# Smartphone-Based Photogrammetry for the 3D Modeling of a Geomorphological Structure
## 5 Results and Comparisons
### C2C Distance Comparison  
In order to assess, with smartphones, the quality and correspondence to reality of the SFM approach, the distance between the clouds was generated and the reference cloud was computed. To this end, the CloudCompare [51] open source software was used, allowing this estimate to be performed using the distance Cloud-to-Cloud (C2C) tool. The C2C tool exploits the Nearest Neighbor algorithm to compute the Euclidean distance between each point of the compared cloud and the nearest point of the reference cloud. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multirow{2}{*}{**Software/Dataset**} & \multicolumn{3}{c}{**Control Points**} & \multicolumn{3}{c}{**Check Points**} \\ \cline{2-7}  & **RMSE (X)** & **RMSE (Y)** & **RMSE (Z)** & **RMSE (X)** & **RMSE (Y)** & **RMSE (Z)** \\  & **[mm]** & **[mm]** & **[mm]** & **[mm]** & **[mm]** & **[mm]** \\ \hline AMP/50 images & 0.409 & 0.378 & 0.900 & 0.574 & 0.169 & 1.102 \\ AMP/25 images & 0.527 & 0.409 & 0.750 & 0.527 & 0.127 & 0.806 \\ AMP/12 images & 0.452 & 0.325 & 0.783 & 0.617 & 0.198 & 0.884 \\ VSFM/50 images & \multicolumn{3}{c}{Total error: 0.487 mm} & - & - & - \\ VSFM/25 images & \multicolumn{3}{c}{Total error: 1.505 mm} & - & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Resulting errors obtained with the different software. Figure 6: The point cloud model realized with the dataset of 25 images using the SCANN3D application. At this point, it was necessary to scale and register the models generated by SCANN3D in a reference system consistent with the other models. In this regard, CloudCompare offers several tools: a rough registration can be performed through pairs of equivalent points identified in the point cloud that is to be registered and in the reference model; subsequently, the automatic method based on the Iterative Closest Point (ICP) algorithm [52] allows the two models to be very finely recorded. This procedure was performed for both models deriving from SCANN3D, with a final RMSE of about 5 mm. Since all of the point clouds were quite noisy in the area related to the supporting surface of the rock sample, the cloud portions that were not part of the study object were manually removed. The C2C tool was launched by setting the points that were more than 5 mm away from the reference model as outliers, since the errors that interest us are lower than this limit. Figure 7 shows some significant results deriving from this procedure in histograms, statistical distributions and through the display in a color scale directly on the point clouds. The computation of the differences (Figure 7) confirmed the metrical accuracy of the models estimated by AMP and VSFM, and showed that the greater discrepancies correspond to the support surface and are greater than 5 mm. This error can be attributed to the noise affecting the point clouds, due to the reflective support surface combined with an external light source close to the test site, which probably caused an incorrect identification of the matching points. Table 8 shows the statistical parameters derived from the analysis with the C2C tool, such as the maximal distance, average distance and standard deviation. From the analysis of these results, it emerges that the three-dimensional models obtained with AMP and VSFM have better statistical values, lower ones, or ones on the order of a millimeter. Furthermore, it must be taken into account that for the model obtained from SCANN3D by processing the dataset of 12 images, although the average distance from the reference model is less than 2 mm, the representation of the object is visibly incomplete, as shown in Figure 7. For a better understanding of these discrepancies, a further analysis on the error distributions is required, as reported in Table 9. The results that are obtained show that more than 84% of the point clouds realized with AMP and VSFM deviate from the reference data by less than 2 mm, while these results were not achieved by the SCANN3D application.