Fast trace mapping on 3D rock point clouds using anomaly detection without normal estimation

Abstract

This study proposes an innovative method for fast mapping rock traces on 3D outcrops directly from point cloud data. Unlike traditional approaches that rely on computationally intensive calculations of normal vectors and curvatures, the proposed method leverages a key geometric insight: points along rock traces typically exhibit geometric deviations from planar surfaces compared to points on a flat plane. This characteristic manifests in larger tetrahedral volumes when these trace points are combined with three random neighboring points. Conversely, points on a plane tend to form tetrahedra with nearly zero volume when combined with random neighbors. By repeatedly sampling tetrahedron volumes around each point and employing the Extended Isolation Forest algorithm for anomaly detection, the proposed method efficiently identifies potential trace points. These points are then refined using a proposed local regression method and connected via a line-growing algorithm to map the complete traces. The proposed approach offers significant computational advantages over traditional methods. While traditional methods have complexity dependent on data dimensionality and neighborhood size, the proposed method calculates tetrahedron volumes with a constant time complexity of O(1) per point, independent of the number of neighboring points. The efficiency and accuracy of this method is validated with multiple synthetic and real-world datasets. Results demonstrate that the proposed method reduces 99 % of the time required by traditional approaches while maintaining the accuracy of trace intensity measurements.