ASSESSMENT OF THE PRECISION OF A SMART-PHONE POLE PHOTOGRAMMETRY FOR A SECOND-ORDER CLIFF SURFACE DEFORMATION STUDIES

Coastal cliff is almost a vertical elongated structure with a wave-cut notch and a landslip. Cliffs are geological formations with an almost unpredictable and unstoppable detachment between constitutes formations. Due to health, safety, environmental, and military restrictions, there are more regulations and restrictions on the use of drones. There are also the issues of portability and high cost for the purchase of hybrid drones and Terrestrial Laser Scanners (TLS). These negate the regular monitoring of the coastal cliff. This research develops a rapid, low-cost, and precise digital photogrammetry methodology for the continuous monitoring of the cliff by using the pole as the platform and a mobile phone as a sensor. The most practical vertical camera angle, image overlaps, survey distance to the cliff, and realistic time range for surveys are all determined from the basic surveying principles. Precise geometrically related point clouds generated are with or without the Global Navigation Satellite Systems (GNSS). The standard deviation for “alignment and surface deviation” at every point on each point cloud is ± 0.05m in the Northing and ± 0.12m on the Easting’s for the self-calibrated digital camera and without the use of GNSS control points. With the GNSS controls, the maximum deviation in the XYZ coordinates is ±5 cm. Change analysis performed identifies areas of cut, fill, and the segment of threats in all point clouds. The photogrammetric technique developed is very cheap, simple, and reliable with minimum labor. The results obtained indicate the applicability of this methodology for second-order cliff Deformation study.


INTRODUCTION
With drones, pre-programmed flight routes are automatically set at the best angle that captures images on a regular grid pattern and flight speed (Varela et al, 2019;Colomina and Molina, 2014;Perez-Alberti and Trenhaile, 2014). To survey the cliff surface on a manual flight mission with the drone requires great experience to obtain an optimal flight mission and generate orthometric and digital models required for mapping purposes (Mancini et al, 2017). Digital images acquired arbitrarily from the ground stations to survey the cliff would be difficult to generate a complete overlapping stereo oriented model for consistent and precise 3D models and 3D maps except as a rare 'accidental success'.
The use of poles and masks as platforms would require ground-based camera locations. The distance between these ground-based stations and the cliff surface (L) is as the height (H) above the ground in aerial surveys. Like the traditional aerial surveys, camera-based stations on the ground would require very careful and systematic planning to achieve the best Ground Sampling Distance (GSD) (Huang et al, 2015), sensor stability (Roncella et al, 2014), overlap and reduce the effects of random errors and accumulation of systematic errors (Aber and Babb, 2018;James and Robson, 2014). The length between the baseline and cliff (L), the linear dimension of the pixel (px), and the camera lens' focal length (f) will determine GSD accuracies as camera pixels will be mapped to the cliff surface Geological formations of limestone, sandstone, chalk, rock shelters, and granite characterize the cliff surface (Terefenko et al, 2018). Several crests of waves on the cliff surface depend on the formation of the sections on the cliff and such irregular spectral frequencies cause both low and high contrast across the electromagnetic spectrum (Young et al, 2016). Digital photogrammetry is more challenging when using lowquality complementary metal-oxide-semiconductor CMOS or the Charge-coupled devices CCD image sensors (Dai et al, 2014) as with this research. The best pattern of forward and side overlap and the distance between the camera's stations to the cliff surface is; therefore, determine to generate the best spatial and spectral resolutions for deformation analysis.
Due to the height of the coastal cliff and considering the very short distance between the camera location and the cliff surface, there must be careful considerations on the angle of the camera, camera calibration, stabilization, and sensor orientation to overcome yaw variation, rolls variation, altitude variation, perspective variation, barrel, and pincushion. The accuracies on the computation of the exterior orientation parameters by the BBA using the Integrated Sensor Orientation (ISO) is usually affected by both the satellite geometry and the lock on the available GNSS constellation (Rau et al, 2011). GNSS radio signals delays are mainly by the free electrons in the ionosphere and by other atmospheric conditions in the troposphere . The Earth rotation induces charged particles into the magnetic field line in the ionosphere and capable of distorting the propagation of radio waves signal (Constable, 2016). Ionospheric propagation delays are of higher magnitude than the tropospheric delays and largely degrade the accuracies in single-frequency GNSS receivers' especially inbuilt GNSS sensors on smartphones and other inexpensive digital cameras (Karaim et al, 2018). Considerations are in place also to obtain the best time-lapse for satellite geometry when mapping the cliff surface using the pole photogrammetry due to drift in the GPS/INS low-quality digital camera/GPS sensor (Masiero et al, 2017). The coastal cliff undergoes regular physical and chemical weathering processes (Earlie et al, 2017 andSciarra et al, 2014) as well as seawater crashing against the surface (Earlie et al, 2017). Cliff surface weathering causes an almost unpredictable and unstoppable detachment between constitutes formations and eventual collapse (Singh et al, 2016). The coastal cliffs are therefore asymmetrical with complex surface discontinuities (Letortu et al, 2018;Westoby et al, 2018;Ruzic et al, 2015;Galea et al, 2014;Somma et al, 2015 andSciarra et al, 2014). It is difficult therefore to establish temporary/permanent control points on the cliff surface. The establishment of GNSS points close to the cliff at either the top or toe in some coastal area is practically difficult due to such high-volume sea wave and cliff surface erosion (Earlie et al, 2017). This is the situation in Penarth (study location) very peculiar with the Bristol Channel and the regular cliff face collapse. GNSS equipment is expensive to buy/ borrow and may not be available in most situations. It is imperative to develop a cost-effective and precise methodology using the Structure from Motion SFM derived point cloud for coastal cliff geotechnical and structural change detection analysis. For existing close-range digital photogrammetry techniques, consistent and accurate time-series orthomosaics and digital models for environmental monitoring are feasible on the availability of GNSS points (Ruzgiene et al, 2015 andTurner et al, 2015). The method developed is a simple and straightforward photogrammetry technique for consistent and precise evaluation of the cliff surface with or without the GNSS controls.

