New Supplementary Photography Methods after the Anomalous of Ground Control Points in UAV Structure-from-Motion Photogrammetry

: Recently, multirotor UAVs have been widely used in high-precision terrain mapping, cadastral surveys and other ﬁelds due to their low cost, ﬂexibility, and high efﬁciency. Indirect georeferencing of ground control points (GCPs) is often required to obtain highly accurate topographic products such as orthoimages and digital surface models. However, in practical projects, GCPs are susceptible to anomalies caused by external factors (GCPs covered by foreign objects such as crops and cars, vandalism, etc.), resulting in a reduced availability of UAV images. The errors associated with the loss of GCPs are apparent. The widely used solution of using natural feature points as ground control points often fails to meet the high accuracy requirements. For the problem of control point anomalies, this paper innovatively presents two new methods of completing data fusion by supplementing photos via UAV at a later stage. In this study, 72 sets of experiments were set up, including three control experiments for analysis. Two parameters were used for accuracy assessment: Root Mean Square Error (RMSE) and Multiscale Model to Model Cloud Comparison (M3C2). The study shows that the two new methods can meet the reference accuracy requirements in horizontal direction and elevation direction (RMSE X = 70.40 mm, RMSE Y = 53.90 mm, RMSE Z = 87.70 mm). In contrast, the natural feature points as ground control points showed poor accuracy, with RMSE X = 94.80 mm, RMSE Y = 68.80 mm, and RMSE Z = 104.40 mm for the checkpoints. This research considers and solves the problems of anomalous GCPs in the photogrammetry project from a unique perspective of supplementary photography, and proposes two new methods that greatly expand the means of solving the problem. In UAV high-precision projects, they can be used as an effective means to ensure accuracy when the GCP is anomalous, which has signiﬁcant potential for application promotion. Compared with previous methods, they can be applied in more scenarios and have higher compatibility and operability. These two methods can be widely applied in cadastral surveys, geomorphological surveys, heritage conservation, and other ﬁelds.


Introduction
With the rapid development of UAV hardware and ground-station software technology, UAVs have become smarter and have an increasingly wide range of applications. Using UAV to acquire earth observation data combined with a structure-from-motion (SFM) algorithm can generate high-precision orthoimages and digital surface models (DSM). The points on the house wall, building corners [1], or farmland [2] on the orthoimages can be down. Eventually, the planimetric accuracy of the RMSE gradually approached two times the GSD, and the elevation accuracy of the RMSE approached three times the GSD. Sanz-Ablanedo et al. [29] deployed 102 GCPs in a 1225 ha coal-mine area, and when 10-20 GCPs were used, the RMSE of the checkpoints was approximately five times the project average GSD. By adding more GCPs to reach more than two GCPs per 100 photos, the RMSE slowly converges to a value approximately twice the average GSD.
At the same time, the GCPs should be uniformly distributed throughout the study area, preferably in a triangular grid structure. This configuration minimizes the maximum distance of any GCPs in the area. Ferrer-González et al. [30] proposed that both horizontal and vertical accuracy in the case of a corridor s survey area increases with the number of GCPs used in bundle adjustment, and that planar accuracy is always better than vertical accuracy. Placing GCPs on the edge of the corridor alternately and placing two GCPs at each end of the study area produced the most accurate results. Liu et al. [31] also concluded that GCPs should be evenly distributed over the study area, with at least one GCP near the center of the area. The local accuracy of DSM decreased significantly when the distance between the adjacent GCPs increased. Ulvi [32] proposed that if the GCPs are concentrated in the center, the planimetric and elevation accuracy of all inspection points in the survey area is the worst, and the GCPs placed at the edge of the study area can obtain the best planimetric accuracy but cannot obtain the best elevation accuracy. When the number of GCPs is increased in the center of the study area, the overall error can be minimized and the best elevation accuracy can be obtained.
There has been a significant number of studies on GCPs; both manually placed GCPs and natural feature points are subject to anomalies due to natural and human factors. However, there is a lack of systematic research on GCP anomalies during UAV collection data. Common GCP anomalies often occur when covered by foreign objects such as vehicles, crops, and vandalism ( Figure 1). In UAV aerial photogrammetry, GCPs are often placed first. Then, the route task is carried out to collect aerial photographs, so the sequence of operations will bring the possibility of GCPs anomalies. Anomalies in the GCPs often cause irreversible damage to the operation in that the GCPs cannot be found in the completed aerials. This paper proposes two solutions in UAV photogrammetry for this anomalous GCP to solve these problems. The surface information of the processed anomalous GCP is complemented by our method and then fused into the nadiral images to achieve the purpose of indirect georeferencing of this GCP, which ensures the accuracy and quality of the data. An innovative way of thinking about problems and solving them from a new perspective is the use of a supplementary photograph. Compared with the previous solutions, the proposed methods can actively perform post-secondary work supplementary photography for anomalous GCPs, which is more controllable and can be applied to more environmental scenarios. At the same time, in the practical operation of the methods, it is more fault-tolerant and operative and can efficiently complete the supplementary photography of the anomalous GCPs. New ideas and methods are provided for solving GCPs anomalies in practical UAV photogrammetry projects. The new methods can be widely used in cadastral surveying, high-precision topographic mapping, and other fields. A widely used method is to find a natural feature around an anomalous GCP to replace that anomaly and achieve indirect georeferencing of the GCPs by reacquiring the geographic coordinates of that natural feature and transcribing them to the initial photograph. However, this method is more dependent on the quality of the natural feature points and the subjective judgement of the data processor. However, it is impossible to find natural feature points that meet the standards in many places. Boon et al. [33] suggested using artificially marked GCPs and Checkpoints (CPs) instead of natural feature points. Forlani et al. [22] proposed that artificially marked GCPs are necessary because it is difficult to find natural feature points of the required quality in areas outside of cities. Therefore, in applications such as high-precision topographic mapping, artificially marked ground control points should be used as much as possible. Natural feature points on the ground often have many uncontrollable factors and drawbacks. This paper proposes two solutions in UAV photogrammetry for this anomalous GCP to solve these problems. The surface information of the processed anomalous GCP is complemented by our method and then fused into the nadiral images to achieve the purpose of indirect georeferencing of this GCP, which ensures the accuracy and quality of the data. An innovative way of thinking about problems and solving them from a new perspective is the use of a supplementary photograph. Compared with the previous solutions, the proposed methods can actively perform post-secondary work supplementary photography for anomalous GCPs, which is more controllable and can be applied to more environmental scenarios. At the same time, in the practical operation of the methods, it is more fault-tolerant and operative and can efficiently complete the supplementary photography of the anomalous GCPs. New ideas and methods are provided for solving GCPs anomalies in practical UAV photogrammetry projects. The new methods can be widely used in cadastral surveying, high-precision topographic mapping, and other fields.

