces with (a) Envi LiDAR; (b) Global Mapper. Table 4. Statistics of geoid height differences between local geoid models (Envi LiDAR and Global Table 4. Statistics of geoid height differences between local geoid models (Envi LiDAR and Global Mapper, respectively) and regional Turkey Geoid (TG03) (m). TableMapper, 4. Statisticsrespectively) of geoid and regionheightal differences Turkey Geoid between (TG03) local (m). geoid models (Envi LiDAR and Global Mapper, respectively) and regional Turkey Geoid (TG03) (m). Geoid HeightGeoid Di Heightfferences Differences Minimum Minimum Maximum Maximum Mean Mean Std. Dev. Std. Dev. Envi LiDARGeoidEnvi HeightTG03 LiDAR Differences − TG03 0.516 Minimum -0.516 0.573 Maximum 0.573 0.029− Mean0.029 Std.0.139 Dev.0.139 − − − Global MapperGlobalEnvi (GM) Mapper LiDARTG03 (GM) − TG03 − TG03 0.330 -0.330-0.516 0.386 0.3860.573 0.010−0.0290.010 0.1390.0980.098 − − − point-wiseGlobalpoint-wise (GM) MapperTG03 (GM) (GM) − TG03− TG03 0.156 -0.330-0.156 0.049 0.3860.049 0.059−0.0100.059 0.0980.0460.046 − − − point-wise (GM) − TG03 -0.156 0.049 −0.059 0.046 Similar comparisons were carried out using global geopotential model EIGEN6C4 as well. Similar comparisons were carried out using global geopotential model EIGEN6C4 as well. FigureSimilar 15 shows comparisons the difference were mapscarried between out using the localglobal geoid geopotential and global model geoid EIGEN6C4(EIGEN6C4) as model well. FiguresurfacesFigure 15 shows 15 for shows Envi the the LiDAR di ffdifferenceerence (a) and maps maps Global between between Mapper the (b)local local geoid geoid geoid and and solutions. global global geoid geoidThe (EIGEN6C4) statistics (EIGEN6C4) for modelgeoid model surfacessurfacesurfaces for and for Envi point-wiseEnvi LiDAR LiDAR comparisons (a) (a) and and Global Global are given MapperMapper in Table (b) local 5. geoid geoid solutions. solutions. The The statistics statistics for geoid for geoid surfacesurface and and point-wise point-wise comparisons comparisons are are given given inin Table 55..

(a) (b) (a) (b) Figure 15. Differences between calculated local geoids and EIGEN6C4 global geoid surfaces. (a) Envi FigureLiDAR;Figure 15. Di15. (bff )Differences erencesGlobal Mapper. between between calculated calculated locallocal geoids and and EIGEN6C4 EIGEN6C4 global global geoid geoid surfaces. surfaces. (a) Envi (a) Envi LiDAR;LiDAR; (b) Global(b) Global Mapper. Mapper.

ISPRS Int. J. Geo-Inf. 2020, 9, 528 21 of 26 ISPRS Int. J. Geo-Inf. 2020, 9, x FOR PEER REVIEW 21 of 26

TableTable 5. StatisticsStatistics of of geoid geoid height height differences differences between local local geoid geoid models models (Envi (Envi LiDAR LiDAR and and Global Global Mapper,Mapper, respectively) and glob globalal geoid (EIGEN6C4) (m).