Determine an Appropriate Vertical Camera Angle to the Cliff
The basic transformational matrixes of each grid cell relate every pixel location in the image relative to the cliff surface elevation. The digital camera self-calibration solution includes the direct computation for the interior and exterior parameters, which allows the transformation from 3D coordinate (X, Y, Z) of the ground point to a 2D coordinate (u, v) of the image in pixels. The basic perspective projection centre of the perspective lens cameras relates the scene properties as pixels where the origin is the camera centre defined by its position and orientation.

Figure 1. Perspective Projection
The origin and geometrical sequence between each grid cell determine the transformation matrix of orientation parameters that form the image of the object by relating the scene properties as pixels (Liu et al, 2016). The origin is the camera centre defined by its position and orientation (Xu et al, 2017). Digital photos acquired from off-nadir angle geometry will generate denser tie-points and create a better model for the cliff surface compared with photos acquired from the nadir positions (Nesbit and Hugenholtz, 2019;Juad et al, 2016;Mancini et al, 2017). The reduction of systematic errors is from the reduction of gaps between adjoining digital images on the cliff surface geometry that is vertically irregular (Nesbit and Hugenholtz, 2019). This section experiment on an appropriate vertical camera angle that would be suitable to; a) High overlapping images that can generate a dense point cloud b) Obtain pixel texture accuracies for cliff surfaces c) Survey the entire height of the cliff with geometric accuracies This practical solution is reliant on the cliff surface characteristics, the resolution of the digital camera, and the pole as a platform using the perpendicular orientation geometry as shown below.

Determining the Best Distance between the Cliff Surface and the Base Line
In close-range photogrammetry, the digital camera could be as close as a few centimeters to the object being monitored which favorably improves on the image resolution (Westoby et al, 2015). However, when monitoring an unstable cliff like the Penarth, 1-2 meters could be dangerous and unfavorable to the field of view (FOV) with constraints on the orientation angle of the digital camera. The best practice would be a trade-off between the distance to the cliff surface, the FOV, and the cliff height. The camera distance to the cliff surface determines the GSD. Shorter distances between the camera and the cliff will turn out into a smaller GSD provided every other photogrammetric constraint is at minimal while larger distances could amount to greater GSD especially with the use of low/medium resolution digital cameras. Smaller GSD will have a higher spatial resolution. The GSD should be at least half of the smallest object on the ground for measurement (Tziavou et al, 2018). Most times the pixels, when projected onto the ground, will not be squared perfectly. The GSD would then be computed for in terms of sensor width and sensor height. GSD = Ground Sampling Distance L = the length between the baseline and cliff f= the focal length of the digital camera px = the pixel linear dimension To determine approximately the GSD For a distance of 3 meters between the baseline and the cliff, using the Samsung (SM-