Study Area
The study area is located in Yanglingzhuang Village, Yexian County, Pingdingshan City, Henan Province, China ( Figure 2). The east-west length is about 880 m, the northsouth length is about 870 m, and the elevation range is from 154 to 185 m. The longitude range of the study area is 113 • 13 27 E~113 • 14 02 E, and the latitude range is 33 • 25 47 N~33 • 26 13 N, with an area of 0.67 km 2 . The study area contains various feature elements, such as arable land, rivers, artificial structures, scrubland, and groves, which are more representative. The wide field of view of the flight and the uninterrupted satellite signal are conducive to collecting images by the UAV.

Overall Workflow
The process of this research ( Figure 3) can be divided into three parts, including data acquisition, data processing, and accuracy evaluation. Our proposed solution and the comparison scheme are processed separately by structure from motion (SFM) and multiview stereopsis (MVS), and the results of the different schemes are evaluated for accuracy after the point clouds are generated. The main evaluation metrics include RMSE and M3C2 distance.

Overall Workflow
The process of this research ( Figure 3) can be divided into three parts, including data acquisition, data processing, and accuracy evaluation. Our proposed solution and the comparison scheme are processed separately by structure from motion (SFM) and multiview stereopsis (MVS), and the results of the different schemes are evaluated for

Overall Workflow
The process of this research ( Figure 3) can be divided into three parts, including data acquisition, data processing, and accuracy evaluation. Our proposed solution and the comparison scheme are processed separately by structure from motion (SFM) and multiview stereopsis (MVS), and the results of the different schemes are evaluated for accuracy after the point clouds are generated. The main evaluation metrics include RMSE and M3C2 distance. Figure 3. Overall experimental workflow. Group I used the "STNG" method, and Group II used the "Oblique and Circle" method. There is often a time lag between the placing of GCPs and UAV operations in UAV photogrammetry. During this time gap, GCPs are prone to be vandalised or covered by foreign objects. These problems are not easily detected during the flight of the UAV route, resulting in a reduced availability of the images due to that anomalous GCPs. In order to solve the problem of anomalous GCPs, we proposed two methods called the "STNG" and the "Oblique and Circle".
"STNG" is a method of taking photographs by descending equidistantly and vertically from sky to near-ground ( Figure 4). We defined a specific altitude, H 1 , directly above the restored GCP as the starting point (H 1 = H + ∆h, where H is the orthometric altitude and ∆h is the difference between the altitude of the orthometric take-off point and the altitude of the anomalous control point). We then hovered at certain intervals D to take pictures during the vertical downward movement of the UAV until it reached the surface to complete the operation.
"Oblique and Circle" is a method of surround photography that maintains the oblique angle of the camera for anomalous GCP ( Figure 5). We defined that the position of H 2 (same as H 1 ) directly above the repaired GCP was the centre O, a certain distance R was the radius to make a circular motion, and the camera was inclined at a certain angle β. The heading angle α was a fixed interval to take images. The main optical axis of the camera was required to align with the GCP. cally from sky to near-ground ( Figure 4). We defined a specific altitude, H1, directly abov the restored GCP as the starting point (H1 = H + Δh, where H is the orthometric altitud and Δh is the difference between the altitude of the orthometric take-off point and th altitude of the anomalous control point). We then hovered at certain intervals D to tak pictures during the vertical downward movement of the UAV until it reached the surfac to complete the operation. "Oblique and Circle" is a method of surround photography that maintains th oblique angle of the camera for anomalous GCP ( Figure 5). We defined that the positio of H2 (same as H1) directly above the repaired GCP was the centre O, a certain distance R was the radius to make a circular motion, and the camera was inclined at a certain angl β. The heading angle α was a fixed interval to take images. The main optical axis of th camera was required to align with the GCP.

