## 2 Global Registration Method Based on the OBB Regional Area-Based Descriptor
### Principle Concept and Flow Chart Diagram of the Global Registration Method
Figure 8: The coarse registration process between series of scans point cloud \(P\) and series of scans point cloud \(Q\): (**a**) hammer point cloud \(Q\) from the first series of scans; (**b–d**) rotation of point cloud \(Q\); (**e**) hammer point cloud \(P\) from the second series of scans; (**f–h**) the OBB regional area-based descriptor of \(P\) and \(Q\); (**i**) overlap rejected model after refine registration; (**j–l**) the triangle meshes of the hammer head. The performance of the registration can be estimated by using the distance from each overlapping point \(q_{i}\) in point cloud \(Q\) to the fitting control point \(p_{i}\) which is the projected point of \(q_{i}\) onto the triangle mesh of \(P\). If \(d_{i}\) denotes the distance between a point \(p_{i}\) in \(P\) and its closest neighbor point \(q_{i}\) in \(Q\), the mean distance \(\mu\) and standard deviation \(\sigma\), which are used to evaluate the performance of the object registration, are computed as follows:

\[\mu=\frac{1}{n}\sum_{i=1}^{n}d_{i} \tag{21}\]

Figure 9: Normalized cross-correlation curves given by Equation (11): (**a**) the coarse registration with rotation \(\Delta\theta=\pi/60\) and \(\alpha_{\text{thresh}}=\pi_{i}\) (**b**) the coarse registration with rotation \(\Delta\theta=\pi/60\) and \(\alpha_{\text{thresh}}=\pi/10\); (**c**) the coarse registration with rotation \(\Delta\theta=\pi/180\) and \(\alpha_{\text{thresh}}=\pi/30\) (OBB segments: \(k_{1}\times k_{2}\times k_{3}=4\times 5\times 6\)); (**d**) the coarse registration with the rough rotation estimate before a rotation increment \(\Delta\theta=\pi/180\) and \(\alpha_{\text{thresh}}=\pi/30\) (OBB segments: \(k_{1}\times k_{2}\times k_{3}=9\times 10\times 11\)). \[\sigma=\sqrt{\frac{\sum\limits_{i=1}^{n}{(d_{i}-\mu)^{2}}}{n-1}} \tag{22}\]

In this experiment, the mean deviation value is 0.0347 mm and the standard deviation value is 0.0235 mm. Figure 10 illustrates the other examples being achieved by the developed method. ### Case Study on Synthetic Data

In this section we provide a discussion on the influence of parameters on the performance of the proposed method. In addition, a comparison against several already published local feature descriptor methods is also introduced. The considered approaches are: Spin Images (SI), Point Signatures (PS), Point Feature Histograms (PFH), and the Signature of Histograms of OrienTations (SHOT). All methods were implemented in C++ using the open source Point Cloud Library (PCL). To estimate the computation cost of the registration process, the experiments are processed on a computer with an Intel core i7 processor with 3.40 GHz and 8 GB RAM. In real application, it is very difficult to distinguish different error sources such as shape measurement error (noise, surface sampling, _etc._), correspondence error (occlusion, outliers, _etc._), and registration error. In order to evaluate the coarse registration errors, we have generated synthetic data, which is provided by the Industrial Technology Research Institute (ITRI) (as shown in Figure 11). The dimensions of the socket model, connector model, cylinder model, and Brazo Control model are \(45\times 25\times 25\times 25\times 25\times 25\times 25\times 25\times 25 \times 25\times 25\times 25



Results obtained show that sampling does not considerably affect the accuracy of the registration results. Thus, low resolution surfaces can be used in the proposed approach to reduce the computation time. Meanwhile, as is shown in Table 1, errors in the proposed registration algorithms extremely depend on the rotation increment \(\Delta\theta\) (rad). To enhance the accuracy, the rotation increment should become smaller. However, the increment has a significant impact on the runtime of the proposed coarse registration process. As an example, the experiment with 1000 points in Table 1, with computation time in the case \(\Delta\theta\) = 0.01 (rad), at 126.439 (s), was much higher than that in the case \(\Delta\theta\) = 0.05 (rad), at only 1.063 (s).