# Rapid Target Extraction in LiDAR Sensing and Its Application in Rocket Launch Phase Measurement
## 3 LiDAR Target Detection Experiment
### Method Effectiveness Verification
#### 3.2.2 Accuracy Verification  
In the method proposed in this paper, the original point cloud is first converted into a scatter plot using cylindrical unfolding projection, then transformed into a 2D grayscale image for target extraction. After the target portion is extracted, the grayscale image is converted back into a scatter plot. Since the grayscale image only contains pixel distance information, while the original scatter plot includes precise coordinates and other attributes such as color, much of this information is lost or blurred during the conversion. Moreover,  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Num** & **Count** & **DBSCAN** & **MST** & **Proposed Method** \\ \hline
1 & 1000 & 0.1 s & 0.23 s & 0.25 s \\
2 & 10,000 & 1.09 s & 1.99 s & 0.26 s \\
3 & 20,000 & 5.14 s & 3.81 s & 0.27 s \\
4 & 30,000 & 248 s & 31.2 s & 0.29 s \\
5 & 50,000 & 1021 s & \textgreater{}1 h & 0.32 s \\
6 & 100,000 & \textgreater{}1 h & \textgreater{}1 h & 0.40 s due to the large volume of 3D point cloud data captured by the LiDAR, the points in the resulting scatter plot tend to be densely packed. Given the limited resolution of the image, it cannot fully preserve the original point cloud details. As a result, when the inverse cylindrical unfolding projection is applied to the grayscale image to generate a new scatter plot, there will be some deviation from the original scatter plot. Specifically, the coordinates of each target point in the new scatter plot will exhibit slight differences from those in the original point cloud. By comparing the target extracted from the new scatter plot with the corresponding points in the original scatter plot, the accuracy of the target extraction process can be evaluated.  
To eliminate the errors introduced when converting the grayscale image back into a scatter plot--errors caused by pixel conversion--it is important to note that these errors are minimal. As a result, the scatter plot derived from the conversion can be used for a reverse target search in the original scatter plot. By matching the coordinates to the nearest points in the original point cloud, target extraction is achieved in the 2D space. Finally, the scatter plot obtained through the reverse search is compared with the scatter plot directly generated by manually extracting the target point cloud from the original 3D point cloud, followed by a cylindrical unfolding projection. The error comparison is shown in the right half of Figure 9. In this image, the depth value of each point represents the error magnitude. The left half shows the error map without applying the target reverse search algorithm. The results indicate that most of the scatter point coordinates exhibit errors around 0.05, while the error for coordinates derived using the proposed method remains within the \(10^{-7}\) range. This confirms that the algorithm can accurately match the original target 3D point cloud without distortion, ensuring precise target extraction. After validating with data collected from different LiDAR systems, the proposed method proves capable of accurately extracting the target 3D point cloud for various resolutions. This also validates the effectiveness and precision of the target reverse search algorithm introduced in this paper.  
Figure 9: Target extraction relative error chart.  
In this section, we have demonstrated that the target point cloud extraction method can achieve high accuracy with an error on the order of \(10^{-7}\), indicating that the extraction process is highly precise. As the method's accuracy has been verified, we have not included a further discussion of the trade-off between processing speed and accuracy, as the speed improvements do not significantly impact the accuracy of the results.