GNSS Survey
According to the characteristics of the field to be studied, we used four corner point combined with a central point to place a total of five GCPs [34]. In order to assess th accuracy, the checkpoints were placed evenly over the study area with a total of 19 CP ( Figure 6). In addition, we searched for the ground natural feature point (the corner poin of the bridge named TZ2) near point K2 as a GCP instead of point K2. As the study are is located in the countryside, with more cultivated land and abundant natural landform we compared several locations. Finally, we chose the bridge corner point with a high leve and more flat terrain as the natural feature point. Two materials were used to place th GCPs and CPs, i.e., pulverized lime for the dirt roads and red paint for the concrete road  According to the characteristics of the field to be studied, we used four corner points combined with a central point to place a total of five GCPs [34]. In order to assess the accuracy, the checkpoints were placed evenly over the study area with a total of 19 CPs ( Figure 6). In addition, we searched for the ground natural feature point (the corner point of the bridge named TZ2) near point K2 as a GCP instead of point K2. As the study area is located in the countryside, with more cultivated land and abundant natural landforms, we compared several locations. Finally, we chose the bridge corner point with a high level and Three measurements of 24 artificial GCPs and one natural feature point were made in CORS mode using a Huace i80 GNSS receiver. The spatial reference was the CGCS 2000 ellipsoid, the projection was the Gauss-Kruger projection, and the elevation datum was "National Vertical Datum 1985"-all in metres (m). Each positioning was verified to be above 12 satellites, with 10 ephemerides collected each time. The device achieved a horizontal accuracy of ± (8 + 0.5 × 10 −6 × D) mm and a vertical accuracy of ± (15 + 0.5 × 10 −6 × D) mm in CORS mode.

UAV Image Acquisition
The photographs for this experiment were collected using a DJI Phantom 4 Pro drone manufactured by DJI. It is a consumer-grade UAV that is portable, flexible, small in weight and low in cost. It carries a DJI FC6310 camera with a field of view (FOV) of 84° and an image size of 5472 × 3648 pixels. The route planning software used for the experiment was DJI Pilot and DJI GO4. The study area boundary was converted to KML format and imported into DJI Pilot software, the flight altitude (H) above the ground was set to 160 m, the forward overlap was 80%, the side overlap was 80%, the Mapping Mode was set, and the take-off point was selected as point K5 (the altitude of this point is 159.8 m). The camera parameter settings (ISO and exposure values, etc.) are automatically adjusted according to the actual brightness of the scene at the time of flight. The experiment was completed on 4 July 2021 with a light breeze and good light at the site. We collected a total of 562 nadiral images with an average ground resolution of 4.32 cm/pixel. The route and images are shown in Figure 6.
After the nadiral images were acquired, the anomalous GCP was photographed using the method proposed in this paper. As the anomaly GCP (K2) was at the same altitude as the ortho take-off point (K5), the starting flight altitude above the ground for data collection was 160 m (nadiral flight altitude), and then hovered every 5 m down to take one photo for a total of 32 images. The DJI GO4 software was used to complete the data acquisition and determine the height of descent based on the value shown on the display. Three measurements of 24 artificial GCPs and one natural feature point were made in CORS mode using a Huace i80 GNSS receiver. The spatial reference was the CGCS 2000 ellipsoid, the projection was the Gauss-Kruger projection, and the elevation datum was "National Vertical Datum 1985"-all in metres (m). Each positioning was verified to be above 12 satellites, with 10 ephemerides collected each time. The device achieved a horizontal accuracy of ±(8 + 0.5 × 10 −6 × D) mm and a vertical accuracy of ±(15 + 0.5 × 10 −6 × D) mm in CORS mode.

UAV Image Acquisition
The photographs for this experiment were collected using a DJI Phantom 4 Pro drone manufactured by DJI. It is a consumer-grade UAV that is portable, flexible, small in weight and low in cost. It carries a DJI FC6310 camera with a field of view (FOV) of 84 • and an image size of 5472 × 3648 pixels. The route planning software used for the experiment was DJI Pilot and DJI GO4. The study area boundary was converted to KML format and imported into DJI Pilot software, the flight altitude (H) above the ground was set to 160 m, the forward overlap was 80%, the side overlap was 80%, the Mapping Mode was set, and the take-off point was selected as point K5 (the altitude of this point is 159.8 m). The camera parameter settings (ISO and exposure values, etc.) are automatically adjusted according to the actual brightness of the scene at the time of flight. The experiment was completed on 4 July 2021 with a light breeze and good light at the site. We collected a total of 562 nadiral images with an average ground resolution of 4.32 cm/pixel. The route and images are shown in Figure 6.
After the nadiral images were acquired, the anomalous GCP was photographed using the method proposed in this paper. As the anomaly GCP (K2) was at the same altitude as the ortho take-off point (K5), the starting flight altitude above the ground for data collection was 160 m (nadiral flight altitude), and then hovered every 5 m down to take one photo for a total of 32 images. The DJI GO4 software was used to complete the data acquisition and determine the height of descent based on the value shown on the display.
We used the DJI GO4 software s Point of Interest (POI) function while manually controlling the shutter to take photos. The flight altitude above the ground was 160 m, the circle s centre was O 1 , the radius (R) was 20 m, the camera oblique angle was β = 78 • , and the heading angle sampling interval α was 20 • , meaning that a total of 18 images were acquired. In addition, we added two sets of routes with a flight altitudes of 140 m and 180 m. The parameters for the "oblique and circle" images acquisition are shown in Table 1.

