On the relationship of fractal geometry and tree–stand metrics on point clouds derived from terrestrial laser scanning
Bibliographic record
Abstract
Abstract 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 between N and 1/ S were 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) than d 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 and d 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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.010 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".