## 2 Methods
### Identification and Information Extraction of Rock Mass Structural Planes  
#### 2.1.1 Rock Mass Structural Planes Identification  
The core idea of region growing is to use certain common features of point cloud data as the basis for judgment. By selecting arbitrary points and comparing them with neighboring  
Figure 1: Flowchart of the Method for Identifying Rock Mass Structural Planes and Extracting Dominant Orientations. points in one or multiple dimensions, points with similar features are segmented and merged. There are three key issues to consider during the region growing process [29]. 1. Selection of Seed Points Region growing is a seed-point-based point cloud segmentation algorithm. The initial seed points should be selected from areas with relatively high flatness to improve the computation speed. The surface variation \(SV_{i}\) of each point is calculated, where \(SV_{i}\) represents the surface roughness within the neighborhood. The points are sorted in ascending order based on their surface variation values, and the point with the smallest \(SV_{i}\) is chosen as the initial seed point. 2. Feature Judging Criteria Rock mass structural planes are typically composed of relatively flat planes and sharp edges, with field investigations primarily using sharp edges as boundaries. In the identification of rock mass structural planes, the normal vector serves as a crucial feature for differentiating between various planes; points within the same rock mass structural plane should have similar or identical normal vector orientations. The difference in normal vectors between adjacent points is used as a criterion for region-growing segmentation of the point cloud data. The Hough transform employs statistical principles to effectively enhance the noise resistance and computation of normal vectors on complex rock surfaces. The core of this method involves randomly selecting two points from the neighborhood and a seed point to form a plane, calculating the normal vector of that plane, and traversing all combinations to statistically identify the most frequently occurring normal vector as the final normal vector for the seed point. In the context of structural surfaces, any given point in space can be classified into three positional states: (1) away from the edge, (2) near the edge, and (3) on the edge. When the seed point is in states 1 or 2, two non-collinear points are randomly selected from the defined neighborhood K to form a plane with the seed point. The normal vectors calculated from all combinations will exhibit a \"random\" normal distribution, allowing for the determination of the most probable normal vector. When the point is in the third positional state (on the edge), due to the potential differences in point cloud density on either side of the edge, the method can still identify the most probable normal vector as the final normal vector for the seed point by appropriately setting the maximum number of plane combinations (\(T_{\text{max}}\)) and confidence level. This approach effectively addresses the challenges posed by complex geometries and enhances the accuracy of rock structural surface extraction. 3. Stopping Conditions for Growth When calculating the normal vector of the point cloud using the Hough space transform, if the \(K\) value is too large or the point cloud density within the neighborhood is too high, numerous planes will be generated during the combination process. Region growing stops when the number of planes exceeds the maximum plane count \(T_{\text{max}}\), or when the confidence level satisfies the requirement. If the number of clustered points in a structural plane is less than the minimum cluster point count \(C_{\text{min}}\), region growing will also stop. The region growing process based on the normal vector differences using the Hough space transform is as follows:  
1.