Data Processing
ContextCapture software is an excellent professional-grade mapping data processing software from Bentley, which can quickly generate real-scene 3D models based on photographs with a certain degree of overlap and output high-precision mapping products, such as TDOM, DSM, and photogrammetric point clouds [35]. It has a robust computer geometry algorithm, an excellent human-computer interface, and is highly operable. We imported the UAV images with various optional additional auxiliary data (camera properties (focal length, sensor size, master point, etc.), photo location information) into the software, used the GCPs for directional aerial triangulation, and then reconstructed it in 3D to obtain a high-resolution triangulated mesh model with realistic textures and a mapping product with a certain degree of accuracy. The software is widely used in China to research and produce topographic products and has a large user base. ContextCapture Center version 4.4.10 was chosen for this experiment to process the data.
The experimental group of "STNG" was named group I; the experimental group of "Oblique and Circle" was named group II. If the K2 point was anomalous, a natural feature point was found as a control point, called "NFP"; four GCPs (K1, K3, K4, and K5) were used to simulate the loss of K2, which was called "4 GCPs"; five GCPs (K1, K2, K3, K4, and K5) were used (K2 is not lost) as the baseline accuracy, which was called "5GCPs". Table 2 shows the detailed description of the overall experiment. In each experiment in Group I and Group II, "NFP", "4 GCPs", and "5 GCPs" were subjected to aerial triangulation operations, and all experiments were performed using uniform parameters ( Table 3). The number and distribution of checkpoints were consistent for all experiments. To reduce the influence of "human factors", georeferenced artificial markers at the same locations (pixel coordinates) were used in all experiments [36]. It should be emphasised that due to our flight altitude above the ground of 160 m and the motion blur phenomenon, the location of natural feature points were found in the images as closely as possible [37]. For group I, the main problems we addressed are as follows: firstly, the effect of different distances between adjacent images on accuracy; secondly, the relationship between the variation of its overall (five images) spatial position and accuracy when the image spacing is fixed. Therefore, we set the spacing between adjacent images to 5 m, 10  In Group II, the following two issues were discussed: firstly, the effect on accuracy was explored by varying the flight altitude (140 m, 160 m, 180 m) ( Figure 8); secondly, after the optimal flight altitude was obtained, further experiments were completed on the 16 photographs taken at that flight altitude, and 6 of the 16 photographs were selected according to the heading angle interval to explore the effect of the spatial position of the photographs on the accuracy was investigated. The six photographs were selected accord- In Group II, the following two issues were discussed: firstly, the effect on accuracy was explored by varying the flight altitude (140 m, 160 m, 180 m) ( Figure 8); secondly, after the optimal flight altitude was obtained, further experiments were completed on the 16 photographs taken at that flight altitude, and 6 of the 16 photographs were selected according to the heading angle interval to explore the effect of the spatial position of the photographs on the accuracy was investigated. The six photographs were selected according to the heading angle interval (20 • , 40 • , 60 • ), and six consecutive aerial photographs were taken, respectively ( Figure 9).

Figure 7.
A schematic diagram of 61 "STNG" experiments is shown. The horizontal axis is the number of the experiment, representing each experimental scheme, and the vertical axis is the flight altitude above the ground of the photographs. Each red dot represents a photograph, and the position of the red dot represents the relative spatial position of the photograph.
In Group II, the following two issues were discussed: firstly, the effect on accuracy was explored by varying the flight altitude (140 m, 160 m, 180 m) ( Figure 8); secondly, after the optimal flight altitude was obtained, further experiments were completed on the 16 photographs taken at that flight altitude, and 6 of the 16 photographs were selected according to the heading angle interval to explore the effect of the spatial position of the photographs on the accuracy was investigated. The six photographs were selected according to the heading angle interval (20°, 40°, 60°), and six consecutive aerial photographs were taken, respectively (Figure 9). heading angle interval α = 40°; (c) heading angle interval α = 60°. We defined the direction to be north, with a heading angle starting at 0°, and the UAV movement direction was clockwise.
A set of experimental data was selected from the results of Group I and Group II, respectively, together with the remaining experiments, including "NFP", "4 GCPs", and "5 GCPs" for a total of five experiments. The photogrammetric point cloud model was generated for each experiment, and the sampling distance of the point cloud was set to 0.1 m.
The point cloud analysis was carried out using the M3C2 plug-in of Cloud compare software. The parameters were adjusted according to the system recommended values  A set of experimental data was selected from the results of Group I and Group II, respectively, together with the remaining experiments, including "NFP", "4 GCPs", and "5 GCPs" for a total of five experiments. The photogrammetric point cloud model was generated for each experiment, and the sampling distance of the point cloud was set to 0.1 m.
The point cloud analysis was carried out using the M3C2 plug-in of Cloud compare software. The parameters were adjusted according to the system recommended values (Guess params), with a projection radius of 0.87 m, an initial value of 0.44 m, a step size of 0.44 m, a final value of 1.74 m, and a calculation depth of 0.40 m. By comparing the point cloud of each scenario with the reference point cloud data, the overall analysis was carried out on the accuracy of the point cloud data. To improve the reliability of the experimental method, we obtained a set of high-precision reference point clouds by adding GCPs [27]. We increased the number of control points from 5 to 15 to enhance the four corner points and the central point [38].

