1. 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.
2. 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 between N and 1/S were used to estimate the fractal dimension (d_MB) and the intercept_MB.
3. At the tree level, the intercept_MB shows a stronger relationship with metrics for leaf‐on (r² = 0.26‒0.90) and leaf‐off point clouds (r² = 0.18‒0.87) than d_MB (r² < 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 and d_MB) tend to predict the variability of stand metrics (r² = 0.61‒0.98).
4. 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.

中文翻译：

---

关于地面激光扫描得出的点云的分形几何形状与树架度量的关系

1. 分形已被广泛用于确定树木的分叉模式或分析植物向不同环境发育的动态平衡。在某些情况下，分形已用于预测树木或林分指标。在这里，我们探索基于体素计数法（VC）的分形几何形状的使用，以预测树和站立在来自陆地激光扫描的点云上的度量。使用来自世界各地七个数据库的189个上落点云进行了探索。
2. 在树级别估计了四个度量：高度，胸高直径，树冠面积和树体积。在林分级别，通过将树木添加到给定的地块中来创建人工林，然后估算基础面积，林分体积和树冠覆盖面积。将VC应用于树木或林分，创建不同体积（S）的体素，同时计算填充它所需的体素数（N）。N和1 / S之间的对数-对数关系用于估计分形维数（d _MB）和截距_MB。
3. 在树的层次上，截距_MB与d _MB（r ²  <0.34） 相比， 与叶上（r ² = 0.26‒0.90）和叶上点云（r ² = 0.18‒0.87）的度量关系更强。但是，d _MB似乎更好地描述了嵌入在叶子/叶子点云中的复杂性。截距_MB的预测受叶子是否存在的影响，但受数据库随机影响的影响较小。在展台水平上，两个分形几何参数（截距_MB和d _MB）倾向于预测林分指标的变异性（r ²  = 0.61‒0.98）。
4. 可以将基于分形几何方程式的树木和林分指标的估计视为预测不规则结构的快速方法。在点云上使用分形还可以使我们了解树木或林分如何占据其3D空间的结构复杂性。这种复杂性可以进一步用作树木或森林生态系统的结构特征。分形几何方程还可以帮助开发不同生态系统的大规模生物量图。