GeoidGeoid Height Height Di ffDifferenceserences Minimum Minimum Maximum Maximum Mean Mean Std. Std. Dev. Dev. EnviEnvi LiDAR LiDAREIGEN6C4 − EIGEN6C4 0.454−0.454 0.6400.640 0.039 0.039 0.140 0.140 − − GlobalGlobal Mapper Mapper (GM) (GM)EIGEN6C4 − EIGEN6C4 0.272−0.272 0.4530.453 0.057 0.057 0.099 0.099 − − point-wise (GM) EIGEN6C4− 0.120 0.195 0.000 0.052 point-wise (GM)− EIGEN6C4 − −0.120 0.195 0.000 0.052

InIn test test results, results, the the fit fit of of the the global global geoid geoid model model to tothe the local local geoid geoid model model is slightly is slightly worse worse than than the regionalthe regional geoid geoid model. model. In point-wise In point-wise evaluation, evaluation, the the geoid geoid height height differences differences of of local local geoid geoid model model (interpolated(interpolated from from Global Global Mapper Mapper grid-wise grid-wise solution solution)) from from the the global global geoid geoid model model (EIGEN6C4) (EIGEN6C4) vary vary betweenbetween −12.012.0 cm cm and and 19.5 19.5 cm cm with 0.0-cm mean and 5.2-cm5.2-cm standard deviation. The The geoid height − differencesdifferences of of the the local local geoid geoid surface surface from from the the TG TG0303 and and EIGEN6C4, EIGEN6C4, respectively, respectively, at at the the geoid geoid control control points,points, are are shown shown in in Figure Figure 16. 16 .

(a) (b)

Figure 16. Point-wise distribution of geoid height differences of calculated local geoid model Figure 16. Point-wise distribution of geoid height differences of calculated local geoid model (interpolated from Global Mapper grid-wise solution) from (a) regional geoid (TG03); (b) global (interpolated from Global Mapper grid-wise solution) from (a) regional geoid (TG03); (b) global geoid geoid (EIGEN6C4) models. (EIGEN6C4) models. In Figures 14 and 15, considering the distribution of geoidal height differences of local geoid modelIn derivedFigures 14 by and the photogrammetric15, considering the methods distribution and regionalof geoidal/global height geoid differences models, of it islocal observed geoid modelthat the derived major dibyff erencesthe photogrammetric are cumulated methods in the urbanized and regional/global area. The reason geoid for models, this can it beis eitherobserved the thatcapability the major limitation differences of the are used cumulated software in in the generating urbanized the area. DTMs—or The reason the change for this in can topography be either duethe capabilityto the constructions limitation inof thethe regionused software between in the generating dates of the the airborne DTMs—or LiDAR the change and UAV in photogrammetrytopography due tomeasurement the constructions campaigns. in the region between the dates of the airborne LiDAR and UAV photogrammetry measurement campaigns. 3.3. Assessment of the Usability of Photogrammetric Techniques for Local Geoid Modeling 3.3. Assessment of the Usability of Photogrammetric Techniques for Local Geoid Modeling In literature, there are various studies reporting the vertical accuracy obtained from photogrammetricIn literature, methodsthere are based various on in situstudies validations. reporting Inthese the studies,vertical theaccuracy reported obtained accuracies from vary photogrammetricbetween centimeter methods to decimeter based depending on in situ onvalidations. the sensor’s In quality,these studie datas, processing the reported strategies, accuracies designed vary betweenmeasurement centimeter plan asto well decimeter as the conditionsdepending of on the the mapping sensor’s area quality, [23,30 ,data38,39 ,processing60,61]. The strategies, published designedstudies proved measurement that with plan an e ffiascient well optimizationas the conditions and feasibility of the mapping analysis area in projects, [23,30,38,39,60,61]. the error budget The publishedcan be professionally studies proved managed that inwith order an toefficient minimize opti themization systematic and andfeasibility random analysis errors in in measurements projects, the errorwith photogrammetricbudget can be professionally techniques. Hencemanaged minimizing in order theto minimize errors significantly the systematic improves and random the accuracy errors of inthe measurements derived 3D coordinates with photogrammetric from these techniques. techniques. Hence minimizing the errors significantly improvesWith the the accuracy increased of use the of derived GNSS techniques 3D coordinates in engineering from these applications, techniques. which base on spatial data and heightWith the information, increased theuse practicalof GNSS need techniques for a regional in engineering geoid model applications, emerged [62which]. The base point on physical spatial dataheights and are height determined information, with the transformationpractical need for of GNSSa regional ellipsoidal geoid model heights emerged using the [62]. geoid The model. point physicalAccuracy heights and spatial are determined resolution of with the employedthe transformation geoid model of GNSS has a dominantellipsoidal role heights in the using accuracy the geoid of the model.obtained Accuracy physical and heights spatial accordingly resolution [63 of]. Dependingthe employed on thegeoid used model modeling has a technique, dominant the role accuracy in the accuracy of the obtained physical heights accordingly [63]. Depending on the used modeling technique, the accuracy and spatial resolution of the geoid model vary. From a general point of view,

