# A Simplification Method for Point Cloud of T-Profile Steel Plate for Shipbuilding
## 5 Experimental Results  
In this section, the proposed simplification method is verified based on the 3-D laser scanner and the Matlab of the MathWorks Incorporation. The experimental data are obtained from the HDS7000 laser scanner of the Leica Geosystems company [31] by scanning a T-profile steel plate. In the experiment, the data reduction rate is defined as the ratio of the remaining point cloud data volume to the total point cloud data volume. The welding zone feature point retention rate is defined as the ratio of the amount of point cloud data remaining in the weld zone to the total point cloud data volume in the weld zone. As shown in Figure 5, the red region has a relatively steep distribution of point cloud, while the blue region is a region with a relatively flat distribution of point cloud. With the improvement of the reduction rate, the shape of the entire measured object can still be seen. Comparing the original point cloud data with the reduced data in Figure 6, it can be seen that the algorithm can reserve the important features for the T-profile steel plate. The original point cloud data of this experiment are divided into areas with relatively flat features of the point cloud, which are simplified by the random sampling method. The experimental results are shown in Figure 6:  
Figure 4: Simplification profile based on the regional gravity center. Figure 5: Point cloud distribution area of T-profile steel plate. As can be seen in Figure 6, the smaller the sampling rate is, the fewer point cloud data points are left. In the flat area, only the complete contour features need to be retained. Considering the time required by the streamlining and its effect, the random sampling method is used to select a sampling rate of 50%. The corresponding reduction rate is 49.20%. For the region where the point cloud distribution is steep, the regional center of gravity method is simplified. As shown in Figure 7, the point cloud data of the region is better preserved after the regional center of gravity method is simplified. As can be seen in Figure 7 and Table 1, the smaller the side length of the set sub-cube grid is the more detail features are retained but the lower the processing speed is. Considering the streamlining time and the retention rate of the feature points in the welding zone, the side length of the sub-cube grid is set to 3 mm when the regional center of gravity reduction method is adopted. It can be seen in Figure 8 that the point cloud simplification method based on the combination of octree coding and the surface feature curvature threshold is used to preserve important feature points for the welding area of the T-shaped steel plate model. Meanwhile, the outline of the appearance is still good, which can help to extract the key geometric feature positions in the next step. The experimental results of the improved reduced algorithm and the four traditional reduced algorithms are shown in Table 2. The simplified effect of each algorithm is shown in Figure 9.  
Figure 6: Simplified results with different sample rates. Figure 8: The effect of point cloud reduction after using this algorithm. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Name**} & **Set Side** & **Set Side** & **Set Side** \\  & **Length 2 mm** & **Length 3 mm** & **Length 4 mm** \\ \hline Original point cloud data volume & 1534 & 1534 & 1534 \\ Remaining point number & 913 & 465 & 291 \\ Reduction rate of point cloud & 59.52\% & 30.31\% & 19.36\% \\ Processing time & 4.0826 s & 1.4228 s & 0.8965 s \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simplified result indicators under different side length bounding boxes. Figure 7: Different simplification effects under the bounding box with different side lengths. In order to analyze the performance of the proposed simplification method for the cloud point of the T-profile steel plate, it is compared with four other simplification methods. The results are shown in Table 2 and Figure 9, in which the reduction rates of these methods are kept approximately equal.