Next Article in Journal
Design, Development and Applicability Evaluation of a Digital Cartographic Model for 3D Cadastre Mapping in China
Previous Article in Journal
A Contributor-Focused Intrinsic Quality Assessment of OpenStreetMap in Mozambique Using Unsupervised Machine Learning
Article

Computational Geometry-Based Surface Reconstruction for Volume Estimation: A Case Study on Magnitude-Frequency Relations for a LiDAR-Derived Rockfall Inventory

Department of Geological Sciences and Geological Engineering, Queen’s University, Kingston, ON K7L 3N6, Canada
*
Author to whom correspondence should be addressed.
Academic Editor: Wolfgang Kainz
ISPRS Int. J. Geo-Inf. 2021, 10(3), 157; https://doi.org/10.3390/ijgi10030157
Received: 12 February 2021 / Revised: 4 March 2021 / Accepted: 7 March 2021 / Published: 11 March 2021
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. View Full-Text
Keywords: rockfall hazard; laser scanning; magnitude-frequency; power-law; point clouds; surface reconstruction; computational geometry; triangulation rockfall hazard; laser scanning; magnitude-frequency; power-law; point clouds; surface reconstruction; computational geometry; triangulation
Show Figures

Graphical abstract

MDPI and ACS Style

DiFrancesco, P.-M.; Bonneau, D.A.; Hutchinson, D.J. Computational Geometry-Based Surface Reconstruction for Volume Estimation: A Case Study on Magnitude-Frequency Relations for a LiDAR-Derived Rockfall Inventory. ISPRS Int. J. Geo-Inf. 2021, 10, 157. https://doi.org/10.3390/ijgi10030157

AMA Style

DiFrancesco P-M, Bonneau DA, Hutchinson DJ. Computational Geometry-Based Surface Reconstruction for Volume Estimation: A Case Study on Magnitude-Frequency Relations for a LiDAR-Derived Rockfall Inventory. ISPRS International Journal of Geo-Information. 2021; 10(3):157. https://doi.org/10.3390/ijgi10030157

Chicago/Turabian Style

DiFrancesco, Paul-Mark, David A. Bonneau, and D. J. Hutchinson. 2021. "Computational Geometry-Based Surface Reconstruction for Volume Estimation: A Case Study on Magnitude-Frequency Relations for a LiDAR-Derived Rockfall Inventory" ISPRS International Journal of Geo-Information 10, no. 3: 157. https://doi.org/10.3390/ijgi10030157

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop