# Rapid Target Extraction in LiDAR Sensing and Its Application in Rocket Launch Phase Measurement
## 2 Principle and Methods  
### Principle of Rapid Target Point Cloud Extraction Method  
#### 2.1.1 Cylindrical Projection  
LiDAR operates by emitting laser pulses and receiving the reflected signals to determine the distance, position, and reflectivity of target objects. The 3D point cloud data generated by LiDAR contains rich spatial information, forming a solid foundation for target extraction and recognition. In this study, the primary point cloud data consists of the 3D coordinates \(P_{i,j}\) and their corresponding reflectance intensities \(q_{i,j}\). However, due to the complexity of 3D data, processing large-scale point cloud datasets often leads to slow processing speeds and low efficiency. To address this issue, we implement a method that transforms the 3D point cloud data obtained from LiDAR into a scatter plot via projection. By adjusting the resolution, this scatter plot is further converted into a 2D grayscale image. This approach effectively simplifies the 3D point cloud data into a 2D representation, making it easier to extract relevant features. LiDAR scans the scene by rotating an internal mirror, and the resulting point cloud data inherently contains angular information, recorded in the order of the laser beam's scanning sequence. Based on this scanning characteristic, cylindrical unfolding projection maps the 3D point cloud data into a 2D image by unfolding it according to angular increments, thereby organizing the spatial data into a structured image based on the scan angles. This method not only preserves the depth information of the point cloud but also significantly reduces the issue of point cloud occlusion, making it particularly suitable for target extraction in complex scenes. In the context of rocket launch scenarios, target point cloud data are typically sparse, and located at long distances with a limited coverage area. Cylindrical projection ensures the uniformity of point cloud distribution and enhances the visualization, providing a solid foundation for subsequent processing tasks such as filtering, segmentation, and extraction. By adjusting the resolution to convert the resulting scatter plot into a grayscale image, the data complexity can be further reduced, while key features of the target region are retained, thereby significantly improving data processing efficiency and real-time performance. The original point cloud data undergoes a 2D projection transformation based on the cylindrical projection method described in the relevant literature [20]. The angle values in the original data are converted to radians to simplify the computation. Each 3D point is then mapped to 2D coordinates through cylindrical unfolding projection, which unfolds the 3D data into a 2D image based on angular projection. The original data are projected in the horizontal direction within the range \(\beta_{\min}<\theta_{i,j}<\beta_{\max}\), and in the vertical direction within the range \(\alpha_{\min}<\phi_{i,j}<\alpha_{\max}\). Cylindrical unfolding projection transformation is illustrated in Figure 1.  
\[P_{i,j}=\left[x_{i,j},y_{i,j},z_{i,j},q_{i,j}\right] \tag{1}\]  
\[\hat{x}_{r}=x_{i,j}*\frac{\pi}{180};\hat{y}_{r}=y_{i,j}*\frac{\pi}{180} \tag{2}\]  
\[S=f\left(\hat{x}_{i,j},\hat{y}_{i,j},\hat{\sigma}_{i,j}\right)\]  
\[S\Longleftrightarrow\left\{ \begin{array}{c}\hat{\sigma}_{i,j}=\left\|x_{i,j}+y_{i,j}+z_{i,j}\right\|_{2},\text{ or }\hat{\sigma}_{i,j}=q_{i,j}\\ \hat{x}_{i,j}=\frac{\tan^{-1}\left(-\frac{y_{i,j}}{z_{i,j}}\right)}{x_{i,j}} \\ \hat{y}_{i,j}=\frac{\tan^{-1}\left(\frac{y_{i,j}}{z_{i,j}}\right)}{y_{r}} \end{array} \right. \tag{3}\]  
The point cloud obtained from a single LiDAR scan is transformed using cylindrical unfolding projection. All the original point cloud data are then projected onto a scatter plot. This projection results in an N \(\times\) 3 matrix, where N represents the number of points in the point cloud from that particular scan.