Investigating the Length, Area and Volume Measurement Accuracy in UAV-Based Oblique Photogrammetry Models produced with and without Ground Control Points

This study was aimed to investigate the performance and sensitivity of a 3D photogrammetric model generated without GCPs (Ground Control Points). To see if the models with no GCPs show the accuracy in every types of terrain as well as climate or metrological conditions, two separate studies are done in two areas with different characteristics such as Altitude, slope, topography, and meteorological varieties. The study areas were initially modelled with GCPs and later without GCPs. Furthermore, some of the dimensions and areas within the modelled area were measured using terrestrial techniques (with GPS/GNSS) for accuracy analysis. After modelling within the areas with and without GCPs, different territories with different slope and geometric shapes were selected. Various measurement in terms of length, area and volume carried out over the selected territories within both model (generated with and without GCPs) of each 2 studies. The datasets obtained as results of measurements were compared to each other and the measurements carried out over the models produced with GCPs were accepted as true values. Results from length measurement provided various level of success. First study area exhibited very promising results in length measurement with a relative error of less than 1% and RMSE (Root Mean Square Error) of 0.139m. In the case of area measurement, in the rst study area (Sivas), a minimum relative error of 0.04% and a maximum relative error of 1.05% with a RMSE of 1.264 m² is obtained. In the second study areas (Artvin) for area measurement a minimum relative error of 0.56% and a maximum relative error of 5.27% with a RMSE of 1.76m² is achieved. And nally, in the case of volume measurement, for st study area (Sivas) a minimum relative error of 0.8% and a maximum relative error of 6.8% as well as 2.301 m³ is calculated. For second study area (Artvin) minimum relative error for volume measurement is 0.502% as well as maximum relative error is 2.01% with a 7.061m³ RMSE.


Introduction
Photogrammetry and especially digital photogrammetry is a versatile tool for aerial surveys and is rapidly becoming the tool of election to generate 3D realistic models from 2D photos for different engineering projects. 3D modelling via Digital photogrammetry is based on combination of vertical and inclined imagery. Oblique photogrammetry offers improved capabilities for 3D reconstruction of different surfaces and terrains. 3D models obtained via oblique photogrammetry have widespread use in different engineering elds and this application area is expanding day by day due to recent advances in technology, hardware, and software development. Nowadays Digital photogrammetry has numerous potential applications in areas such as surveying, civil engineering, urban planning, architecture, archeology, mining, monitoring mass movements, industry, urban management, agriculture, real estate etc.
Digital photogrammetry or three-dimensional (3D) mapping which is the most famous discipline of the digital age is expanding quickly overall the world majorly due to low-cost facility for data acquisition and fast work ow. Basically, UAV photogrammetry makes possible three-dimensionally (3D) reconstruction of objects via two-dimension (2D) photos. Besides, a model produced via oblique photogrammetry does not aims just viewing and displaying but it also provides accurate geometric and spatial information about the object. In oblique photogrammetry UAV (unmanned aerial vehicle) also known as drone are used for aerial imagery. Recently UAV photogrammetry is used in different areas such as cultural heritage documentation [1,2] agriculture [3,4] architectural restoration [5,6], archeology [7,8], mining [9,10], monitoring coastal habitats [11], urban and infrastructure planning [12,13]. The old challenging methods for data acquisition are eliminated by photogrammetry. Sense 2D cadaster information does not meet today's needs, the world is moving into the 3D cadaster system, as its name clearly shows that in this application third dimension's information is needed for and such information could be supplied just with oblique photogrammetry [14].
Three-dimensional photogrammetric modeling play an important role in designing three-dimensional city modeling as well as in urban management especially during the planning stage it helps the urban planners to make optimum planes for the city.
In another research [15] states that since two dimensional cadaster is insu cient to solve the problems occurring due to lack of third dimension reveals the need for 3D cadaster implementation.
[16] used the UAV-based oblique photogrammetry for purpose of determining the characteristics of city trees and modeled a speci c area for this purpose and determined the characteristics of city trees through the threedimensional model. In [17] for obtaining better 3D city models they used a new method in which the aerial images are combined to the terrestrial images and at the results they obtained good 3D city models with properly geometries of the buildings. in a research namely Quantifying uncertainties in snow depth mapping from structure from motion photogrammetry in an alpine area, used the structure from motion photogrammetry to characterize uncertainties in snow depths spatially [18]. For this purpose, a study was conducted in the Combe de Laurichard which is located in the French Alps. Two different time of June 1st and October 5th, 2017 was chosen (one snow-on and one snow-off condition) for aerial data acquisition and two DEM (digital elevation model) from two datasets were made and compared, in this study a method was presented for calculating a spatially varying estimate of snow depth precision and detection limits using UAV repeated surveys. In their study [19] namely High-accuracy UAV photogrammetry of ice sheet dynamics with no ground control points, presented the application of an alternative SFM-MVS (structure from motion-multi view stereo) geolocation method named as GNSS-supported aerial triangulation, in this method an onboard carries-phase GNSS receiver to georeference SFM-MVS (structure from motion-multi view stereo) point cloud which signi cantly reduced the need for GCP (ground control points). Considered various ight con gurations such as linear strips, radial strips and curved strips; the obtained various dataset are evaluated in terms of density of the extracted point clouds and also distance between the reconstructed surface and control points are evaluated [20].