Accuracy Assessment
In photogrammetry projects, checkpoints (CPs) are often used to assess accuracy, using the Root Mean Square Error (RMSE) [39][40][41]. After aerial triangulation was completed using ContextCapure software, a quality report was automatically generated, and the RMSE of the CPs were calculated by comparing the CPs coordinates calculated from aerial triangulation with the precise coordinates from the GNSS survey to obtain the RMSE X , RMSE Y , and RMSE Z of the CPs. The detailed equations are given in (1)-(4).
where n is the number of CPs; X GNSSi , Y GNSSi , Z GNSSi are the X, Y, Z actual geographic coordinates of the i-th CP measured by GNSS, respectively; X GNSSi , Y GNSSi , Z GNSSi are the X, Y, Z actual geographic coordinates of the i-th CP measured by GNSS, respectively. For an overall accuracy comparison, we generated photogrammetric point clouds from the different scenarios and used CloudCompare 2.12 software point clouds for comparison [42]. The primary use of the Multiscale Model to Model Cloud Comparison (M3C2) plug-in is one of the more widely used ways to evaluate distance calculation methods for 3D change features [43]. In M3C2, a set of highly accurate and precise point cloud data was used as a reference, and the distance in the direction of the normal to the local surface was calculated for the reference and comparison point clouds by using two parameters (custom normal scale and projection scale). The accuracy and precision of the point cloud data were assessed using the mean value and Standard Deviation (std.dev), respectively. By plotting the errors and their distribution curves, we determined the spatial distribution of the M3C2 distances for the different experiments, thus completing the error assessment [44].

