## 1 Introduction  
The presence of rock mass discontinuities, such as bedding planes, joints, faults, and other planes, plays a crucial role in the field of rock mechanics [1], altering the mechanical properties of rock masses, and consequently influencing the stability of rocky slopes [2, 3]. The International Society for Rock Mechanics [4] proposed a set of quantitative parameters for characterizing rock discontinuities, including orientation, spacing, persistence, roughness, aperture, filling, wall strength, seepage, number of sets, and block size. Among these parameters, orientation, as a critical factor influencing the deformation of rock masses, holds extraordinary significance in the analysis of rock mass stability [5, 6, 7, 8, 9]. The traditional approach necessitates manual measurements of discontinuity orientation using a compass and inclinometer in accessible regions [10]. This technique is characterized by notable labor intensity and time consumption. Meanwhile, its application in regions featuring substantial topographical variations not only jeopardizes the safety of surveyors but also lacks assurance in ensuring the precision of data [11]. With the advancement of remote sensing technology, non-contact measurement methods such as photogrammetry [12] and LiDAR [13] have been introduced, facilitating rapid scanning of the rock surfaces within the study area. This generates high-precision point clouds composed of numerous three-dimensional coordinates, overcoming the limitations associated with traditional methods [14, 15]. Currently, a growing number of scholars are actively involved in extracting discontinuities from point clouds to gather comprehensive parameter information. The extraction process essentially involves segmenting points belonging to distinct discontinuities within the point cloud. The predominant methods for extracting discontinuities from point clouds can be classified into two distinct perspectives. Considering that rock mass discontinuities often exhibit a planar feature, one method involves linear or nonlinear fitting through geometric analysis and mathematical models to achieve plane extraction. Some researchers have employed plane detection algorithms, such as Random Sample Consensus (RANSAC) [16; 17; 18; 19], 3D Hough Transform [20; 21], and Principal Component Analysis (PCA) [22; 23], to extract points belonging to the same plane within a point cloud, treating them as individual discontinuities. The Region Growing algorithm [24; 25; 26] relies on normal vectors and curvature to identify the nearest neighbors that share the same plane with the seed point, treating them as growth points, and carries out plane expansion to achieve the extraction of discontinuities. However, the method is very time-consuming. In the modified Region Growing algorithm proposed by [PERSON] et al. [25], the homogeneity criterion is modified to increase the probability of potential growth points to become growth points, which improves the computational efficiency. By applying the Region Growing algorithm to the voxelized point cloud, some scholars [27; 28] have greatly improved the efficiency of the extraction of the discontinuity. Aiming at the problems caused by the threshold selection of the traditional Region Growing algorithm, [PERSON] et al. [26] improved on it and proposed a multi-rule Region Growing algorithm with higher accuracy. [PERSON] et al. [29] found that the vertical and horizontal angle variations of points belonging to the same discontinuity set in a certain area appear as a sinusoidal signal, and proposed a new method to realize discontinuity set extraction by using the amplitude and phase of this signal. While such methods typically demonstrate effectiveness in simple scenarios, their application becomes time-consuming and vulnerable to interference from factors like noise when confronted with large and complex point clouds.