## 2 Global Registration Method Based on the OBB Regional Area-Based Descriptor
### Principle Concept and Flow Chart Diagram of the Global Registration Method
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Points**} & **OBB Segments: \(k_{1}\)** & \multirow{2}{*}{**Translation Error (mm)**} & \multirow{2}{*}{**Rotation Error (rad)**} & \multirow{2}{*}{**Time (s)**} \\  & \(\times\)\(k_{2}\times k_{3}\) & & & \\ \hline \multirow{3}{*}{1000} & 4 \(\times\) 5 \(\times\) 6 & 1.371 & 0.057 & 4.052 \\  & 7 \(\times\) 8 \(\times\) 9 & 1.371 & 0.017 & 15.328 \\  & 10 \(\times\) 11 \(\times\) 12 & 1.371 & 0.017 & 50.953 \\ \hline \multirow{3}{*}{5000} & 4 \(\times\) 5 \(\times\) 6 & 1.352 & 0.073 & 43.570 \\  & 7 \(\times\) 8 \(\times\) 9 & 1.352 & 0.013 & 110.212 \\  & 10 \(\times\) 11 \(\times\) 12 & 1.352 & 0.013 & 329.641 \\ \hline \multirow{3}{*}{10,000} & 4 \(\times\) 5 \(\times\) 6 & 1.368 & 0.035 & 67.327 \\  & 7 \(\times\) 8 \(\times\) 9 & 1.368 & 0.015 & 203.795 \\ \cline{1-1}  & 10 \(\times\) 11 \(\times\) 12 & 1.368 & 0.015 & 936.841 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experimental results using the connector model obtained by the proposed coarse registration method with different numbers of the oriented bounding box (OBB) segments \(k_{1}\times k_{2}\times k_{3}\). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Models**} & **Ratio of** & \multirow{2}{*}{**Translation Error (mm)**} & \multirow{2}{*}{**Rotation Error (rad)**} & \multirow{2}{*}{**Time (s)**} \\  & **Overlapped Area** & & & \\ \hline \multirow{6}{*}{Connector} & 90\% & 1.066 & 0.013 & 15.328 \\  & 80\% & 1.371 & 0.017 & 13.543 \\ \cline{1-1}  & 60\% & 2.452 & 0.042 & 10.476 \\ \cline{1-1}  & 50\% & 5.796 & 0.137 & 9.548 \\ \cline{1-1}  & 30\% & 12.347 & 0.532 & 7.365 \\ \hline \multirow{6}{*}{Brazo} & 90\% & 1.023 & 0.012 & 16.462 \\ \cline{1-1}  & 80\% & 1.455 & 0.015 & 13.443 \\ \cline{1-1}  & 60\% & 2.674 & 0.044 & 11.348 \\ \cline{1-1}  & 50\% & 5.357 & 0.159 & 8.348 \\ \cline{1-1}  & 30\% & 15.642 & 0.758 & 6.769 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experimental results using the connector model obtained by the proposed coarse registration method with different ratios of overlapped area. surface contours. We demonstrate the developed approach by using four test cases comprising two regular shapes, a Brazo and a connector, and two featureless models, a cylinder and a socket with 80% shape similarity which was provided by the Industrial Technology Research Institute (ITRI) (as shown in Figure 11). Given the reported results, it is clear that the proposed approach performs more accurately than the other methods on all the tested data. The computation efficiency of the proposed method is approximately the half of the fastest method, the Signature of Histograms of OrienTations SHOT. However, its time efficiency still ranks within a reasonable range. To test the noise influence, the synthetic experiments were carried out with respect to three different levels of Gaussian noises: \(\sigma\) = 0.01, 0.02 and 0.03 (standard deviation). The coarse registration results on the connector point-sets are shown in Table 5. We found that the proposed approach is able to achieve acceptable results with a certain level of noise. ## 4 Conclusions

In this study, a global registration method is developed to overcome one of the most challenging problems remaining in current 3D scanning systems for accurate image registration, even with no reference coordinate existing between the neighboring scanned surface patches. The key innovation in this work is the strategy in determining a robust registration transformation between two neighboring scans. The experimental results demonstrate the validity and applicability of the proposed approach.