Determine a Practicable forward and side overlap
The terrain topography and purpose of the photogrammetric project determine the choice and percentage of overlap (Pepe et al, 2018). Recommendations, however, are for a regular grid pattern (Carter et al, 2019) of 60% side overlap and 80% forward overlap (Cwiakala et al, 2018;Turner et al, 2015;Colomina and Molina, 2014). To generate tie-points with maximum density, every point in the object space should be in a minimum of 4-5 images (Ruzgiene et al, 2015). The painters' pole used is 11m long and segmented at every 1m. The average percentage of overlap is 55% horizontal and 58% vertical. Figure 5 below illustrates the number of overlapping images.

Determine an Appropriate Time-Lapse for Surveying the Cliff with the Pole Using the Integrated Sensor Orientation (ISO)
In the ISO, the computation of the Bundle Block Adjustment BBA is by the use of the inbuilt GNSS sensors and the compact Micro-Electro-Mechanical Systems Inertial Measurement Unit (MEMS IMU) without GNSS controls and pre-defined tie points (Pepe et al, 2018 andBenassi et al, 2017). Although the ISO is straight to use, the cheap miniature sensors with cheap inbuilt GPS are downgraded easily especially in very dynamic environments (Benassi et al, 2017). The accelerometer and gyros of the MEMS-IMU are also flexible and can easily drift during use due to their microstructure compartments. The tropospheric signal delays characterized by pressure, temperature, and water vapour are relative to geographical elevation (Yu et al, 2018 andZhu et al, 2017) with water vapour predominant in the coastal areas. The accuracies of close-range photogrammetric surveys will improve on favourable atmospheric conditions (Pepe et al, 2018) likely on lesser time durations.
Inexpensive GNSS sensors would be difficult to generate consistent and reliable dense point cloud due to inherent anomalies in the Scale Invariant Feature Transformations (SIFT) (Qu et al, 2018) which detects and extract the local features in the corresponding digital images. It would be difficult then to minimize errors from transformation and misalignments which ideally are reduced by the GNSS controls and tie points as with the Integrated Sensor Orientation (ISO) and GNSS-supported Aerial Triangulation (GNSS-AT) in digital photogrammetry (Benassi et al, 2017). To balance off systematic and random errors from the ionospheric and tropospheric delays, drifting, and downgrading of the inbuilt GPS, this research relies on the systematic field procedure(s) developed in the foregoing sections. The aim is to obtain the maximum number of images that would be calibrated for SIFT. The cliff surface was surveyed at different time-range to establish the level-oftolerance of the inexpensive Samsung SM-G850F MEMS-IMU/inbuilt GNSS sensors on favourable atmospheric and illumination (shadow cast) conditions.

EVALUATING THE GEOMETRIC PRECISIONS OF THE POLE SURVEY FOR CLIFF SURFACE DEFORMATION STUDIES
The different point clouds generated should be geometrically precise for evaluative purposes (Kromer et al, 2015). Comparisons were on four different point clouds obtained from four weekly surveys to determine the consistencies and reliability of the new pole mapping field sequence.  The standard deviation for "alignment and surface deviation" (Westoby et al, 2018) at every point on each point cloud is ± 0.05m in the Northing and ± 0.12m on the Easting's for the selfcalibrated digital camera and without the use of GNSS control points. This shows that each of the point cloud models geometrically fits into the other for a second-order cliff monitoring deformation study (Westoby et al, 2018 andRuzic et al, 2015).

