Computational Geometry-Based Surface Reconstruction for Volume Estimation: A Case Study on Magnitude-Frequency Relations for a LiDAR-Derived Rockfall Inventory
Bibliographic record
Abstract
Key to the quantification of rockfall hazard is an understanding of its magnitude-frequency behaviour. Remote sensing has allowed for the accurate observation of rockfall activity, with methods being developed for digitally assembling the monitored occurrences into a rockfall database. A prevalent challenge is the quantification of rockfall volume, whilst fully considering the 3D information stored in each of the extracted rockfall point clouds. Surface reconstruction is utilized to construct a 3D digital surface representation, allowing for an estimation of the volume of space that a point cloud occupies. Given various point cloud imperfections, it is difficult for methods to generate digital surface representations of rockfall with detailed geometry and correct topology. In this study, we tested four different computational geometry-based surface reconstruction methods on a database comprised of 3668 rockfalls. The database was derived from a 5-year LiDAR monitoring campaign of an active rock slope in interior British Columbia, Canada. Each method resulted in a different magnitude-frequency distribution of rockfall. The implications of 3D volume estimation were demonstrated utilizing surface mesh visualization, cumulative magnitude-frequency plots, power-law fitting, and projected annual frequencies of rockfall occurrence. The 3D volume estimation methods caused a notable shift in the magnitude-frequency relations, while the power-law scaling parameters remained relatively similar. We determined that the optimal 3D volume calculation approach is a hybrid methodology comprised of the Power Crust reconstruction and the Alpha Solid reconstruction. The Alpha Solid approach is to be used on small-scale point clouds, characterized with high curvatures relative to their sampling density, which challenge the Power Crust sampling assumptions.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".