RECONSTRUCTION, QUANTIFICATION, AND VISUALIZATION OF FOREST CANOPY BASED ON 3D TRIANGULATIONS OF AIRBORNE LASER SCANNING POINT DATA

Abstract. Reconstruction of three-dimensional (3D) forest canopy is described and quantified using airborne laser scanning (ALS) data with densities of 0.6–0.8 points m^-2 and field measurements aggregated at resolutions of 400–900 m². The reconstruction was based on computational geometry, topological connectivity, and numerical optimization. More precisely, triangulations and their filtrations, i.e. ordered sets of simplices belonging to the triangulations, based on the point data were analyzed. Triangulating the ALS point data corresponds to subdividing the underlying space of the points into weighted simplicial complexes with weights quantifying the (empty) space delimited by the points. Reconstructing the canopy volume populated by biomass will thus likely require filtering to exclude that volume from canopy voids. The approaches applied for this purpose were (i) to optimize the degree of filtration with respect to the field measurements, and (ii) to predict this degree by means of analyzing the persistent homology of the obtained triangulations, which is applied for the first time for vegetation point clouds. When derived from optimized filtrations, the total tetrahedral volume had a high degree of determination (R²) with the stem volume considered, both alone (R²=0.65) and together with other predictors (R²=0.78). When derived by analyzing the topological persistence of the point data and without any field input, the R² were lower, but the predictions still showed a correlation with the field-measured stem volumes. Finally, producing realistic visualizations of a forested landscape using the persistent homology approach is demonstrated.