Verifying the Correctness of the CloudCompare Global Coordinates
To verify the correctness of the CloudCompare coordinates, the DSM of one of the Pole Survey Point Cloud (PSPC) was imported into ArcMap and the coordinates of the control points in CloudCompare as in Figure 10 is found to be the same as in ArcMap. Figure 11. Verification of the CloudCompare Global Coordinates in ArcMap The geometric accuracy defines the comparative evaluation with datasets obtained from other reliable photogrammetric techniques while the absolute accuracy is the difference of the x, y, and z coordinates of every point on the point cloud to their true geographical position on ground (Harwin and Lucieer, 2012). The 3D reconstruction process in the bundle adjustment may distort the original shape of the cliff surface alignment.
The TLS and the Pole survey were both used to survey the same stretch of the cliff surface on the 13 th of March 2020. This is to be able to determine the global correctness of the digital image EXIF and structure from motion computation for bundle adjustment that optimizes the 3D location between the tie-points and the camera internal parameters (Turner et al, 2012).
The TLS survey was using the Topcon Laser scanner GLS-2000M series. The 8.9-degree telephoto camera provided the complete stereoscopic coverage of the cliff surface at 6.3 mm at 10 m resolution. Two different prism scan locations provided the precise and accurate modelling of the cliff section monitored. The fixed pole at (window scanning) enhances accuracies although it takes longer to scan but reduces the registration of the point cloud in the Topcon ScanMaster software. The height of the pole for this survey was 2 m and the prisms are 125 mm. Georeferencing was by the GEOMAX Zenith 35 series on Real-Time Kinematic (RTK) mode.

Control Points for Georeferencing the Pole Survey
Four markers at the bottom of the cliff with other visible points on both surveys in the middle of the inaccessible clifftop were used as manual tie-points for geolocating the pole survey in Pix4D on OSGB 1936 coordinate system as shown in figure 12 below.   The maximum deviation in the XYZ coordinates of the PSPC at every point as compared with the TLSPC is 5 cm.
The accuracies of the geometry of the PSPC and the TLSPC are subject to further scrutiny by creating their contours using the triangulation and the linear interpolation gridding method in the Surfer Golden Software (Sufer, 2018). The triangulation with linear interpolation uses the anisotropy to determine its contour (Bayazit, 2019). Anisotropy is dependent on the direction irrespective of the properties of the surface materials will generate an unbiased contour interpretation (Bayazit, 2019). The choice to use the multiple refractive indexes is due to the irregular surface nature of the cliff that has the capabilities for change in direction within the shortest possible period resulting from falls and collapse. Recent studies show that the M3C2 will be more effective for comparing irregular surfaces like the cliff (Lague et al, 2013). This is because the algorithm distance computation is not dependent on the spatial correlation and the dimensional orientation between the surfaces .
In figure 20 below, the M3C2 in the open-source Cloudcompare is used to perform change analysis between four weekly surveys. The evaluation of the detectable surface changes is at a minimum of ±6mm. From week 1 to 2, the fuller Earth is obvious and completely erodes from week 4 to week 5. There are insignificant changes from week 2 to week 3 and complete cliff erosion at points a. b, c, d, e, f, g, h, I. Figure 20. Explains the significant changes between four weekly surveys at 6mm detectable surface change.

CONCLUSION
The contribution to knowledge is a new pole digital photogrammetry methodology for coastal cliff monitoring. This research utilizes the very basic principles of photogrammetry in developing a systematic flight plan and camera orientation to able to generate precise and accurate 3D reconstructed point cloud by terrestrial pole survey for coastal cliff monitoring. The methodology developed is simple, straightforward with a regular grid network for complete stereoscopic coverage. The verification of results obtained has been by third-party software and an alternative remote sensing survey.
This methodology generates precise geometrical related point clouds with or without the GNSS controls. For use in the photogrammetry community, the most appropriate vertical camera inclination and distance to the cliff surface has been practically demonstrated and theoretically documented.
The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLIV-M-2-2020, 2020 ASPRS 2020 Annual Conference Virtual Technical Program, 22-26 June 2020 Depending on the area been mapped, surveys can be from 10 minutes to 2 hours. It is possible to attach the different digital cameras on the pole with the higher resolution cameras resulting in higher spectral accuracies. The limitation is to perform a survey in an almost equal atmospheric condition to avoid the drifting of the MEMS-IMU during the survey. Surveys performed at a very close range can detect hidden sections/crack on the cliff, but care must be not to change the viewing angle of the digital camera during use. Surveys do not require the drone licence, but care must be not to drop the pole during use.