The Aim Of Study
The purpose of this paper is to indicate the usability of photogrammetric models generated without GCPs (ground control points) in some engineering application such as length, area, and volume measurements.
For this purpose, two different areas with different characteristics were modelled with and without GCPs.
The areas and lengths are measured from orthophoto and the volumes are calculated from DEM (Digital Elevation Model).
The measurements mentioned above are done over same areas in both models produced with and without GCPs and the results are discussed in detail.

Case Study
To investigate the usability of 3D (Three-dimensional) photogrammetric models generated without GCPs (ground control points), two studies were conducted in two different provinces of Turkey with different characteristics. First one in Siva located in the south of Turkey with 1650 m. elevation (Altitude above sea level) and the second one in Artvin located in the northeast of Turkey with an elevation of 450 m. Since there is a big difference in height between two regions as well as another variety factors such as meteorological difference, slope, terrain topography and etc to investigate that, whether this principle is applicable in everywhere or not. The two areas were modelled once with GCPs and afterwards without GCPs. The data acquisition in the both areas are as follow.

Sivas
This study is presented in Fig. 1 and conducted in Shugul Canyon located in the Sivas province of Turkey.
Oblique imagery of the work area is carried out and with the help of data obtained once the area is modelled with GCPs and once without GCPs and to compare the sensitivity of the two models, the length, area and volume of the same regions were measured in both models and the results were compared.
To model the area with oblique aerial photogrammetry method a DJI Phantom 4pro model UAV is used ( Fig. 2). 10 well distributed GCPs (ground control points) were used to georeference the model. The measurement of GCPs was conducted with (CHC X91 GNSS) model RTK-GNSS receiver.
At the rst step 9 well distributed ground control points were established in the work area, during establishing of these points, care was taken to ensure that they can be easily seen in the photos and were establish away from the natural and arti cial objects such as trees and buildings that would prevent these points from appearing in the pictures (Fig. 3).
After establishing the GCPs the measurement of these points was done in Turkish National Reference System as TUREF / TM36 and (ITRF96 in universal system as EPSG: 5256) with a sensitivity of (2cm) and the obtained coordinates are given in Table 1. In the second step the ight plan and ight time was determined, since the work area was mountainous area so the appropriate time for ight was determined as 12:00-14:00. By selecting this time, the effect of shading that would cause errors in the photogrammetric evaluation was tried to be minimized. DJI Phantom 4Pro model UAV was used for the aerial photography, Phantom 4Pro is equipped with a 20MP camera which is able to take photos with 4K quality and also has a 1-inch sensor. DJI Phantom 4Pro model UAV is presented in Fig. 4.
The imagery was conducted with the above UAV and nadir and oblique images of the work area were obtained. The cross overlap in the imagery was 85% and forward overlap was %80, this overlap is su cient to represent the topography and reconstruct the area virtually in three-dimension. Positions of GCPs, image overlap ratios and camera calibration are given graphically in Fig. 5. The errors of GCPs used during the photogrammetric evaluation are given in Table 2. The GCP errors calculated by the Agisoft/Metashape are given in Table 3.  Afterwards, the obtained aerial photographs were subjected to photogrammetric evaluation and the measured coordinates of GCPs were also used during the evaluation. Finally, geometry of the subject area has been reconstructed formally and computationally in virtual form. As a result of the evaluation, a dense cloud including 8,193,681 points with global coordinates, 3D model, orthophoto and digital elevation model were obtained as shown in Fig. 6. After the 3D model was generated with GCPs, once again 3D model of the work area was generated without GCPs.