Accuracy Based on RMSE
In Group I, we used the sampling interval of the photographs as a variable for a total of 61 experiments. We evaluated the accuracy of all the experiments to obtain the error values of all CPs in the plane and elevation directions for each experiment and the RMSE X , RMSE Y , and RMSE Z of the CPs for each experiment. In Figure 10a, the overall planimetric error of the CPs of group I converges to 0.2 m, which is relatively stable. It is evident that the curves of CPs (J1, J2, and J3) are steeper and have more significant Measures of Dispersion compared with the rest of the CPs. The errors of J1, J2, and J3 in different experiments in group I differ greatly, while J1, J2, and J3 are distributed around the GCP K2, which indicates that the "STNG" method had a greater impact on the local accuracy. However, the absolute error of the CPs of each experiment is small, and the overall planimetric error is very stable.   j1  j2  j3  j4  j5  j6  j7  j8  j9  j10  j11  j12  j13  j14  j15  j16  j17  j18 Figure 10 shows that the distribution of error values in the elevation direction is not as concentrated as the plane, and the overall convergence was −0.5 m~0.2 m. There are apparent differences in the elevation errors between the different experiments in group I, which was unstable. The instability of CPs (J1, J2, J3, J4, and J10) is more pronounced, as these 5 points were distributed around K2, further verifying that the "STNG" method has a greater impact on local accuracy. On the other hand, the crests indicate the convergence of error values for the overall CPs of this experiment, and elevation errors were smaller. It can be found that the experiments in the case of full photo participation (experiment numbers 1, 28, 41, 49, 54, 58, and 61) are at the wave crest in the group of seven different sampling interval distances; this means that a uniform distribution of photographs within 160 m according to the sampling interval has less error than a partial take of five, while the number of uniformly distributed photographs is greater compared to five (five photos for 35 m sampling distance). Figure 11 represents the fitted curve between sampling interval and CPs RMSE for these seven experiments. The results show that the effect of the sampling interval on the CPs was significant, with the RMSE of the CPs gradually decreasing and then stabilising as a power function relationship as the distance between the sampling intervals increases (regression coefficients R 2 = 0.610, significance level p < 0.05). However, larger sampling intervals (40 m and above) would not satisfy the experimental conditions, which were limited by the flight height of the data itself.
Drones 2022, 6, x FOR PEER REVIEW 15 of 24 apparent differences in the elevation errors between the different experiments in group I, which was unstable. The instability of CPs (J1, J2, J3, J4, and J10) is more pronounced, as these 5 points were distributed around K2, further verifying that the "STNG" method has a greater impact on local accuracy. On the other hand, the crests indicate the convergence of error values for the overall CPs of this experiment, and elevation errors were smaller. It can be found that the experiments in the case of full photo participation (experiment numbers 1, 28, 41, 49, 54, 58, and 61) are at the wave crest in the group of seven different sampling interval distances; this means that a uniform distribution of photographs within 160 m according to the sampling interval has less error than a partial take of five, while the number of uniformly distributed photographs is greater compared to five (five photos for 35 m sampling distance). Figure 11 represents the fitted curve between sampling interval and CPs RMSE for these seven experiments. The results show that the effect of the sampling interval on the CPs was significant, with the RMSE of the CPs gradually decreasing and then stabilising as a power function relationship as the distance between the sampling intervals increases (regression coefficients R 2 = 0.610, significance level p < 0.05). However, larger sampling intervals (40 m and above) would not satisfy the experimental conditions, which were limited by the flight height of the data itself. The main focus of Group II was to investigate the effect of different flight altitudes and heading angle intervals on accuracy. In the nomenclature of the experiment, II_140 m_20° (18) indicates an "Oblique and Circle" of 18 photographs at a flight height of 140 m and a heading angle interval of 20°. Table 4 shows the RMSE of the CPs for the different solutions of the "Oblique and Circle" method. Different schemes can meet the accuracy requirements of "5GCPs" (RMSEX = 70.40 mm, RMSEY = 53.90 mm, RMSEZ = 87.70 mm) in both horizontal and elevation directions, indicating the effectiveness and stability of the "Oblique and Circle" method. When the number of images was reduced to six, the overall accuracy does not change significantly, so we preferred to use six images. After comparison, the 140 m aerial height shows a higher elevation accuracy, with the best being at CPs RMSEZ = 75 mm. From the results of the above experiments, it can be concluded that the accuracy was better at a flight altitude of 140 m. Therefore, data with a flight altitude of 140 m was used to explore the effect of different spatial positions of the photographs on accuracy. The number of photographs was six, and three sets of experiments were designed (Figure 9). The results of the experiments are shown in Table 5 Table 4 shows the RMSE of the CPs for the different solutions of the "Oblique and Circle" method. Different schemes can meet the accuracy requirements of "5GCPs" (RMSE X = 70.40 mm, RMSE Y = 53.90 mm, RMSE Z = 87.70 mm) in both horizontal and elevation directions, indicating the effectiveness and stability of the "Oblique and Circle" method. When the number of images was reduced to six, the overall accuracy does not change significantly, so we preferred to use six images. After comparison, the 140 m aerial height shows a higher elevation accuracy, with the best being at CPs RMSE Z = 75 mm. Table 4. RMSE in the horizontal and elevation direction for different flight altitudes and different numbers of photographs using the "Oblique and Circle" method. From the results of the above experiments, it can be concluded that the accuracy was better at a flight altitude of 140 m. Therefore, data with a flight altitude of 140 m was used to explore the effect of different spatial positions of the photographs on accuracy. The number of photographs was six, and three sets of experiments were designed (Figure 9). The results of the experiments are shown in Table 5. The errors show fluctuations as the relative spatial positions of the photographs vary. The smallest error is in experiment II_140m_60 • (6), representing a uniform distribution of images, with the heading angle of every two images differing by 60 • and the RMSE Z being 75 mm. However, the RMSE Z for the rest of the experiments was less than 87.70 mm (5 GCPs), which further validates the stability of the "Oblique and Circle" method. Experiment I_54 and experiment II_140m_60 • (6) were used as the representative results of group I and group II, respectively, and the accuracy was compared with "NFP" (using natural feature points as control points), "4 GCPs" (K2 point loss), and "5 GCPs". From Figure 13, in the X-direction, the largest error was NFP with CPs RMSE X = 94.80 mm, followed by 4 GCPs, CPs RMSE X = 75 mm. The results show that adding a natural feature point as a GCP did not improve the accuracy but reduced it to some extent. The RMSE X of Experiment I_54, Experiment II_140 m_60 • (6), and 5 GCPs were 70.37 mm, 70.60 mm, and 70.40 mm, respectively, and the accuracy in the X-direction remained the same for all three. The error distribution pattern in the Y-direction is consistent with that in the X-direction. It is verified that our methods can meet the requirements of 5GCPs accuracy in the horizontal direction.  (6) were used as the representative results of group I and group II, respectively, and the accuracy was compared with "NFP" (using natural feature points as control points), "4 GCPs" (K2 point loss), and "5 GCPs". From Figure 13, in the X-direction, the largest error was NFP with CPs RMSEX = 94.80 mm, followed by 4 GCPs, CPs RMSEX = 75 mm. The results show that adding a natural feature point as a GCP did not improve the accuracy but reduced it to some extent. The RMSEX of Experiment I_54, Experiment II_140 m_60° (6), and 5 GCPs were 70.37 mm, 70.60 mm, and 70.40 mm, respectively, and the accuracy in the X-direction remained the same for all three. The error distribution pattern in the Y-direction is consistent with that in the X-direction. It is verified that our methods can meet the requirements of 5GCPs accuracy in the horizontal direction.

Experiment RMSE X (mm) RMSE Y (mm) RMSE Z (mm)
In the Z-direction of elevation, the four GCPs exhibited the largest error, with CPs RMSEZ = 145.10 mm being greater than the 5 GCPs (CPs RMSEZ = 87.70 mm), which indicates that the absence of a GCP has a greater impact on the overall elevation accuracy. The NFP solution RMSEZ was 104.40 mm, which is between 4 GCPs and 5 GCPs, indicating that the addition of a natural feature point can improve the overall accuracy to some extent, compared to the elevation accuracy of 4 GCPs, but cannot achieve the accuracy (5 GCPs). In contrast, both the "STNG" and the "Oblique and Circle" met the accuracy of the 5 GCPs with an CPs RMSEZ of 71.41 mm and 75.00 mm, respectively, to a certain extent, thus improving the elevation accuracy.  Figure 13. RMSE in the X-, Y-and Z-directions for the checkpoints of the five key scenarios.
In the Z-direction of elevation, the four GCPs exhibited the largest error, with CPs RMSE Z = 145.10 mm being greater than the 5 GCPs (CPs RMSE Z = 87.70 mm), which indicates that the absence of a GCP has a greater impact on the overall elevation accuracy. The NFP solution RMSE Z was 104.40 mm, which is between 4 GCPs and 5 GCPs, indicating that the addition of a natural feature point can improve the overall accuracy to some extent, compared to the elevation accuracy of 4 GCPs, but cannot achieve the accuracy (5 GCPs). In contrast, both the "STNG" and the "Oblique and Circle" met the accuracy of the 5 GCPs with an CPs RMSE Z of 71.41 mm and 75.00 mm, respectively, to a certain extent, thus improving the elevation accuracy.

