## 3 Results and Discussion
### Geometrical Measurements Extraction  
Before extracting any geometrical measurements, it is important to compare the model pairs (i.e., DC and SP models of the same specimen) based on their scale to assess the difference in their size representation of the actual specimen's size. This is achieved by registering and aligning the two models of the same specimen together. In this study, the four targets' points were used as reference points to align the models' pairs. After every two models were perfectly aligned, the absolute distance between them was computed using a CloudCompare plugin [47]. For each face in the compared model (i.e., smartphone's model), its distance to the nearest face in the reference corresponding model (i.e., digital camera model) was calculated. For all specimens, the digital camera model was set as the reference model to which the smartphone model was compared. Figure 21 presents the absolute distance variation for each compared specimen, along with its color map indicating the absolute distance values. The figure also provides the histograms for each specimen, demonstrating the absolute distance ranges for the count of faces. All three histograms in Figure 21 have the same number of bins (16 bins). The mean absolute distances (\(\mu\)) are 0.657422, 0.963073, and 0.610173 mm, with standard deviation (\(\sigma\)) values of 0.660495, 1.06704, and 0.677724 mm for the square beam, cylinder, and sandpile models, respectively. These readings report a slight variation between the two models of the same specimen in terms of their sizes. This difference is demonstrated in the geometrical estimations extracted from the two models of the same specimen. Table 13 presents the specimens' volumes and surface areas estimated from the final scaled 3D models of both cameras. The table provides the estimation errors calculated by comparing the estimated measurements with the actual measurements for each specimen. As the results indicate, the digital camera models present a better geometrical accuracy compared with the smartphone models. Nevertheless, the estimation errors associated with the smartphone models are insignificantly higher. It can also be noticed that the volume estimation errors are highest with the sandpile models. This is mainly due to the unprecise measurement of the actual volume caused by the soil compaction and looseness factors. The soil actual volume was measured by placing the soil in a calibrated container, which causes the soil to be slightly compact. However, when the soil gets poured to form the irregularly shaped pile, it becomes loose, hence resulting in a slight volume increase. On the other hand, the estimation errors are lowest in the case of the cylinder models of both cameras, which is a result of its relatively smaller size compared with the other two specimens. Furthermore, it can be highlighted that the errors of surface area estimations are generally less than those of the volumetric estimations. This suggests higher reliability of CRP in estimating surface areas compared with volumetric estimations. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Specimen** & **Capturing Device** & \
\begin{tabular}{c} **Scale Bar 1** \\ **Error (cm)** \\ \end{tabular} &
\begin{tabular}{c} **Scale Bar 2** \\ **Error (cm)** \\ \end{tabular} \\ \hline \multirow{2}{*}{Beam} & DC & 0.0008 & \(-\)0.0004 \\  & SP & \(-\)0.0037 & 0.0037 \\ \multirow{2}{*}{Cylinder} & DC & \(-\)0.0009 & 0.0012 \\  & SP & \(-\)0.0053 & 0.0053 \\ \multirow{2}{*}{Sand Pile} & DC & 0.0011 & \(-\)0.0003 \\  & SP & 0.0026 & 0.0026 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Scaling distance errors associated with the created scale bars. The bar distance = 12.1 cm with a set accuracy = 1 mm for both bars in all data sets.