# Automatic Point-Cloud Registration for Quality Control in Building Works
## 3 Results and Discussion
### Quality Control
Seven pillars of the first study case and seven pillars of the second study case were subjected to measurements of their width at three different heights: low height at 0.20 m, medium height at 1.20 m and high height at 2.50 m from the floor. Each measurement is performed five times, and robust statistical estimators are calculated from these measurements. Table 5 shows the theoretical measurements (performed on the BIM) in each pillar and the measurements performed on the as-built model resulting from our methodology. Table 6 shows the results of the robust statistical parameters calculated from the dimensional analysis (median and BWMV). Provided that the tolerance for pillar section control is established at 8-10 mm (Table 4), the results obtained with the methodology proposed are applicable in this type of scenario. \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{2}{c}{**Tolerances in Construction Elements**} \\ \hline Cross Section (\(D\) \(<\) 30) & +10–8 mm \\ Cross Section (30 \(<\)\(D\) \(<\) 100) & +12–10 mm \\ Cross Section (100 \(<\)\(D\)) & +24–20 mm \\ Vertical deviation outer edges columns & \(\pm\)6 mm \\ Wall Thickness \(<\) 25 cm & +12–10 mm \\ Wall Thickness \(>\) 25 cm & +16–10 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Tolerances in the different structural elements according to [26]. \"\(D\)\" represents the transversal dimension of the elements. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Bias** & \multicolumn{2}{c}{**Dispersion**} \\ \cline{2-4}  & **Median (m)** & **NMAD (m)** & **(BWMV) (m)** \\ \hline Study Case 1 & 0.007 & \(\pm\)0.007 & \(\pm\)0.00005 \\ Study Case 2 & 0.008 & \(\pm\)0.008 & \(\pm\)0.00007 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Bias and dispersion results of the TLS vs. BIM for the two study cases. An additional test of the dimensions of one pillar on each study case is performed by adjusting planes to each face of the pillars (Figure 11). This test is performed as an evaluation method of the quality of the results. This additional evaluation is necessary, because the point cloud is formed by discrete points, and the punctual measurements can present non-robust results, since they depend on the points used for the measurements. The metrical verification in the planar case consists in computing the size of the pillars by measuring the distance between opposite sides of the pillars and comparing the distances measured with the real dimensions of the pillars (Table 7). Thus, the width of the pillar is denoted as \(d1\) (distance between planes 3 and 4), and the length of the pillar is \(d2\) (distance between planes 1 and 2), as shown in Figure 11c. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Bias**} & \multicolumn{2}{c}{**Dispersion**} \\ \cline{3-5}  & \multicolumn{2}{c}{**Median (mm)**} & \multicolumn{2}{c}{**NMAD (mm)**} & \multicolumn{2}{c}{**(BWMV) (mm)**} \\ \hline \multirow{5}{*}{Study Case 1} & Pillar 1 & 503 & \(\pm\)1.5 & \(\pm\)0.5 \\  & Pillar 2 & 450 & \(\pm\)4.4 & \(\pm\)9.6 \\  & Pillar 3 & 352 & \(\pm\)3.0 & \(\pm\)9.0 \\ \cline{1-1}  & Pillar 5 & 449 & \(\pm\)3.0 & \(\pm\)9.8 \\ \cline{1-1}  & Pillar 6 & 451 & \(\pm\)1.5 & \(\pm\)7.6 \\ \cline{1-1}  & Pillar 7 & 348 & \(\pm\)1.5 & \(\pm\)3.3 \\ \cline{1-1}  & Pillar 8 & 600 & \(\pm\)1.5 & \(\pm\)2.3 \\ \hline \multirow{5}{*}{Study Case 2} & Pillar 1 & 597 & \(\pm\)1.5 & \(\pm\)2.9 \\ \cline{1-1}  & Pillar 2 & 452 & \(\pm\)1.5 & \(\pm\)1.6 \\ \cline{1-1}  & Pillar 3 & 451 & \(\pm\)1.5 & \(\pm\)1.8 \\ \cline{1-1}  & Pillar 4 & 447 & \(\pm\)1.5 & \(\pm\)1.6 \\ \cline{1-1}  & Pillar 5 & 448 & \(\pm\)2.9 & \(\pm\)4.4 \\ \cline{1-1}  & Pillar 6 & 398 & \(\pm\)2.9 & \(\pm\)7.7 \\ \cline{1-1}  & Pillar 7 & 497 & \(\pm\)1.5 & \(\pm\)3.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Bias and dispersion data for the analysed data in both study cases.