Point Cloud Evaluation Based on M3C2 Distance
The photogrammetric point cloud of the "15 GCPs" scheme was used as the reference point cloud, and the M3C2 distance operation was performed with the above five sets of experimental point clouds respectively, to obtain the point cloud change results ( Figure 14). The comparative analysis shows that the"4 GCPs" (mean = −0.0409, std. dev = 0.1223) was greatly affected in terms of accuracy and precision compared to "5 GCPs" (mean = −0.0239, std. dev = 0.0666), and the use of natural feature point as a GCP (mean = −0.0320, std. dev = 0.0734) could improve the accuracy but failed to achieve the 5 GCPs accuracy. When five additional images with different altitudes (I_54) were added (mean = 0.0040, std. dev = 0.0652), the accuracy greatly improved (Figure 14a). When five oblique-circle images (II_140 m_60 • (6)) were added (mean = 0.0017, std. dev = 0.0694), the overall accuracy and precision improved significantly and were closer to that of the 15 GCPs (Figure 14b). Figure 13. RMSE in the X-, Y-and Z-directions for the checkpoints of the five key scenarios.

Point Cloud Evaluation Based on M3C2 Distance
The photogrammetric point cloud of the "15 GCPs" scheme was used as the refe point cloud, and the M3C2 distance operation was performed with the above five s experimental point clouds respectively, to obtain the point cloud change results (F 14). The comparative analysis shows that the"4 GCPs" (mean = −0.0409, std. dev = 0 was greatly affected in terms of accuracy and precision compared to "5 GCPs" (m −0.0239, std. dev = 0.0666), and the use of natural feature point as a GCP (mean = −0 std. dev = 0.0734) could improve the accuracy but failed to achieve the 5 GCPs accu When five additional images with different altitudes (I_56) were added (mean = 0 std. dev = 0.0652), the accuracy greatly improved (Figure 14a). When five oblique images (II_140 m_60° (6)) were added (mean = 0.0017, std. dev = 0.0694), the overall racy and precision improved significantly and were closer to that of the 15 GCPs (F 14b).
When the GCP (K2) is lost, it significantly impacted the accuracy of the study especially around the anomalous GCP and houses, which could be improved b "STNG" and "Oblique and Circle" solution, and was significantly better than the u natural feature points (Figure 14c).  When the GCP (K2) is lost, it significantly impacted the accuracy of the study area, especially around the anomalous GCP and houses, which could be improved by the "STNG" and "Oblique and Circle" solution, and was significantly better than the use of natural feature points (Figure 14c).

