## 3 Results  
### Geometric Consistency  
#### 3.1.1 Reliability of the ICP-Derived Transformations  
Since geometric consistency is based on ICP, it is mandatory to find a way to quantify the quality of this procedure, because if ICP fails, the estimated distance will not correspond to the actual one. It is known that the ICP estimation is not always reliable, especially when it is used to register almost flat clouds, as in our case. Registration is performed between two point clouds, namely PCA and PCB; it is possible to estimate the transformation PCA-to-PCB, which when applied to PCA, aligns it to PCB. This transformation is constituted by a roto-translation (i.e., the composition of a 3D shift  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Index** & **Name** & **Formula** & **References** \\ \hline NDVI & Normalized Difference Vegetation Index & \(\frac{\text{Nir-Rad}}{\text{Nir-Rad}}\) & [43] \\ \hline GNDVI & Green Normalized Difference Vegetation Index & \(\frac{\text{Nir-Grant}}{\text{Nir+Green}}\) & [44] \\ \hline NDRE & Normalized Difference Red-Edge Index & \(\frac{\text{Nir-RadEdge}}{\text{Nir-RadEdge}}\) & [45] \\ \hline NDVIre & Red-Edge Normalized Difference Vegetation Index & \(\frac{\text{RedEdge-Rad}}{\text{RedEdge+Rad}}\) & [46] \\ \hline NGRDI & Normalized Green Red Difference Index & \(\frac{\text{Green-Rad}}{\text{Green+Rad}}\) & [47] \\ \hline \hline \end{tabular}
\end{table}
Table 1: Vegetation indices (VIs) used in this study.  
and a 3D rotation). Of course, it is possible to estimate the PCB-to-PCA transformation, which should coincide, aside from uncertainties, with the inverse of the first one. We used the comparison between the estimated and calculated inverse transformation to infer the precision of our estimations.  
Results are shown in Table 2, where columns 3-5 report the components of the estimated shift (delta E, delta N, delta H) in meters and columns 6-8 show the rotation angles (\(\omega\), \(\varphi\), \(\kappa\)) in degrees. Rows are grouped in fours, with each chunk being associated with one processing configuration. Row 1 reports the transformation (3-to-4) aligning point cloud 3 to cloud number 4. Row 2 shows the parameters of the calculated inverse transformation. Row 3 displays the parameters of the 4-to-3 estimated transformation and row 4 shows the differences between rows 2 and 3.  
Excluding the DG scenario, in which direct georeferencing is adopted and point clouds are slightly deformed, the worst residual is 6 cm for the shift components and 0.06 deg for rotations. A distance-equivalent error (\(e\)) can be computed for the resulting angular residual (\(\alpha\)) by assuming a distance (\(d\)) of 100 m, corresponding to the half-width of the considered test area. By applying the simple formula \(e=d\alpha\), where the angle \(\alpha\) is expressed in radiants, it can be found that \(e=12\) cm.  
Now, we must consider the granularity of the datasets (i.e., the points' linear spacing). For the skeleton, this is considered for ICP estimation; as already explained, the spacing is 12.5 cm for dense parts and 100 cm elsewhere. As residuals of the transformation equal the discretization size of the considered datasets, we consider the estimated transformations reliable and precise.