## 3 Results and Discussion
### Dense Point Cloud  
The parameters of the generated dense clouds are provided in Table 9 and Figure 16. The size of the dense clouds associated with the digital camera data is almost 3 times the size of the smartphone dense clouds. This significant difference indicates that the DC's clouds offer a better representation of the objects' details, which results in a higher mesh quality with a precise geometry resulting in accurate geometrical measurements.  
Figure 15: Cross sections from the square beam point clouds for a qualitative noise assessment: (**a**) digital camera sparse cloud; (**b**) smartphone sparse cloud; (**c**) digital camera densified cloud; (**d**) smartphone densified cloud. All clouds are scaled in meters, and the provided scale bar is in meters.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Specimen**} & \multirow{2}{*}{**Capturing**} & \multirow{2}{*}{**Cloud Size**} & \multirow{2}{*}{**N\({}^{\circ}\) of Depth**} & \multicolumn{2}{c}{**Depth Maps**} & \multicolumn{2}{c}{**Dense Cloud**} \\ \cline{4-8}  & & & & **Maps** & **Time** & **Memory** & **Time** & **Memory** \\  & & & & **(min)** & **Usage (GB)** & **(min)** & **Usage (GB)** \\ \hline \multirow{2}{*}{Beam} & DC & 17,756,572 & 43 & 7.85 & 3.26 & 8.97 & 4 \\  & SP & 6,115,497 & 43 & 4.32 & 1.59 & 4.85 & 3.12 \\ \multirow{2}{*}{Cylinder} & DC & 14,542,288 & 24 & 4.18 & 3.01 & 2.83 & 3.55 \\ \multirow{2}{*}{Sand Pile} & SP & 5,197,385 & 24 & 3.35 & 1.42 & 2.05 & 2.62 \\  & DC & 3,600,957 & 33 & 3.08 & 3.12 & 4.23 & 3.34 \\ \multirow{2}{*}{Sand Pile} & SP & 1,246,089 & 35 & 2.32 & 1.49 & 3.18 & 2.58 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Dense point clouds’ parameters of both cameras’ data sets.  
To quantify this difference, the cloud density can be estimated and analyzed using CloudCompare. Taking the sand pile as an example, the volume density of its dense clouds can be computed. The volume density is computed by dividing the number of points enclosed by a sphere of a given radius (in this case \(r=5\) cm) by its volume, Equation (10). The given sphere radius and the estimated density are expressed with the same corresponding unit of the point cloud coordinates. In this study, all point clouds were scaled in meters.  
\[D_{v}=\frac{N}{v=(4/3\times\pi\times r^{3})} \tag{10}\]  
where \(D_{v}\) is the volume density, \(N:\) the number of points inside a sphere of radius \(r,v\) is the sphere volume.  
The number of points and volume density of the sandpile dense clouds are demonstrated in Figures 17 and 18 for both cameras, along with the volume density histograms and their normal distribution fitting. The mean density of the digital camera cloud is \(\mu_{Dv}=75\times 10^{6}\) pts/m\({}^{3}\), whereas the smartphone cloud has a mean value of \(\mu_{Dv}=24\times 10^{6}\) pts/m\({}^{3}\). For the number of points (N), the mean value of the DC cloud is \(\mu_{N}=39,224\) pts, while the SP cloud has \(\mu_{N}=12,604\) pts. By comparing these values, it can be confirmed that DC's point cloud has a higher density that is 3 times the SP's, which results in a higher mesh quality and a more reliable representation of object details--thus, accurate measurements estimations. This difference in points density is mainly caused by the higher resolution of the DC's images that result in more detected and reconstructed features (i.e., points) compared with SP's images.  
Figure 16: Dense point clouds of the three specimens (square beam, cylinder, sandpile) reconstructed from: (**a–c**) the digital camera data; (**d–f**) the smartphone data. All clouds are scaled in meters, and the provided scale bar is in meters.