Discussion
We placed GCPs at each of the four corners and central points within the approximately rectangular study area, and this approach was feasible. Both Rangel et al. [45] and Patricio Martínez-Carricondo et al. [46] argued that a uniform distribution around the experimental area and the addition of uniformly distributed GCPs in the middle of the experimental area can improve the elevation accuracy. The errors introduced when a corner point K2 is lost are significant, especially in elevation, with the RMSE Z of the CPs reaching 145.10 mm compared to the 5 GCPs RMSE Z = 87.70 mm. Therefore, the quality of the photographs after the loss of a GCP should be questioned and should not be used directly.
The anomalies in GCPs have rarely been discussed in previous studies. The general method of a "natural feature point" has limitations and is very dependent on the quality of the natural feature points and the subjective judgement of the data processor. It was found that when natural feature points were used as control points (NFP scheme), the error in the elevation direction of the CPs reached 104.40 mm, which is not possible to achieve the accuracy of 5 GCPs. There is a significant increase in error in the horizontal direction, with the CPs RMSE X reaching 94.80 mm compared to the 5 GCPs checkpoints RMSE X of 70.40 mm, further verifying that NFP is unable to achieve the 5 GCPs' accuracy in both the horizontal and elevation directions. Such instability is determined by the quality of the natural feature point-its actual position is not easy to find on the aerial images and is often met with some deviation. Francisco-Javier Mesas-Carrascosa's study shows that instead of using well-defined artificial checkpoints, the use of natural feature points in the study area as checkpoints would increase the checkpoint RMSE from a GSD of 3.7 times to a GSD of five times [47].
The idea of the "STNG" method is to improve the ground resolution of the area around the GCP by progressively taking additional images downwards and fusing them with the nadiral images, thus improving the accuracy. Quoc Long et al. [48] mentioned that increasing the ground resolution by reducing the flight altitude of the UAV could improve the accuracy, and Agüera-Vega et al. [38] showed that the effect of GSD on elevation accuracy was significant. In contrast, the effect on planimetric accuracy was smaller.
It was found that the "STNG" showed high stability in the horizontal direction but less stability in the elevation direction. The first experiment of each group represents the best case for each group, all the images in each group are involved, and their spatial locations are shown in Figure 7. As the interval between adjacent photos increased, the elevation accuracy showed a nonlinear trend of gradual improvement and stability (regression coefficients R 2 = 0.610, significance level p < 0.05), which is consistent with the accuracy of "5 GCPs", indicating that the "STNG" is feasible. The best solution is to set the sampling interval as 25 m (I_54), where all seven images were involved and the RMSE X = 70.37 mm, RMSE Y = 53.77 mm, RMSE Z = 71.41 mm of the CPs. The RMSE Z of the CPs of the sampling interval of 30 m (I_58) and 35 m (I_61) were 88.61 mm and 73.85 mm-both of which met the 5 GCP's accuracy requirements. Therefore, we suggest that in the actual operation, the sampling interval D should be determined with reference to the nadiral flight altitude ((H + ∆h)/7 ≤ D ≤ (H + ∆h)/5, where H is the nadiral flight altitude and ∆h is the difference between the altitude of the nadiral take-off point and the altitude of the anomalous GCP).
In experiments with a sampling interval of 5 m, we found a linear trend in the accuracy of the data with decreasing photo height (regression coefficients R 2 = 0.6434, significance level p < 0.001). This observation will need to be verified in further studies.
A total of six experiments were set up in Group II to verify the influence of altitude and number of photographs on the accuracy, and three experiments were set up to verify the influence of different spatial positions of photographs at the same altitude on accuracy. The results show that the accuracy of the 5 GCPs can be achieved at different flight altitudes, indicating that the "Oblique and Circle" method has high stability. The highest elevation accuracy was demonstrated at an altitude of 140 m. The difference between the accuracy of 18 additional images and six images is not significant, so using six images was a better choice. When the spatial position of six images was evenly distributed, and the heading angles of different images were spaced 60 • apart, which is more accurate. The horizontal error of the above experiment is about one-to-two times the GSD, and the elevation error is about two-to-three times the GSD, which satisfies the general law of photogrammetry [49].
By using the "Oblique and Circle" method, there is a clear tendency to improve accuracy in the elevation direction further. The RMSE Z of the CPs of the II_140m_60 • (6) experiment is 75.00 mm, which is about 10 mm higher elevation accuracy than the 5 GCPs. Wackrow et al. [50] suggested that the angle between homologous rays could be increased by introducing oblique images in the nadiral dataset, thus reducing systematic errors. Bi et al. [51], Harwin et al. [52], and Štroner et al. [25] have shown that adding additional oblique images to the nadiral images can improve the accuracy of the results and increase the elevation accuracy. Sanz-Ablanedo et al. [53] showed that square POI flights, where the camera angle is always aligned with the centre of the region of interest, produce a smaller systematic error. Therefore, we believe that the "Oblique and Circle" method is valid and is valuable for further research.
The M3C2 point cloud comparison confirms our viewpoint as well. Using the "STNG" and "Oblique and Circle" methods can improve the elevation accuracy to a certain extent while still meeting the 5 GCPs' accuracy. The "Oblique and Circle" method provides the highest elevation accuracy and is more stable. The "natural feature point" method has a significant local error (Figure 14c), and the overall accuracy is not as good as required.
In UAS, the height above the ground level can be measured based on barometer sensors. The DJI Phantom 4 Pro UAV used in this study has a vertical positioning accuracy of ±0.5 m, which means that height deviations at the decimetre level may occur during data acquisition and that the centimetre level (or smaller) positioning accuracy cannot be accomplished [54]. However, the two methods are experimentally compatible, and the decimetre-level positioning errors have less impact on the two methods. Therefore, the vertical positioning errors of the UAV itself can be ignored when using the methods.
At the same time, the limitations of fixed-wing UAVs make it challenging to use the method proposed in this paper to collect images. Therefore, the fusion of images using different camera sensors is proposed, such as using a more flexible multirotor UAV to complement images; this will be the next stage of our research.

Conclusions
In this paper, two different solutions based on ground control point anomalies were put forward, and the optimum of which was verified. By adopting the "5 GCPs" as the reference project and the "NFP" method as the comparison solution, the following conclusions can be drawn.
It is not easy to find natural feature points that meet the requirements outside urban areas. The location of the feature points in the image depends on the subjective judgment of professionals with a large error caused by "human factors". For this reason, it is not recommended that "natural features" be the preferred option for aerial photogrammetry when high accuracy is required.
In practical projects, only when horizontal accuracy is required, can our proposed "STNG" and "Oblique and Circle" methods meet the accuracy requirements. The "NFP" demonstrates that neither the horizontal nor the elevation direction can meet the requirements of the 5 GCPs' accuracy. The "STNG" method is simple and easy to use, so it is recommended. When using the "STNG" method, the spacing between the adjacent images is D ((H + ∆h)/7 ≤ D ≤ (H+ ∆h)/5, where H is the nadiral flight altitude, ∆h is the difference between the elevation of the nadiral take-off point and the elevation of the anomaly GCP, and the number of photographs must not be less than 5.).
When elevation accuracy is considered, the "Oblique and Circle" method has higher stability and meets the accuracy requirements. In the horizontal direction, the accuracy is maintained and consistent with the data s accuracy from the 5 GCPs. There is a tendency to improve the accuracy further in the elevation direction. When using the "Oblique and Circle" method, the accuracy requirements can be met by keeping the flight height the same as the flight height of the nadiral. To improve the elevation accuracy, the flight height can be reduced by a small amount, e.g., about 20 m in the experiment of this paper. At the same time, the selection of photographs should be evenly distributed around the entire circumference, and the results are better when the heading angle is 60 • . In sum, the "Oblique and Circle" method is highly effective when the GCPs are anomalous.