ISPRS Int. J. Geo-Inf. 2020, 9, 528 22 of 26 and spatial resolution of the geoid model vary. From a general point of view, the global geopotential models have an advantage to provide the geoid height in global, but the disadvantage with the sparse spatial resolution because of limited degrees of spherical harmonic expansion, thus limited accuracy as a result of the omitted spectral bands of the gravity field spectrum. Other than global geopotential models, regional geoid models determined using a gravimetric approach are commonly used. However, the accuracy of these models is affected by the quality of used gravity data in their computations. Required gravity data density and accuracy for determining a centimeter accuracy geoid model is discussed in [54]. Since the regional gravimetric geoid model does not provide sufficient accuracy in Turkey, in many surveying and mapping projects, local GNSS/leveling geoid models are offered and used as an alternative to gravimetric solution. [11] and [64] provide a discussion on the required accuracy and distribution of the GNSS/leveling control benchmarks for determining centimeter accuracy local geoid model. Each of these geodetic methods for calculating centimeter accuracy geoid model requires dense and precise terrestrial observations that are laborious, time-consuming and expensive. In challenging areas such as mountainous regions, dense forestry areas, large lakes and river basins, carrying out the terrestrial measurements for geoid modeling purposes is even impossible. Considering difficulties in terrestrial data acquisition for geoid modeling purpose, we suggested and investigated a novel approach where the photogrammetric techniques are used as an alternative for local geoid model determination and validation in this study. The high spatial resolution of the DTMs obtained from photogrammetric techniques is an advantage in geoid modeling in order to contain the full spectrum of geoid in the model. By means of accuracy, our results shown that using photogrammetric techniques, determining a local geoid model with an accuracy better than global geoid model is possible. The photogrammetric methods provide even higher accuracies in plain areas when they are compared with the accuracy of the regional gravimetric geoid models calculated with low accuracy and sparse terrestrial gravity data. In light of the drawn results in our study, it is concluded that the photogrammetric techniques have good potential for providing local geoid model solutions or validation data to the geoid modeling. However, in the present case, these technologies cannot be said to be the most appropriate option for the geoid modeling purpose. Further investigations are necessary to discover the utmost vertical accuracy limits of the DTMs, which are generated from the photogrammetric techniques, in order to make a final decision and suggest this novel approach to the professionals for modeling centimeter accuracy geoid in all types of topographic patterns.

4. Conclusions Integration of GNSS/INS sensors mounted on the aerial vehicles in photogrammetric applications brought the direct georeferencing opportunity, which made a positive impact on the implementation of these techniques. In the result of direct georeferencing, the DTMs are generated in the ellipsoidal height system. In order to transform the ellipsoidal heights of the generated DTMs to the physical height system, a precise geoid model is used. On the other hand, with indirect georeferencing, a high-resolution DTM can be generated in a specific height system, which is defined by the vertical datum of the ground control points. This is an advantage of indirect georeferencing and in this study, we benefitted from this advantage and employed the photogrammetric techniques in modeling the local geoid surfaces. Hence, we introduced a novel approach to the local geoid modeling studies. The main results of the study are summarized as follows:

