Rock mass discontinuity trace mapping using a voxel-based morphology-topology framework

Discontinuity trace is a critical geological information element in engineering geology. However, existing point cloud-based methods still face challenges, including insufficient trace connectivity and ambiguous topological relationships between trace. To address these limitations, this paper proposes a voxel-based morphology-topology approach instead of complex point connection algorithms. Initially, we coarsely extract trace points by applying the elbow method to optimize K-means++ clustering, which based on normal vector neighborhood deviations of point clouds. After voxelizing the trace points, we enhance and refine spatial connectivity through morphological dilation and an improved secondary erosion process. We then define Euler characteristics to characterize the topological properties of the voxels. Finally, obtain a simplified voxel skeleton containing trace points through topological iterative deletion, generate vectorized trace paths by connecting voxel centers, followed by post-processing. We validate the method through three slope cases, the topological connectivity rate compared to existing methods is the highest reaching 90.48 %, 90.91 %, and 91.97 %, respectively. demonstrating its ability to identify finer trace details more precisely than alternative approaches. The proposed method enables robust extraction of vectorized paths from the trace spatial skeleton, which shifting from connecting points to simplifying a topological structure. This approach offers reliable technical support for digital geological logging and intelligent assessment of engineering stability.