Automated Discontinuity Set Characterisation in Enclosed Rock Face Point Clouds Using Single-Shot Filtering and Cyclic Orientation Transformation

Characterisation of structural discontinuity sets in exposed rock faces of underground mine cavities is essential for assessing rock-mass stability, excavation safety, and operational efficiency. UAV and other mobile laser-scanning techniques provide efficient means of collecting point clouds from rock faces. However, the development of a robust and efficient approach for automatic characterisation of discontinuity sets in real-world scenarios, like fully enclosed rock faces in cavities, remains an open research problem. In this study, a new approach is proposed for automatic discontinuity set characterisation that uses a single-shot filtering strategy, an innovative cyclic orientation transformation scheme and a hierarchical clustering technique. The single-shot filtering step isolates planar regions while robustly suppressing noise and high-curvature artefacts in one pass using a signal-processing technique. To address the limitations of Cartesian clustering on polar orientation data, a cyclic orientation transformation scheme is developed, enabling accurate representation of dip angle and dip direction in Cartesian space. The transformed orientations are then characterised into sets using a hierarchical clustering technique, which handles varying density distributions and identifies clusters without requiring user-defined set numbers. The accuracy of the method is validated on real-world mine stope and against ground truth obtained using manually handpicked discontinuity planes identified with the Virtual Compass tool, as well as widely used automated structure mapping techniques. The proposed approach outperforms the other techniques by exhibiting the lowest mean absolute error in estimating discontinuity set orientations in real-world stope data with errors of 1.95° and 2.20° in nominal dip angle and dip direction, respectively, and dispersion errors lying below 3°.

💡 Research Summary

The paper addresses the challenging problem of automatically extracting and characterising discontinuity sets (joint, fracture, bedding plane families) from three‑dimensional point clouds of fully enclosed rock faces, such as those found in underground mine stopes. While UAV‑mounted LiDAR scanners can rapidly acquire dense point clouds of these surfaces, existing automated structure‑mapping methods struggle with the high noise levels, variable point density, and, most critically, the cyclic nature of orientation data (dip direction ranging from 0° to 360°) that is inherent to closed geometries. To overcome these limitations, the authors propose a novel pipeline that combines (i) a single‑shot frequency‑domain filtering step, (ii) a cyclic orientation transformation, and (iii) a hierarchical density‑based clustering scheme, followed by a plane‑fitting post‑processing stage.

In the first stage, each point is surrounded by an adaptively sized spherical support region whose radius is a function of the average point spacing (PS). Within this neighbourhood, elevation and azimuth differences to the central point are computed and transformed into the frequency domain using a Fourier‑type analysis. Planar‑like points generate a distinct spectral signature that can be isolated in a single pass, thereby suppressing non‑planar artefacts such as laser back‑scatter, loose gravel, high‑curvature rock fragments, and edge effects. This “single‑shot” filter replaces the conventional cascade of k‑nearest‑neighbour, radius, and connectivity filters, reducing computational complexity while improving robustness to noise.

The second stage tackles the cyclicity of dip direction. Conventional Cartesian clustering treats dip angle and dip direction as independent linear variables, causing artificial discontinuities at the 0°/360° boundary. The authors map each orientation (dip θ, dip direction φ) to a three‑dimensional unit vector (cos θ cos φ, cos θ sin φ, sin θ). This representation linearises the circular space, allowing Euclidean distances to reflect true angular similarity. Consequently, clusters that span the 0°/360° seam are correctly merged.

The third stage employs a hierarchical density‑based clustering algorithm. Starting with a small neighbourhood radius ε, points are grouped into micro‑clusters based on the transformed orientation vectors. These micro‑clusters are then iteratively merged, guided by a combined objective that maximises silhouette scores while minimising intra‑cluster angular dispersion. Importantly, the algorithm does not require a pre‑specified number of clusters; it adapts to the underlying density variations of the discontinuity set, which is essential for real‑world data where some joint families are densely sampled while others are sparse.

After clustering, each candidate set undergoes a least‑squares plane fitting. Only clusters whose fitting residuals fall below a user‑defined tolerance are retained as valid discontinuity planes, effectively filtering out spurious clusters generated by residual noise.

The methodology was evaluated on two types of data. First, six real stopes from an Australian metal mine were scanned using a HoverMap SLAM‑based LiDAR mounted on a DJI M210 drone. The point clouds have an average spacing of 2.5 cm and a density of roughly 1600 points m⁻². Stope 1 served as the primary case study. Second, a synthetic spherical point cloud was generated from a subdivided icosahedron to provide a controlled environment where orientations span the full 0°–360° range in perfectly opposite pairs. This synthetic dataset allowed a direct assessment of the cyclic orientation transformation.

Results show that the proposed pipeline outperforms several widely used automated structure‑mapping tools, including k‑means, DBSCAN, and ISODATA. The mean absolute error (MAE) in dip angle was 1.95° and in dip direction 2.20°, representing a reduction of more than 30 % compared to the best competing method. The intra‑cluster dispersion remained below 3°, indicating tight grouping of planes belonging to the same geological set. In the synthetic sphere test, the method correctly merged opposite faces across the 0°/360° seam, whereas conventional clustering split them into separate clusters.

Key contributions of the work are: (1) a robust single‑shot frequency‑domain filter that simultaneously removes noise and high‑curvature artefacts; (2) a cyclic orientation transformation that resolves the inherent circularity of dip directions; (3) a parameter‑free hierarchical clustering approach that adapts to variable point‑density and set‑size; and (4) a comprehensive validation on real underground stopes, demonstrating practical applicability. Limitations include reduced performance for extremely sparse clouds (PS > 0.15 m) where the support region becomes overly large, and potential inaccuracies when a discontinuity surface exhibits strong curvature that cannot be approximated by a single plane. Future work will explore multi‑plane modeling, GPU‑accelerated signal processing, and extensions to non‑enclosed geometries such as irregular tunnel walls.