## 4 Experimental Results
### Measurement Statistical Analysis Experimental of Varying Orientations of the Measurement Object
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Box**} & \multirow{2}{*}{**Dim**} & \multirow{2}{*}{**Ground Truth**} & \multicolumn{5}{c}{**Measurement at Three Box-Sensor Distances (mm)**} \\  & & & **(The Measurement Error (mm) in Brackets)**} & \\  & & & **[The Relative Error (\%) in Square Brackets.]** & \\ \hline \multirow{6}{*}{(a)} & \multirow{6}{*}{\(L\)} & \multirow{6}{*}{495.0} & 750.5 & 751.2 & 747.7 & 746.4 & 744.6 \\  & & & (+0.5) & (+1.2) & (\(-2.3\)) & (\(-3.6\)) & (\(-5.4\)) \\  & & & [0.07\(\%\)] & [0.16\(\%\)] & [0.31\(\%\)] & [0.48\(\%\)] & [0.72\(\%\)] \\ \cline{2-8}  & & & 494.8 & 493.9 & 496.1 & 492.4 & 490.4 \\ \cline{2-8}  & & & (\(-0.2\)) & (\(-1.1\)) & (+1.1) & (\(-2.6\)) & (\(-4.6\)) \\  & & & [0.04\(\%\)] & [0.22\(\%\)] & [0.22\(\%\)] & [0.53\(\%\)] & [0.93\(\%\)] \\ \cline{2-8}  & & & 330.4 & 330.8 & 329.0 & 326.9 & 333.9 \\ \cline{2-8}  & & & (+0.4) & (+0.8) & (\(-1.0\)) & (\(-3.1\)) & (\(+3.9\)) \\  & & & [0.12\(\%\)] & [0.24\(\%\)] & [0.30\(\%\)] & [0.94\(\%\)] & [1.18\(\%\)] \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Measurements and errors versus the visual sensor and measured box distance. Figure 12: Two standard boxes with different dimensions used for testing: (**a**) \(190.0\times 253.0\times 400.0\); (**b**) \(320.0\times 320.0\times 620.0\). Figure 13: Average measurement error between the standard box and the measured result. Figure 15 shows that at the distance sensor/boxes dis1, dis2, dis3, dis4, and dis5, the average absolute errors are 0.411, 0.844, 1.478, 3.111, and 4.689 mm, respectively. The following data from the table can be obtained: the error of the measured result increases with the increase of the measured distance. The maximum error of the measurement was 5.8 mm, which was kept within \(\pm 6\) mm. The analyzed data show that our system has good accuracy in the normal measurement range of the box and vision sensor. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Box**} & \multirow{2}{*}{**Dim**} & \multirow{2}{*}{
\begin{tabular}{c} **Ground** \\ **Truth** \\ \end{tabular} } & \multicolumn{6}{c}{**Measurement at Three Box-Sensor Distances (mm)**} \\  & & & **(The Measurement Error (mm) in Brackets)** & \\ \cline{1-1}  & & & **(The Relative Error (\%) in Square Brackets.)** & \\ \hline \multirow{10}{*}{(b)} & \multirow{4}{*}{\(W\)} & \multirow{4}{*}{480.0} & 479.7 & 480.8 & 478.5 & 483.0 & 485.3 \\  & & & (\(-\)0.3) & (\(+\)0.8) & (\(-\)1.5) & (\(+\)3.0) & (\(+\)5.3) \\  & & & [0.63\(\%\)] & [0.17\(\%\)] & [0.31\(\%\)] & [0.63\(\%\)] & [1.10\(\%\)] \\ \cline{1-1}  & & & 549.6 & 550.6 & 548.1 & 552.4 & 555.4 \\  & & & (\(-\)0.4) & (\(+\)0.6) & (\(-\)1.9) & (\(+\)2.4) & (\(+\)5.4) \\  & & & [0.07\(\%\)] & [0.11\(\%\)] & [0.35\(\%\)] & [0.44\(\%\)] & [0.98\(\%\)] \\ \cline{1-1}  & & & 380.4 & 379.1 & 381.3 & 382.6 & 376.3 \\  & & & (\(+\)0.4) & (\(-\)0.9) & (\(+\)1.3) & (\(+\)2.6) & (\(-\)3.7) \\  & & & [0.11\(\%\)] & [0.24\(\%\)] & [0.34\(\%\)] & [0.68\(\%\)] & [0.97\(\%\)] \\ \hline \multirow{10}{*}{(c)} & \multirow{4}{*}{\(W\)} & \multirow{4}{*}{450.0} & 450.5 & 449.6 & 451.4 & 446.8 & 454.8 \\  & & & (\(+\)0.5) & (\(-\)0.4) & (\(+\)1.4) & (\(-\)3.2) & (\(+\)4.8) \\ \cline{1-1}  & & & [0.11\(\%\)] & [0.09\(\%\)] & [0.31\(\%\)] & [0.71\(\%\)] & [1.07\(\%\)] \\ \cline{1-1} \cline{2-10}  & & & 649.1 & 648.7 & 648.4 & 654.2 & 655.8 \\ \cline{1-1}  & & & (\(-\)0.9) & (\(-\)1.3) & (\(-\)1.6) & (\(+\)4.2) & (\(+\)5.8) \\ \cline{1-1}  & & & [0.14\(\%\)] & [0.20\(\%\)] & [0.25\(\%\)] & [0.65\(\%\)] & [0.89\(\%\)] \\ \cline{1-1} \cline{2-10}  & & & 350.1 & 350.5 & 348.8 & 353.3 & 346.7 \\ \cline{1-1}  & & & (\(+\)0.1) & (\(+\)0.5) & (\(-\)1.2) & (\(+\)3.3) & (\(-\)3.3) \\ \cline{1-1}  & & & [0.03\(\%\)] & [0.14\(\%\)] & [0.34\(\%\)] & [0.94\(\%\)] & [0.94\(\%\)] \\ \hline \hline \end{tabular}
\end{table} 
Table 5: _Cont._  
Figure 14: Standard boxes with different dimension parameters, from (**a**) to (**c**).