Artvin
This study was conducted in the Artvin dam built on the Çoruh Riverwhich is located in the Artvin province of Turkey (Fig. 7). A 3D model of the area is generated by oblique photogrammetry, once with and once without GCP.
For modelling this work area via aerial photogrammetry method a DJI Phantom 4pro model UAV was used.
5 GCPs (ground control points) were used to georeference the model. The measurement of GCPs was conducted with TRIMBLE R6 GPS (CORS/GNSS) receiver (Fig. 8). The coordinates of GCPs were measured in Turkish National Reference System as TUREF / TM42 (3 Degree) and (ITRF96 in universal system as EPSG: 5258) with a sensitivity of (2cm) and the obtained coordinates are given in Table 4. The imagery was conducted with the UAV in accordance with photogrammetric principles and as a result nadir and oblique images were obtained. The cross overlap in the imagery was 85% and forward overlap was %80, this overlap is su cient to represent the topography and reconstruct the area virtually in threedimension. GCP positions and image overlaps are given in the Fig. 9.
Positions and errors of GCPs used during the photogrammetric evaluation, image overlap, and camera calibration coe cients and correlation matrix are given graphically in Fig. 9. The correlation matrix is given in the Table 5. The GCPs position errors are also calculated and are given in Table 6. Afterwards, the obtained aerial photographs were processed in accordance to photogrammetric principles, the measured coordinates of GCPs were also used during the photogrammetric process of images. Finally topography of the area has been reconstructed in three dimension with its global position. As a result of process, a dense cloud including 18,958,130 points with global coordinates, 3D model, orthophoto and digital elevation model were obtained as shown in Fig. 10.
After reconstructing the work area virtually in three dimensions using GCPs, once 3D model was generated without GCPs.

Finding And Examination
In this section an accuracy assessment is initially done for models generated with GCPs. Afterwards a comparison study is done among the nal 3D models (one with GCPs and other without GCPs) obtained from photogrammetric process. Length, area and volume measurements are selected as comparison criteria. These measurements are done for different areas over models generated with GCPs and afterwards over models without GCPs and at the end these results are compared to the measurement of the same areas done with terrestrial method (GPS/GNSS) the results are compared in details.
6.1 Assessment of Length, Area and Volume Measurement

First Study Area (Sivas) Experimental Studies
Length, area, and volume measurement of areas with different geometric shapes and slopes are carried out for rst study area.

Length measurement for accuracy analyse of model
Initially two areas are selected for the accuracy analysis of both models, a length measurement is done for those areas with the terrestrial method (using RTK (Real Time Kinematic/GNSS)) and afterwards same areas are measured in both models (model with GCPs and model without GCPs) and. The results of the measurements are given in Table 7.  Fig. 11.
After the model accuracy was con rmed, measurements in areas with different shapes are done in both models. The measurements are given in Table 8 and are compared as well. Measurements done in two models are graphically indicated as shown in Fig. 12.

