Evaluation of the effect of MLS density level data on DEM Evaluation of the effect of MLS density level data on DEM

Mobile laser scanning (MLS) systems are quickly establishing themselves as the primary source of high-quality digital elevation models (DEM). Data density is the key element that determines the quality of DEMs. Moreover, point density acts a vital role in MLS operation planning and MLS project's cost. This goal of the study was to evaluate the impact of point density from MLS on creating DEMs and the accuracy of computed volume in different interpolation methods. The ﬁ nding demonstrated that the DEM's quality and the volume are more impacted by the density level and the interpolation method. Interpolation methods are affected by point density. There is no single interpolation approach that is appropriate for all data sources. From this study, the different interpolation methods are suitable for use with dense sample data. In this study, the difference between interpolation approaches is very small because the surface is roughly ﬂ at.

1. Introduction 1.1. Digital terrain models D igital elevation models (DEMs) are utilized to the classic ground surface topography and are usually utilized in numerous environmental, military, engineering, and GIS applications. The generation of high-quality elevation models is one of the most pressing challenges for the scientific community and commercial industry.
Grid elevation models are many products involving DEMs, digital terrain models (DTMs), and digital surface models (DSM).
A DEM displays the bare soil topography with Z values that are spaced regularly. The absolute altitude is expressed by the Z value, which calculates height beyond a datum. A DTM is identical to a DEM, but it may contain the elevation of major topographic characteristics like river ridge lines, as well as irregularly spaced mass points and break lines. DTMs are more commonly utilized to represent the terrain features. DSMs are similar to DEMs or DTMs, except that a DSM includes the elevation of a structure's top surface over the level of the surrounding bare earth (Wood, 2008).
The DEMs' production mostly includes two major steps: (1) Capturing the terrain or elevation data.
(2) To develop a DEM and to build a model that describes a correlation between the noticed data.
There are many approaches to gather elevation data involving photogrammetric techniques, total station, and laser scanning. Laser scanning or light detection and ranging devices gather 3D data from a tripod, mobile vehicle, or aircraft using lasers. Terrestrial laser scanners (static or kinematic) produce highly accurate (cm level) 3D point clouds, which are a collection of vertices that indicate the object's surface (Baldi et al., 2002). By seeing and controlling point clouds in computer-aided design tools, these 3D vertices enable designers to directly encounter and deal with real-world circumstances by visualizing and operating point clouds in computer-aided design software (Lari, 2014). Mobile laser scanning (MLS) is a powerful technology for getting elevation data. An MLS is a system that uses an image metrological system (imaging system) placed on any moving platform, such as trucks, boats, rail vehicles, vans, vessels, and so on to take measurements while the platform is moving (Kukko et al., 2012).
MLS technology is becoming more widely used in traditional surveying and photogrammetric applications. This rise is attributed to ongoing advancements in data capture speed, precision, and density of point data collected from these devices (Zhu et al., 2013).
The MLS method generates a point cloud, which is a cloud of unevenly spaced 3D points. To create a DEM, this point cloud must be interpolated to generate a grid with regular spacing. Interpolation is the method of approximating a variable's values in unknown places using the values of the surrounding observed points (Chaplot et al., 2006).
There are several ways of spatial interpolation that can be used to interpolate a surface, involving triangulation with linear interpolation (TIN), nearest neighbor (NN), kriging (K), polynomial regression (PR), and inverse distance weighted (IDW). All of these interpolation approaches are based on the principle that the similarity between objects increases with decreasing distance (Anderson et al., 2005).

Area of study
The current research's study area is in the Kuwait's Al Wafrah city. The Trimble MX2 mobile mapping device was used to collect the point clouds for Section (1), which is shown in Fig. 1. Table 2 displays MLS information for Section 1 (Fig. 2).

Technique properties
The Trimble MX2, a mobile mapping tool, was used to collect the point clouds for the study area. Table 1 shows the specifications of the technique used in this study.

