Data from: Leveraging a new branchbased taper curve and form factor from terrestrial laser scanning proxies
Data files
Jul 13, 2023 version files 1.05 GB
Dec 27, 2023 version files 1.05 GB
Abstract
Modeling branch taper curve and form factor contributes to increasing the efficiency of tree crown reconstruction: the branch taper, defined as the sequential measure of diameters along the course of the branch, is pivotal to accurately estimate key branch variables such as biomass and volume. Branch diameters or volumes have commonly been estimated from terrestrial laser scanning (TLS) based on automatized voxelization or cylinderfitting approaches, given the whole branch length is sufficiently covered by laser reflections. The results are, however, often affected by ample variations in point cloud characteristics caused by varying point density, occlusions, and noise. As these characteristics of TLS have been difficult to be sufficiently controlled or eliminated in automatizedtechniques, we proposed a new branchbased taper curve model and form factor (BFF), which can be employed directly from the laser reflections and under variable point cloud characteristics.
In this paper, the approach is demonstrated on primary branches using a set of TLSderived diameter datasets from a sample of 20 trees of 6 species. The result shows an improvement in the accuracy of the diameter estimates and, at best, enabled for predicting encompassing finer branch scales (<10 cm), with R2 of 0.86 and a mean relative absolute error of 1.03 cm (29%) when validated with fieldmeasured diameters. This approach was also capable of retrieving branch diameters for a large percentage of explicitly identified primary branches (>85%) directly from the filtered points when validated with panoramic images acquired concurrently with laser scanning. Frequently used automatized crown reconstructions from the quantitative structural model (QSM), on the other hand, was largely obscured by discrepancies in the point clouds, with the crowntops and finer branches being the most critical.
Furthermore, our approach provides mean BFF of 0.35 and 0.49 with the diameters determined from 5% and 10% of the total branch length, respectively, which may have the potential to produce branch volume information with reasonable accuracy from only knowing the length and respective diameter.
Although our model can be regarded as a first approximation to the taper curve and form factor for the primary branches on a relatively small set of samples, the approach can further our understanding of alternative ways to improve the accuracy of the assessment of branch diameter and volume. The approach may also be extended to other branch orders. This could expand the horizon for volumetric calculations and biomass estimates from nondestructive TLS proxies in tree crowns.
README
Abstract
Modeling branch taper curve and form factor contributes to increasing the efficiency of tree crown reconstruction: the branch taper, defined as the sequential measure of diameters along the course of the branch, is pivotal to accurately estimate key branch variables such as biomass and volume. Branch diameters or volumes have commonly been estimated from terrestrial laser scanning (TLS) based on automatized voxelization or cylinderfitting approaches, given the whole branch length is sufficiently covered by laser reflections. The results are, however, often affected by ample variations in point cloud characteristics caused by varying point density, occlusions, and noise. As these characteristics of TLS have been difficult to be sufficiently controlled or eliminated in automatizedtechniques, we proposed a new branchbased taper curve model and form factor (BFF), which can be employed directly from the laser reflections and under variable point cloud characteristics.
In this paper, the approach is demonstrated on primary branches using a set of TLSderived diameter datasets from a sample of 20 trees of 6 species. The result shows an improvement in the accuracy of the diameter estimates and, at best, enabled for predicting encompassing finer branch scales (<10 cm), with R2 of 0.86 and a mean relative absolute error of 1.03 cm (29%) when validated with fieldmeasured diameters. This approach was also capable of retrieving branch diameters for a large percentage of explicitly identified primary branches (>85%) directly from the filtered points when validated with panoramic images acquired concurrently with laser scanning. Frequently used automatized crown reconstructions from the quantitative structural model (QSM), on the other hand, was largely obscured by discrepancies in the point clouds, with the crowntops and finer branches being the most critical.
Furthermore, our approach provides mean BFF of 0.35 and 0.49 with the diameters determined from 5% and 10% of the total branch length, respectively, which may have the potential to produce branch volume information with reasonable accuracy from only knowing the length and respective diameter.
Although our model can be regarded as a first approximation to the taper curve and form factor for the primary branches on a relatively small set of samples, the approach can further our understanding of alternative ways to improve the accuracy of the assessment of branch diameter and volume. The approach may also be extended to other branch orders. This could expand the horizon for volumetric calculations and biomass estimates from nondestructive TLS proxies in tree crowns.
Keywords: Branch diameter; Branch form factor; Branch taper curve; Branch volume; QSM; TLS
Methods
Terrestrial laser scanning (TLS) was used to acquire point cloud datasets of individual trees during the leafoff season. Scanning was performed for six tree species using Trimble TX5 3D Laser Scanner (Trimble Inc., Sunnyvale, CA, USA). The point clouds are collected based on the scanner setup with 43 million points (mpts) per scan with a quality setting 4x. With this setup, the scan duration was ~11 minutes. We scanned each tree from six scan positions, distributed circularly at a regular interval of 60 from each other.
The processed datasets comprise commadelimited files (.csv), Excel (.xlsx), Rscript (.R), sample tree point clouds (.asc + .las), quantitative structural model (QSM) pipeline scripts (.xsct2), and the corresponding fitted cylinders (.ply).