Area Measurements for Sivas
In order to observe the usability of the model produced without GCPs in the case of area measurement, 5 areas with different features are measured within both models as shown in Fig. 13. The area measurement results are given in Table 9 as follow. Measurements done in two models are showed graphically as shown in Fig. 14.  Fig. 15.
In Photoscan, the "reference surface" to be used for the calculation of the volumes, can only be a plane.
This surface can be de ned in three ways: 1. as an inclined at surface and interpolated by the vertices of the delimitation of the object (best t plane).
2. as a horizontal at surface with a medium height determined by the heights of the vertices of the delimitation of the object (mean level plane); 3. as a horizontal at surface at a reference height determined by the user (custom level plane).
The results of volume measurements given as Table 10 and Fig. 16.

Length Measurements
Lengths of regions with different shapes was measured for intended goal as shown in Fig. 17 and the measurements are given in Table 12. Graphical vision of length measurements as shown in Fig. 18. Areas of different objects are measured in both model and as given in Fig. 19. Graphically representation of area measurement as given in Fig. 20. Volumes of different objects are measured for intended goal (usability investigation of model generated without GCPs) as shown Fig. 21.
The measured values of volumes are given in Table 13. The volumes measured over both model are given graphically in Fig. 22.

Discussion And Conclusion
These studies were conducted to investigate the usability of 3D photogrammetric models produced without using any GCPs (ground control points), for this goal two different areas were modeled, each twice once with GCPs and once without GCPs. For the mentioned goal lengths, areas and volumes of same areas were measured on both models. The results obtained from the models generated with GCPs were accepted as true values (reference values) and the results obtained from models generated without GCPs were compared to them and the relative errors as well as RMSE were also calculated and given in tables above.

Length Measurements Assessment
Results from length measurement provided various level of success. The accuracy of each measurement was assessed by comparing reference data (obtained from model with GCPs) to estimations determined through photogrammetric models without GCPs. In rst study area (Sivas) length measurements of three types of terrain ( at, sloping and rocky terrain) were conducted. As seen in Table 5 the errors of length measurement in at areas are less than the errors of the inclined areas, similarly the length measurement errors of inclined areas are less than the errors of rocky areas. It is important to know that some objects used for length measurement especially in inclined areas were in close proximity to other objects and were complex enough. But overall rst study area exhibited very promising results in length measurement with a relative error of less than 1% and RMSE of 0.139m and this result is accurate enough.
In second study area (Artvin) length of various places were measured. The relative error value is 0.15% and the RMSE is 0.153m and these errors are also within acceptable error limits.
Based on analysis of length measurements performed in models generated with GCPs and those performed over models without GCPs no marked difference was found. The majority of relative error calculations was less than 1%. The in uence of object shape, size and con guration on the accurate estimation of length obtained from models without GCPs were examined in this study. As seen in Table 5, the areas with greater slope and complexity contain more errors than the at areas. In rst study the at area has a majority relative error of 0.10% whereas inclined area has a majority relative error of 0.20% and nally length measured in the rocky area has a relative error of 0.36%. The rocky area has the highest error as well as the most complex structure in the rst study area. So as result the higher the inclination and the complexity of the object, the greater the error The maximum relative error of length measurement among study area is 0.36% which is an acceptable length accuracy. Given the acceptable accuracy assessment in various elds it is possible to conclude that the photogrammetric models produced without GCPs are adequate for estimating lengths of objects for different engineering applications, some quantity estimations within civil engineering projects, as well as disciplines that do not require very high accuracy, while it may not be suitable for disciplines that require a very high level of accuracy (millimetric accuracy). According to the above descriptions, we can indicate that models generated without GCPs can be used for length measurement as an accurate length measurement tools.