Considering the DTMs accuracies, the difference between the local geoid model solutions by • two classification algorithms was insignificant, but anyway, the local geoid surface calculated in the result of morphologic filtering method fitted the TG03 and EIGEN6C4-geoid surfaces slightly better; In results of comparisons with TG03 and EIGEN6C4 geoids, the local geoid model in gridwise • format by morphologic filter has ~29% better fit by means of the standard deviation of geoid ISPRS Int. J. Geo-Inf. 2020, 9, 528 23 of 26

height differences (standard deviations for TG03, 13.9 cm vs. 9.8 cm and for EIGEN6C4, 14.0 cm vs. 9.9 cm); In pointwise comparison results, the local geoid surface model by using the morphologic filtering • algorithm fitted the TG03 model slightly better than the EIGEN6C4 model (standard deviations of geoid height differences: 4.6 cm vs. 5.2 cm); Considering the estimated accuracy of the local geoid surface model (~9.2 cm) by means of the • RMSE values of the ellipsoidal heights by DTMI and orthometric heights by DTMII, its performance in fitting to the regional TG03 and the global EIGEN6C4 in the test site was as expected; Aerial LiDAR and UAV photogrammetric methods provided local geoid model solution with an • accuracy equivalent to the regional TG03 and global high-resolution EIGEN6C4 models; Obtained accuracy is at almost 10 cm level, but it is not sufficient for large scale mapping and • engineering surveying applications that require a height accuracy better than 5 cm. Airborne LiDAR measurements are not economical to carry out in a project solely for the decimeter • level accuracy geoid model; However, if further studies focus on photogrammetric imagery as well as laser scanning • measurements by using UAV and special strategies are developed in order to improve height accuracies using these techniques, significant contribution to the determination and validation of local geoid models with photogrammetric techniques are expected. UAV-based photogrammetry techniques, LiDAR and imagery as well, are found promising for • the economic and precise solution of local geoid model determination problem in the future.

With possible improvements in height accuracies obtained from aerial and UAV-based photogrammetric techniques (LiDAR and imagery), the recommended approach for local geoid model solution in this study provides a contribution to the applications in small project areas with moderate topography. However, in larger areas with rough topography, photogrammetric solutions stay insufficient to model the detailed geoid and may cause aliasing error in the model.

Author Contributions: Conceptualization, Serdar Erol; methodology, Serdar Erol and Bihter Erol; software, Emrah Özögel and Ramazan Alper Kuçak; validation, Emrah Özögel, Serdar Erol and Ramazan Alper Kuçak; Formal Analysis, Emrah Özögel, Serdar Erol and Bihter Erol; investigation, Emrah Özögel; resources, Serdar Erol and Ramazan Alper Kuçak; data curation, Emrah Özögel, Serdar Erol and Bihter Erol; writing—original draft preparation, Bihter Erol; writing-review & editing, Serdar Erol and Bihter Erol; visualization, Serdar Erol; supervision, Serdar Erol; project administration, Serdar Erol; funding acquisition, Serdar Erol and Ramazan Alper Kuçak. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Acknowledgments: This research was carried out as part of the second author’s graduate thesis study (Council of Higher Education database no. 510451), which was prepared and successfully defended at Istanbul Technical University, Graduate School of Science Engineering and Technology. Part of the provided results in this article was presented by the authors in Turkish as a poster in 17th National Map and Cadastral Scientific and Technical Congress in April 2019. The airborne LiDAR data were provided by the general directorate of mapping and UAV data were provided by the General Directorate of geographic information systems of Turkey. DTM generation were carried out using Envi LiDAR and Global Mapper GIS Software. The point cloud data were prepared for DTM generation using CloudCompare Software. In statistical evaluation of the products, Surfer Golden Software was used. Global geopotential model was obtained from International Center for Global Earth Models (ICGEM) database. The authors acknowledge the editors and three anonymous reviewers for their valuable comments that significantly improved the quality of the manuscript. Conflicts of Interest: The authors declare no conflict of interest.

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