Data1.csv file provides the list of tree species with the details of stem and crown variable metrics. All the variables were determined and computed directly from the laser reflections using CloudCompare software version 2.12.0 (CloudCompare, 2021). Data2.csv is the dataset used for the modeling of the branch taper curve. The series of diameters (D) along the branch was determined from the point slice of TLS laser reflections. Initially, a series of thin point slices (~10 mm long crosssections) at 0.50 m intervals along the course of the branch were crosssectioned using CloudCompare software by flattening the branch point clouds horizontally. Each slice was then transformed to vertical straightness to correct the effect of the branch inclination. We performed the correction based on a threedimensional rotation matrix using CloudCompare software by picking up three points after leveling the slice horizontally. After inclination correction, we projected the slices horizontally in the xy plane and then applied the Random Sample Consensus (RANSAC) circlefitting algorithm (Fischler and Bolles, 1981). The package TreeLS (de Conto, 2020) in R language (RStudio Team, 2021) was used for RANSAC circlefitting. This served as a nondestructive TLSbased dataset used to fit the branch taper curve and calculate the respective branch form factor (BFF). Data3.xlsx comprises the model prediction and validation datasets. The groundtruth manual diameter measurements were collected in the field using a caliper for the few branches in the lower parts of the crown that were reached from a standing position. Data4.csv comprises the BFF determined at two reference diameters: 5% (BFF0.05) and 10% (BFF0.10) of the branch relative lengths. The BFF is computed based on the ratio of the actual branch volume to the volume of the cylinder over the reference diameters. The actual branch volumes were calculated based on fitted taper curves. The Taper curve of individual isolated sample branches was fitted based on the cubic spline model. From the smoothed cubic spline model, the volume was calculated at every 0.1 m section. The volume of each section was calculated based on Hubers formula. The total actual branch was obtained by summing the volumes of overall sections from the base (0 m) up to the total branch length.
TaperCurveBFF.R is the Rscript for the taper curve using the multivariate spline regression model. The optimal submodel was determined using the generalized crossvalidation (GCV) approach. The modeling process was performed using the Earth package in R language (Milborrow, 2021). The script also comprises the BFF calculations.
PSP28.asc; PSP28.las; APS30.asc; and APS30.las are two examples of filtered tree point clouds (Platanus species and Acer platanoides). MNQSMasc.xsct2 and MNQSMlas.xsct2 are QSM cylinder pipeline model scripts developed for asc and las points, respectively, following Hackenberg et al. (2015) using the Computree software version 5.0.221b (Computree, 2021) with a plugin of SimpleForest version 5.3.2 (SimpleForest, 2021). PSP28.ply and APS30.ply are the corresponding QSM cylinder fits.
Reference
CloudCompare. (2021). CloudCompare Software, 3D point cloud and mesh processing Project, Open Source (Version 2.12.0). https://www.danielgm.net/cc/
Computree. (2021). Computree: a platform for processing 3D point clouds (version 5.0). http://rdinnovation.onf.fr/projects/computree/wiki
de Conto, T. (2020). TreeLS: Terrestrial Point Cloud Processing of Forest Data (R package version 2.0.4.). https://mran.microsoft.com/snapshot/20200216/web/packages/TreeLS/index.html
Fischler, M. A., & Bolles, R. C. (1981). Random Sample Consensus: A Paradigm for Model Fitting with Applications to Image Analysis and Automated Cartography. Communications of the ACM, 24(6), 381395. https://doi.org/10.1145/358669.358692
Hackenberg, J., Spiecker, H., Calders, K., Disney, M., & Raumonen, P. (2015). SimpleTree An Efficient Open Source Tool to Build Tree Models from TLS Clouds. Forests, 6(11), 42454294. https://doi.org/10.3390/f6114245
RStudio. 2021 RStudio: A language and environment for statistical computing. Boston, MA. https://www.rstudio.com/
SimpleForest. (2021). SimpleForest: a 3D tree modelling software from point cloud data (version 5.3.2). https://www.simpleforest.org/
Trimble Inc., Sunnyvale, CA, U. (2021). Trimble TX5 Scanner: A 3D laser instrument. https://www.laserscanningeurope.com/de/glossar/trimbletx5scanner
Methods
Terrestrial laser scanning (TLS) was used to acquire point cloud datasets of individual trees during the leafoff season. Scanning was performed for six tree species using Trimble TX5 3D Laser Scanner (Trimble Inc., Sunnyvale, CA, USA). The point clouds are collected based on the scanner setup with 43 million points (mpts) per scan with a quality setting 4x. With this setup, the scan duration was ~11 minutes. We scanned each tree from six scan positions, distributed circularly at a regular interval of 60° from each other.
The processed datasets comprise commadelimited files (.csv), Excel (.xlsx), Rscript (.R), sample tree point clouds (.asc + .las), quantitative structural model (QSM) pipeline scripts (.xsct2), and the corresponding fitted cylinders (.ply).
Data1.csv file provides the list of tree species with the details of stem and crown variable metrics. All the variables were determined and computed directly from the laser reflections using CloudCompare software version 2.12.0 (CloudCompare, 2021). Data2.csv is the dataset used for the modeling of the branch taper curve. The series of diameters (D) along the branch was determined from the point slice of TLS laser reflections. Initially, a series of thin point slices (~10 mm long crosssections) at 0.50 m intervals along the course of the branch were crosssectioned using CloudCompare software by flattening the branch point clouds horizontally. Each slice was then transformed to vertical straightness to correct the effect of the branch inclination. We performed the correction based on a threedimensional rotation matrix using CloudCompare software by picking up three points after leveling the slice horizontally. After inclination correction, we projected the slices horizontally in the xy plane and then applied the Random Sample Consensus (RANSAC) circlefitting algorithm (Fischler and Bolles, 1981). The package ‘TreeLS’ (de Conto, 2020) in R language (RStudio Team, 2021) was used for RANSAC circlefitting. This served as a nondestructive TLSbased dataset used to fit the branch taper curve and calculate the respective branch form factor (BFF). Data3.xlsx comprises the model prediction and validation datasets. The groundtruth manual diameter measurements were collected in the field using a caliper for the few branches in the lower parts of the crown that were reached from a standing position. Data4.csv comprises the BFF determined at two reference diameters: 5% (BFF0.05) and 10% (BFF0.10) of the branch relative lengths. The BFF is computed based on the ratio of the actual branch volume to the volume of the cylinder over the reference diameters. The actual branch volumes were calculated based on fitted taper curves. The Taper curve of individual isolated sample branches was fitted based on the cubic spline model. From the smoothed cubic spline model, the volume was calculated at every 0.1 m section. The volume of each section was calculated based on Huber’s formula. The total actual branch was obtained by summing the volumes of overall sections from the base (0 m) up to the total branch length.
TaperCurveBFF.R is the Rscript for the taper curve using the multivariate spline regression model. The optimal submodel was determined using the generalized crossvalidation (GCV) approach. The modeling process was performed using the ‘Earth’ package in R language (Milborrow, 2021). The script also comprises the BFF calculations.
PSP28.asc; PSP28.las; APS30.asc; and APS30.las are two examples of filtered tree point clouds (Platanus species and Acer platanoides). MNQSMasc.xsct2 and MNQSMlas.xsct2 are QSM cylinder pipeline model scripts developed for ‘asc’ and ‘las’ points, respectively, following Hackenberg et al. (2015) using the Computree software version 5.0.221b (Computree, 2021) with a plugin of SimpleForest version 5.3.2 (SimpleForest, 2021). PSP28.ply and APS30.ply are the corresponding QSM cylinder fits.
Usage notes
Column Name 
Description 
Unit 
Source 
Calculation or Measurement Methods 
Software 
Data1.csv 

