On the relationship of fractal geometry and tree-stand metrics on point clouds derived from terrestrial laser scanning

Fractals have been widely used to determine bifurcation patterns in trees or to analyse the homeostasis of the development of plants to different environments. In a few instances, fractals have been used to predict tree or stand metrics. Here, we explore the use of fractal geometry based on the voxel-counting method (VC) to predict tree and stands metrics on point clouds derived from terrestrial laser scanning. This was explored using 189 leaf-on and leaf-off point clouds from seven databases around the world. Four metrics were estimated at the tree level: height, diameter at breast height, crown area and tree volume. At the stand level, artificial stands were created by adding trees to a given plot, and then the basal area, stand volume and area coverage by crowns were estimated. The VC was applied to trees or stands creating voxels of different volumes (S) while counting the number of voxels (N) required to fill it. Log-log relationships betweenNand 1/Swere used to estimate the fractal dimension (d(MB)) and the intercept(MB). At the tree level, the intercept(MB)shows a stronger relationship with metrics for leaf-on (r(2) = 0.26-0.90) and leaf-off point clouds (r(2) = 0.18-0.87) thand(MB)(r(2) < 0.34); however,d(MB)seems to describe better the complexity embedded within leaf-on/leaf-off point clouds. The predictions by the intercept(MB)are affected by the presence/absence of leaves, but less affected by the random effects of the databases. At the stand level, both fractal geometry parameters (intercept(MB)andd(MB)) tend to predict the variability of stand metrics (r(2) = 0.61-0.98). The estimation of tree and stand metrics based on fractal geometry equations can be considered a fast approach for predicting irregular structures. Using fractals on point clouds also allows us to understand the structural complexity of how trees or stands occupy their 3D space. This complexity can be further used as a structural trait of trees or forest ecosystems. Fractal geometry equations can also help towards the development of large-scale biomass maps at different ecosystems.