Capturing tree crown formation through implicit surface reconstruction using airborne lidar data

Forest structure data derived from lidar is being used in forest science and management for inventory analysis, biomass estimation, and wildlife habitat analysis. Regression analysis dominated previous approaches to the derivation of tree stem and crown parameters from lidar. The regression model for tree parameters is locally applied based on vertical lidar point density, the tree species involved, and stand structure in the specific research area. The results of this approach, therefore, are location-specific, limiting its applicability to other areas. For a more widely applicable approach to derive tree parameters, we developed an innovative method called 'wrapped surface reconstruction' that employs radial basis functions and an isosurface. Utilizing computer graphics, we capture the exact shape of an irregular tree crown of various tree species based on the lidar point cloud and visualize their exact crown formation in three-dimensional space. To validate the tree parameters given by our wrapped surface approach, survey-grade equipment (a total station) was used to measure the crown shape. Four vantage points were established for each of 55 trees to capture whole-tree crown profiles georeferenced with post-processed differential GPS points. The observed tree profiles were linearly interpolated to estimate crown volume. These fieldwork-generated profiles were compared with the wrapped surface to assess goodness of fit. For coniferous trees, the following tree crown parameters derived by the wrapped surface method were highly correlated (p < 0.05) with the total station-derived measurements: tree height (R² = 0.95), crown width (R² = 0.80), live crown base (R² = 0.92), height of the lowest branch (R² = 0.72), and crown volume (R² = 0.84). For deciduous trees, wrapped surface-derived parameters of tree height (R² = 0.96), crown width (R² = 0.75), live crown base (R² = 0.53), height of the lowest branch (R² = 0.51), and crown volume (R² = 0.89) were correlated with the total station-derived measurements. The wrapped surface technique is less susceptible to errors in estimation of tree parameters because of exact interpolation using the radial basis functions. The effect of diminished energy return causes the low correlation for lowest branches in deciduous trees (R² = 0.51), even though leaf-off lidar data was used. The wrapped surface provides fast and automated detection of micro-scale tree parameters for specific applications in areas such as tree physiology, fire modeling, and forest inventory.