Area Measurements Assessment
Area estimations show varying results. The accuracy of each estimation (measurement) was assessed by comparing reference data (obtained from model with GCPs) to estimations determined through photogrammetric models without GCPs.
In the area estimation, out of 8 areas measured within three study areas, ve have a relative error of less than 1%. one of them has a relative error of less than 2% and one with a relative error of 3.51% and the last one contains the maximum relative error of 5.27%. The in uence of the shape and size can be seen such as in length measurement. As seen in Table 6 of rst study, the at area has a majority relative error of 0.16% whereas the inclined area has a majority relative error of 1.05%. As said for the length, the higher the inclination and the complexity of the object, the greater the error.

Volume Measurement Assessment
Results of volume estimations obtained from two studies are convincing. Within the rst study area (Sivas), the largest area exhibited a relative error of 0.8% and the maximum relative error of volume estimation is 6.8%. However the error looks to be a bit higher but absolute error is no more than 1.641m³.
The average relative error is calculated as 3.115% and RMSE is calculated as 2.301 m³ likely coming from the failure of the software to model the object structure properly.
Similarly within volume estimation of second study a maximum relative error of 2.01% has been identi ed with an RMSE of 7.061. It should be noted that the objects with the least accurate results have poor photo coverage, which sometime cause by the location of the object which is in the edge of the study area as well as insu cient image overlap and sometimes due to external factors. The errors can be reduced considering these factors.

Conclusions
Based upon the obtained results, several conclusions can be made as well as the decision to accept or reject the usability of models produced without GCPs. Considering the errors calculated above, the following conclusions are made pertain to the ability of photogrammetric models with no GCPs.
Photogrammetric models generated with no GCPs are usable for different engineering applications.
The photogrammetric models produced with no GCPs can be used as an accurate length measurement tool within modelled area.
A relative error of 0.12% in rst study area (Sivas) and 0.143% in second study area (Artvin) is obtained.
Photogrammetric models with no GCPs can be used as an accurate area measurement tool within modelled area.
Relative error in the case of area measurement of rst study area (Sivas) is %0.306 and relative error for second study area (Artvin) is 3.11%.
Photogrammetric models with no GCPs can calculate accurate volume of objects or/and areas with different shapes and slopes.
A 3.115% relative error of volume measurement is calculated for rst study area (Sivas), this value is 1.01% for second study area (Artvin).
The length measurement within the at areas of the model is more accurate than the measurement done within the inclined or rocky areas.
The area measurements done in at areas are also more accurate than those done in inclined area The area measurement of the object with smooth shapes are more accurate than the areas having complex shapes.
The volume measurement's accuracy is based upon the identi ed base surface, if the surface is identi ed accurately, there is no effect of the shape or slope.
The studies above are conducted in two areas with different characteristics such as elevation altitude above sea level, different climate conditions, different work area topographies, different ight planes and etc, but the results, the accuracies the relative errors and the absolute errors of these models are about the same. As a result, it can be indicated that the above principles (usability of models with no GCPs) are acceptable and applicable for every conditions.

Declarations Declaration of Con icting Interests
None of the authors of this paper has a nancial or personal relationship with other people or organisations that could inappropriately in uence or bias the content of the paper. No competing interests are at stake and there is no con ict of interest with other people or organisations that could inappropriately in uence or bias the content of the paper. Square concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. This map has been provided by the authors.  Second Study area a) Turkey b) Artvin b) Artvin Dam. Note: The designations employed and the presentation of the material on this map do not imply the expression of any opinion whatsoever on the part of Research Square concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. This map has been provided by the authors.

Figure 8
Equipment used to obtain datasets. Measurements done in two models are graphically indicated Figure 13 Area measurements done over both model Page 24/28

Figure 14
Measurements done in two models are showed graphically Figure 15 Page 25/28 Volume measurements of 4 rock done within both model Figure 17 Length measurements for third study area Page 26/28 Figure 18 Graphical vision of length measurements Figure 19 Areas measured in two models

Figure 20
Graphically representation of area measurements