Results and discussions
The evaluation of point density is made through the following: (1) Calculating RMSE at different density levels and different interpolation methods.
(2) Calculating the volumes at different density levels and different interpolation methods.
Calculating RMSE at different density levels and different interpolation methods.
The vertical difference between each confirmation point and the DEM's correspondent forecast point was discovered for each DEM grid using Surfer10's "Residual" tool (Golden Software Inc., 2004). For each validation point, the vertical difference was determined using Equation (1): where E (s i ) is the error at a location; P (s i ) is the DEM's predicted value at location (s i, ), and M (s i ) is the measured value from the confirmation MLS data at location (si).
To contrast the DEMs' overall accuracy at different density levels, RMSE was computed for each DEM utilizing the equation: where n is the overall number of points and E (s i ) is the error at location (s i ). RSME is the most broadly utilized global accuracy measure for validating the DEM quality.
To contrast the findings well across various density levels and interpolation methods, RMSE was plotted in separate graphs. RMSE across different density levels in different interpolation methods for the study site is presented in Table 3, which show the number of points for each density level. Overall, the results demonstrated satisfactory accuracies for each of the generated DEMs using various interpolation algorithms at all data density levels. The largest RMSE happened at the lowest density (0.44% of the original dataset) and was less than 0.1 m. Fig. 3 shows RMSE mapped against the density level in different interpolation methods. The findings confirm that the density level has a negative impact on prediction error; in other words, RMSE rises as the density level reduces. RMSE was found to change from 0.008 to 0.087 m in TIN DEM. It can be shown that the RSME growth pattern is linear up to a certain density level. Fig. 4 shows the mean RMSE mapped against the density level. The findings show that the density level impacts the prediction error negatively; in other words, mean RMSE elevates as the density level reduces. Mean RMSE was found to change from 0.016 to 0.094 m. It can be shown that the mean RSME growth's trend is linear up to the density level. Fig. 5 shows RMSE mapped against different interpolation methods in different densities. It can be shown that the RSME's trend is linear to different interpolation methods at the same density level. Fig. 6 shows the mean RMSE mapped against different interpolation methods. The mean RMSE was found to change from 0.043 to 0.061 m.

Calculating the volume at different density levels and different interpolation methods
The volume at various level density with different interpolation methods was recorded utilizing the "volume" command in Surfer10 (Golden Software Inc., 2004) for each DEM grid. The lower surface to compute the volume is 98 m.
To contrast the findings well across various density levels and interpolation methods, volume was plotted in separate graphs. Volumes across various density levels in different interpolation methods for the study site are expressed in Table 4, which show the number of points for each density level. In general, the findings displayed the volumes for each of the created DEMs using various interpolation algorithms at all data density levels.       At the highest density (100% of the original dataset), the highest volume (848.3 m 3 ) occurred. The smallest volume was 830.11 m 3 happened at the lowest density (0.44% of the original dataset). The difference between volumes at the same level density in different interpolation methods is acceptable. The difference between volumes at different level densities in the same interpolation method is not acceptable. Fig. 7 shows volumes mapped against density level in different interpolation methods. Volume was found to change from 847.960 to 832.032 m 3 in     TIN DEM. It can be shown that the volume growth's trend is linear down to the density level. Fig. 8 shows the mean volumes mapped against the density level. Volume was found to change from 848.056 to 830.545 m 3 in TIN DEM. It can be shown that the volume growth trend is linear down to the density level. Fig. 9 shows volume mapped against different interpolation methods in different density levels. It can be shown that the volume's trend is linear to different interpolation methods at the same density level. Fig. 10 shows mean volumes mapped against different interpolation methods. Mean volumes were found to change from 841.854 to 843.277 m 3 .
In supplement to the above-mentioned analytical comparison, the DEM's quality is visually assessed utilizing 3D surface models generated in Surfer. Figs. 11e16show the 3D surface using the Kriging (K) interpolation method in different density levels.

Conclusion
As expected, data density decrease affects DEM accuracy. As data density declined, errors were discovered to increase. This alteration in RMSE trend was anticipated because decreasing density meant increased MLS point spacing. The difference between minimum height and maximum height   from point clouds for Section (1) is 0.323 m and the difference between RMSE at density level 100% and density level 0.44% is 0.078 m. This means the large difference between the minimum and maximum height from point clouds increase the difference between the RMSE at the difference density levels and increase the effects on DEM accuracy. So, if the difference between the minimum and maximum height is large, the density level should be increased to reduce the RMSE and DEM accuracy. To calculate the volumes with high accuracy the density level should be increased. In this study, the difference between interpolation approaches is very small because the surface is roughly flat. The author was capable of visually examining the quality of produced DEMs at different density levels by constructing 3D surface DEM models.