# 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
#### 2.1.3 Target Point Cloud Extraction  
To extract the target point cloud data, it is necessary to first distinguish the different depth regions in the filtered grayscale image I\({}^{\prime}\) for edge extraction. The Sobel operator is used for this purpose, which approximates the discrete derivative of the image intensity function to calculate the gradient. We used edge detection techniques, such as the Sobel operator, to identify significant boundaries within the image. A depth threshold was applied to segment the target regions based on depth information. Additionally, a minimum area threshold was set to exclude smaller regions, ensuring the validity of the target areas. The specific threshold values were determined empirically, based on experimental data, and optimized through cross-validation to achieve the best performance. The grayscale image I\({}^{\prime}\) is convolved with the operator, as shown in Equation (15). By applying the selected operator, the surface and edge features of the original grayscale image are differentiated, resulting in an edge mask matrix \(M_{\varepsilon}\). The grayscale image is then multiplied element-wise with the matrix \(M_{\varepsilon}\) to obtain the edge-detected image of the grayscale data. \[M_{\varepsilon}= \begin{bmatrix}-1&0&1\\ -2&0&2\\ -1&0&1\end{bmatrix} *\text{I}^{\prime} \tag{15}\]  
\[\text{I}^{\prime}_{\varepsilon}=\text{I}^{\prime}\bigodot M_{\varepsilon} \tag{16}\]  
\[\text{I}^{\prime}_{S}=\text{I}^{\prime}-\text{I}^{\prime}_{\varepsilon} \tag{17}\]  
After obtaining the edge matrix I\({}^{\prime}_{\varepsilon}\), the surface features of the image can be obtained by subtracting the edge matrix I\({}^{\prime}_{\varepsilon}\) from the original image I\({}^{\prime}\). Each distinct closed region in the resulting image corresponds to the surface of the target object. Figure 3c,d show the point cloud images corresponding to the extracted edge features and surface features from the grayscale image, respectively. The edge map obtained using the Sobel operator is based on changes in grayscale values. From this edge map, connected regions (as shown in Figure 3e) can be identified. Figure 3: (**a**) Grayscale image; (**b**) the filtered grayscale image; (**c**) edge map; (**d**) surface diagram; (**e**) connected block diagram; and (**f**) target section. These connected regions are then binarized, and the area of each connected region is computed. After segmentation, further filtering was applied based on depth variation and the size of connected regions. Regions smaller than a certain area threshold were excluded to avoid noise interference. The screening criteria were established based on the expected size and depth range of target regions in the experiment, and these thresholds were typically determined through empirical methods. By setting the range for the depth variation of the point cloud and the size of the region's area, the target point cloud can be extracted (as shown in Figure 3f). The extracted target point cloud is denoted as \(I^{\prime}{}_{T}\). After extracting the target edges using the Sobel operator, a Target Retrospective Search Algorithm (TRSA) is proposed to accurately extract the target portion from the original scatter plot. Once the target point cloud portion I\({}^{\prime}{}_{T}\) is obtained from the grayscale image, the conversion matrix \(K\) between the scatter plot and the grayscale image is used to perform the inverse cylindrical unfolding projection transformation. By applying the transformation matrix \(K\) to the target grayscale image, a new scatter plot \(S^{\prime}\) is generated. The four corner points of \(S^{\prime}\) are denoted as \(A_{0}\), \(B_{0}\), \(C_{0}\), \(D_{0}\). However, since the conversion of pixels from the grayscale image to the scatter plot introduces some errors, the new scatter plot \(S^{\prime}\) will differ from the original scatter plot \(S_{k}\) derived from the cylindrical projection.