## 2 Global Registration Method Based on the OBB Regional Area-Based Descriptor
### Principle Concept and Flow Chart Diagram of the Global Registration Method
Another important characteristic of the developed method is the total number of subdivided boxes in the OBB, \(n=k_{1}\times k_{2}\times k_{3}\). From Table 2, it can be seen that if the OBB contains many subdivided boxes, it is more expensive to find the best rotation. For a fast registration procedure, fewer subdivided \begin{table}
\begin{tabular}{l c c c c} \hline
**Points** & **Increment \(\Delta\theta\) (rad)** & **Translation Error (mm)** & **Rotation Error (rad)** & **Time (s)** \\ \hline  & 0.05 & 1.371 & 0.036 & 1.063 \\
1000 & 0.02 & 1.371 & 0.017 & 15.328 \\  & 0.01 & 1.371 & 0.009 & 126.439 \\ \hline  & 0.05 & 1.352 & 0.039 & 7.244 \\
5000 & 0.02 & 1.352 & 0.013 & 110.212 \\  & 0.01 & 1.352 & 0.012 & 904.237 \\ \hline  & 0.05 & 1.368 & 0.035 & 18.332 \\
10,000 & 0.02 & 1.368 & 0.015 & 203.795 \\  & 0.01 & 1.368 & 0.009 & 1762.824 \\ \hline \end{tabular}
\end{table} 
Table 1: Experimental results using the connector model obtained by the proposed coarse registration method with different samplings and increments \(\Delta\theta\). Figure 11: The synthetic data used in experiments: (**a–d**) CAD models of the objects; (**e–h**) point cloud of the objects; (**i–l**) point cloud of the objects from the virtual camera. boxes are preferable. However, it is also required that the number of subdivided boxes is great enough to achieve the expected rotation. For instance, in the experiment using a connector model of 1000 points, the rotation error rose to 0.057 (rad) for the OBB of \(n=k_{1}\times k_{2}\times k_{3}=4\times 5\times 6\), while it reached just 0.017 (rad) if the OBB of \(n=k_{1}\times k_{2}\times k_{3}=7\times 8\times 9\). Besides, the ratio of the overlapped area is especially crucial. As shown in Table 3, translation and rotation errors in the proposed approach grow in direct proportion to the percentage of the non-overlapping region. This change is especially significant with over 40% of the outliers. This is because it is difficult to estimate translation exactly without a high level of overlapping. The excellent results are obtained for over 80% of shape the overlapping. In this case, the translation and rotation for tested models were at under 1.5 (mm) and 0.02 (rad), respectively. As described in the Introduction, the proposed registration method is developed to register two series of surface scans which exist with a certain degree of optical occlusion from each individual viewpoint of the probe scanning. To accurately register two series of scans under such a circumstance, it is important to have them overlap as much as possible. However, realistically, the overlapped ratio really depends on the complexity of the scanned object's geometry and how the object is placed on the rotation table. In general, the higher the overlapped ratio between two series of scans, the more accurate the registration that can be achieved. The result of Table 4 reveals the performances of the proposed approach and 3D key point descriptors. It shows that the developed method in this paper outperforms in registration accuracy with reasonable operation efficiency. As we know, one significant common problem using feature descriptors is that they usually fail to deal with object geometry that has symmetrical or plural repeated