## 2 Methods
### Identification and Information Extraction of Rock Mass Structural Planes
#### 2.1.3 Application Analysis of Rock Mass Structural Planes Identification and Information Extraction
After visualizing the normal vectors in the previous section, we further validate the reliability of this method using point cloud data generated for a regular hexagonal pyramid through the Open3D library. The hexagonal pyramid has a height of 1 m and a base edge  
Figure 2: Visualization of Normal Vectors on a Cube. (**a**,**b**) PCA method; (**c**,**d**) Hough space transform method. length of 0.5 m, with an average point spacing of 4 mm. The number of points on each face is known, with a total of 146,913 points. Each face of the hexagonal pyramid represents a structural plane, and two opposite faces form a group, resulting in three groups of structural planes. First, we use both the PCA method and the Hough space transform to calculate the normal vectors of the hexagonal pyramid point cloud data. The same region growing parameters are set, and then region growing segmentation is performed on the point cloud data of the hexagonal pyramid. The results of the region growing process are shown in Figure 3.  
After region growing, the point cloud data within the same plane is assigned random colors and projected onto the XOZ and XOY planes to draw the front views (a), (c) and top views (b), (d) of the region growing results using the PCA method and Hough space transform. As shown in Figure 3, it is clear from the front and top views that each side of the regular hexagonal pyramid has been successfully identified and segmented. In Figure 3a,b, the point clouds along the edges and vertices of the hexagonal pyramid are red, indicating points that were not successfully identified. In contrast, in Figure 3c,d, only a small number of points in the same areas remain unrecognized. According to the study by [PERSON] [19], to quantify the effect of region growing, statistical analysis was performed on the number of identified and unidentified points within each plane. The recognition accuracy of region growing is measured by the identification rate \(\omega\), which is calculated using the following formula:  
\[\omega=\frac{j_{n}^{i}}{J_{n}} \tag{2}\]  
Figure 3: Region Growing Result Graph for Hexagonal Pyramid. (**a**) Front View using PCA; (**b**) Top View using PCA; (**c**) Front View using Hough space transform; (**d**) Top View using Hough space transform. In the formula: \(J_{n}\) represents the total number of points within the structural plane, and \(J_{n}^{i}\) represents the number of successfully identified points within the structural plane. Table 1 first lists the total number of points within the six structural planes of the hexagonal pyramid before region growing. Then, it shows the number of identified points within the six structural planes after region growing using the PCA method and the Hough space transform. The identification rate \(\omega\) for both methods is calculated using Formula (2). The lowest identification rate using the PCA method was 94.45%, and the highest was 97.23%. In contrast, the lowest identification rate using the Hough space transform was 99.12%, and the highest was 99.65%. For each structural plane, the identification rate of the Hough space transform was higher than that of the PCA method. In terms of overall identification rate, the Hough space transform improved the identification rate by 3.9%. Based on the visual results of region growing and the identification rate statistics in Table 1, both methods achieved similar identification accuracy in the central regions of the structural planes. However, the Hough space transform was less affected by sharp spatial changes, resulting in higher identification accuracy at the edges of the structural planes.