# Smartphone-Based Photogrammetry for the 3D Modeling of a Geomorphological Structure
## 5 Results and Comparisons
### Estimate of the Size of the Pixel on the Rock Sample  
As demonstrated, the procedure described so far is easily feasible, even by non-experienced operators, thanks to the enormous potential of modern software. However, depending on the objective of the survey, it is of primary importance to establish, as the first key step, the final definition of the product to be obtained, namely the representation scale. In the context of this research work,  
Figure 7: A comparison of the point clouds generated with different software products and the reference solution. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Software/Dataset**} & \multicolumn{5}{c}{**Absolute Distance C2C [\%]**} \\ \cline{2-5}  & **D \textless{} 0.5 mm** & **0.5 \textless{} D \textless{} 0.8 mm** & **0.8 \textless{} D \textless{} 1 mm** & **1 \textless{} D \textless{} 2 mm** & **2 \textless{} D \textless{} 5 mm** \\ \hline AMP/50 images & \textless{}27.10 & \textless{}21.81 & \textless{}16.91 & \textless{}18.05 & \textless{}16.16 \\ AMP/25 images & \textless{}44.02 & \textless{}25.62 & \textless{}7.70 & \textless{}11.27 & \textless{}11.40 \\ AMP/12 images & \textless{}56.01 & \textless{}18.18 & \textless{}8.19 & \textless{}11.72 & \textless{}5.91 \\ VSFM/50 images & \textless{}46.87 & \textless{}22.87 & \textless{}8.07 & \textless{}11.31 & \textless{}10.89 \\ VSFM/25 images & \textless{}17.03 & \textless{}14.09 & \textless{}10.52 & \textgreater{}37.86 & \textless{}20.51 \\ SCANN3D/25 images & \textless{}6.59 & \textless{}6.52 & \textless{}3.85 & \textless{}22.04 & \textless{}60.99 \\ SCANN3D/12 images & \textless{}26.07 & \textless{}14.36 & \textless{}8.39 & \textless{}19.99 & \textgreater{}31.20 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Point distances distribution. it is fundamental to obtain 3D representations of objects at large or very large scales, in order to be able to conduct specific geomorphological analyses. These particular objects, as well as some areas of the underground caves, cannot always be inspected or, for different reasons, a prolonged on-site observation over time is not allowed. It is therefore essential to set the photogrammetric survey in such a way as to obtain the desired detail or, on the contrary, according to the operating conditions of the relevant site, in order to assess which resolution can be reached by the instruments that are available to us. To this purpose, it is necessary to estimate which is the so called Ground Sample Distance (GSD) [17] achievable by the camera of our smartphone device, namely the distance between the center of two pixels expressed in the unit of measurement of the object, as a function of the distance acquisition. GSD was introduced in the field of aerial photogrammetry as fundamental information for flight planning [53]. However, by defining a target GSD for a specific project of terrestrial photogrammetry, it is possible to calculate the most suitable acquisition distance with respect to the object of study to be maintained. Table 10 lists the characteristics of the processed data as shown in the APM report; these are average values calculated with respect to the images of the entire dataset. The GSD is a function of the acquisition distance, focal length and digital sensor size, as explained by the following formula:  
\[GSD=\frac{d*p}{f} \tag{1}\]  
where \(d\) is the image acquisition distance, \(p\) is the pixel pitch and \(f\) is the focal length. The GSD values can be estimated by taking into account the characteristics of the OnePlus 5 smartphone and the focal length calculated in previous sections, in order to define the model resolution that can be reached with this specific device. Since the relationship between the GSD and the acquisition distance is directly proportional, it is easy to deduce that, if with an acquisition distance of 37.7 cm we have an average GSD of 0.0920 mm/px, at a distance of 100 cm the GSD will reach a size of 0.2440 mm/px, and at 200 cm it will increase to 0.4881 mm/px.