# 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
 \tag{21}\]

\[En=\sum\
olimits_{i=1}^{n}En_{i}. \tag{22}\]

Figure 7 shows the information entropy of PCD under different simplified algorithms, as can be seen from the Figure 7, according to the calculation results of entropy under the condition of the same reduction rate, the FCM simplified point cloud entropy value is the largest and the retained point cloud feature information is the most. Therefore, compared with the other four algorithms, the FCM point cloud algorithm proposed in this paper has better point cloud simplification effect. Figure 6: Point cloud simplification experiment. (**a**) is the initial point cloud data, (**b**) is the calculation result of random sampling, (**c**) is the calculation result of curvature sampling, (**d**) is the calculation result of grid sampling, (**e**) is the calculation result of octree-based sampling, and (**f**) is the calculation result of our sampling algorithm in this paper. #### 3.2.4 Registration of PCD

The ICP (Iterative Closest Point) algorithm is a classical point cloud registration algorithm proposed by [PERSON] [48], which established the foundations of this field. The basic principle of this algorithm is to find the closest corresponding location between two sets of point clouds. The ICP algorithm does this by calculating the mean square of the distances between the target point cloud and the measurement point cloud in Euclidean Space. Specifically, through matrix transformation, this method transfer the moving point cloud to the target point cloud's location and completes the point cloud registration via a number of iterations of point cloud movements. To move a spatial point, the point's initial coordinate is defined as \(p=(x,y,z)\), while the coordinate after moving is defined as \(p^{\prime}=(x^{\prime},y^{\prime},z^{\prime})\), When \(p\) is shifted in space, its motion is as follows:

Based on the ICP calculation principle, its general error function [48], \(F\), can be described as:

\[F\Big{(}\alpha,\beta,\gamma,d_{x},d_{y},d_{z}\Big{)}=\text{Min}(\frac{1}{N} \sum\
olimits_{i=1}^{N}\parallel V_{i}-(Rp_{i}+T)\parallel^{2}), \tag{23}\]

where \(V_{i}\) is the target point cloud. When \(F\) is the minimum value, the final position of the point cloud registration and the spatial motion parameters \(\Big{(}\alpha,\beta,\gamma,d_{x},d_{y},d_{z}\Big{)}\) of the measurement point cloud are calculated. In this way, point cloud registration is transformed into a minimization problem. The remaining parameters are shown in the Appendix A (A5)-(A9). However, the point cloud registration process is a complex nonlinear problem, which generally needs to be solved in two stages. Coarse Registration of PCD

The coarse registration process of the point cloud is an important step to complete the spatial alignment. The coarse registration process can provide a good initial position for fine registration and avoid the process of fine registration falling into the local optimum too early. There are many kinds of coarse registration algorithms. We chose the sample consensus initial alignment (SAC-IA) [49] because of its good coarse registration performance. In this paper, the SAC-IA algorithm is used to complete the coarse registration process of the point cloud. The calculation process is as follows:

**Step 1. ** For the measurement point cloud \(P(p_{1},p_{2},\ldots,p_{n})\), first, the normal vector information of the point cloud is obtained from the Equations (7)-(9), and \(m\) sampling points are selected from \(P\) to construct their fast point feature histograms (FPFH). To avoid similarities among the selected feature

Figure 7: Entropy under different simplified algorithms. points, the distance threshold value \(d_{\varepsilon}\) is set to distinguish them.