# An Advanced Vehicle Body Part Inspection Scheme Based on Scattered Point Cloud Data
## 3 Materials and Methods
### Methods
#### 3.2.2 Denoising of PCD Based on a Hybrid Filtering Algorithm
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & **Part** & \(\alpha\) & \(\beta\) & \(\gamma\) & \(d_{x}\) & \(d_{y}\) & \(d_{z}\) & \(F\) \\ \hline \multirow{4}{*}{Fine registration} & ICP & 0.135 & \(-\)1.393 & 6.823 & \(-\)4.142 & \(-\)1.486 & \(-\)2.198 & 0.331 \\  & HS & 0.133 & \(-\)1.341 & 6.790 & \(-\)4.139 & \(-\)1.450 & \(-\)2.137 & 0.1132 \\ \cline{1-1}  & DA & 0.132 & \(-\)1.347 & 6.797 & \(-\)4.140 & \(-\)1.433 & \(-\)2.139 & 0.0740 \\ \cline{1-1}  & TLBO & 0.131 & \(-\)1.332 & 6.792 & \(-\)4.148 & \(-\)1.455 & \(-\)2.139 & 0.0132 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: PCD after registration in Figure 3a. Figure 8: Point cloud fine registration experiment. (**a**) is the initial point cloud data position of the vehicle part, (**b**) is the coarse registration result of FPFH, (**c**) is the fine registration result of ICP, (**d**) is the fine registration result of Harmony search (HS), (**e**) is the fine registration result of Dragonfly algorithm (DA) and (**f**) is the fine registration result of TLBO algorithm. ### Denoising Experiment

To reduce the influence of noise points on the subsequent point cloud processing process, the point cloud denoising algorithm described in Section 3.2.2 is first used to denoise the initial point cloud data. The denoising results of the PCD are shown in Figure 9.

In Figure 9, the amount of PCD after denoising was 97,868 (Figure 9a), 75,456 (Figure 9b), 143,516 (Figure 9c), 267,308 (Figure 9d), 164,473 (Figure 9e), 410,265 (Figure 9f), 228,189 (Figure 9g) and 289,115 (Figure 9h). Therefore, the number of data removed by the point cloud denoising algorithm was 36,856 (Figure 9a), 25,908 (Figure 9b), 42,967 (Figure 9c), 59,227 (Figure 9d), 50,361 (Figure 9e), 27,487 (Figure 9f), 11,437 (Figure 9g), 30,840 (Figure 9h). The pass-through filtering parameters are defined according to different parts, while the statistical filtering parameters are \(k=10\), \(\sigma=1\). As can be seen in Figure 9, the point cloud noise data were largely removed through the denoising algorithm designed in this paper and the target PCD was thus accurately extracted, providing an accurate data foundation for the subsequent point cloud processing. ### Simplification Experiment

The target PCD extracted after denoising retained a large amount of data and redundant point clouds, resulting in a heavy workload for subsequent analysis and low analytical efficiency. Therefore, the point cloud simplification algorithm designed in Section 3.2.3 was used to simplify the PCD. The simplified point cloud model is shown in Figure 10. For the point cloud simplification algorithm, the relevant calculation parameters are \(k=15\), \(m=2\), \(C=20\), \(\sigma=2\), \(\varepsilon=0.02\) and \(T=50\). To reduce the influence of redundant points on the subsequent analysis of PCD, a feature preserving retention FCM algorithm was designed to simplify the PCD. Figure 10 illustrates the simplified point cloud model. The number of point clouds after simplification was 13,911 (Figure 10a), 9,794 (Figure 10b), 13,576 (Figure 10c), 30,502 (Figure 10d), 15,150 (Figure 10e), 41,367 (Figure 10f), 22,019 (Figure 10g), 28,528 (Figure 10h). The number of redundant points removed was 83,957, 65,662, 129,940, 236,806, 149,323, 368,898, 206170 and 260,587. The simplified rate equation is as:

\[rate=\frac{N_{before}-N_{after}}{N_{before}}\times 100\%, \tag{30}\]

Figure 9: PCD after denoising. (**a**)–(**h**) are a series of denoising results of vehicle body parts PCD in Figure 3, respectively. where, \(N_{before}\) is the number of point clouds before simplification and \(N_{after}\) is the number of point clouds after simplification. According to Equation (30), the point cloud simplification rate was 85% (Figure 10a), 87% (Figure 10b), 90% (Figure 10c), 88% (Figure 10d), 90% (Figure 10e), 90% (Figure 10f), 90% (Figure 10g) and 90% (Figure 10h).