Species 
The scientific name of the scanned trees 




Scan_Code 
Given code during scanning 




Branch_ID 
Isolated sample branch in each tree. Repetition of similar ID numbers indicates the series point slices taken along the corresponding branch. 




BP

Branch position, indicating where the sample branch was positioned across the crown profile: LCB – lower crown branch MCB – middle crown branch UCB – upper crown branch 




BO 
Branch order, where all the analysis was made for primary branches (BO 01) 




DBH 
Branch diameter at breast height 
cm 
Field 
Diameter tape 

H 
Height of the tree. The vertical distance between the base of the trunk and the treetop 
m 
Point Cloud 
Z_{max }– Z_{min } 
R Programming Language 
H1 
Crown base height. The vertical distance between the base of the trunk and the lowest live branch 
m 
Point Cloud 
Z_{firstlivebranch }– Z_{min} 
CloudCompare 
H2 
Crown length. Distance between the base of the lowest live branch and treetop 
m 
Point Cloud 
Z_{max} – Z_{firstlivebranch} or H_{ }– H_{1} 
CloudCompare 
CR 
Crown ratio. The ratio of the crown length to the tree height 

Point Cloud 
H_{2}/H 

BH 
Branch base height. Height of the primary branch attachment to the trunk from the base of the stump 
m 
Point Cloud 
Z_{primarybranchbasepoint }– Z_{min} 
CloudCompare 
BRH 
Branch base relative height. Height of the base of the primary branch relative to the tree height 

Point Cloud 
BH/H 

Data2.csv 

Species – BRH 
Similar to Data1.csv 




BL 
Branch length. The total length of the primary branch 
m 
Point Cloud 
Manual length measurement from laser reflections

CloudCompare 
BSL 
Branch slices length. Absolute length of each branch slice (BS) (used for series of diameter determination with circle fitting) from the base of the primary branch 
m 
Point Cloud 
Manual length measurement from laser reflections

CloudCompare 
BRL 
Branch relative length. The relative length of each BSL from the BL 

Point Cloud 
Normalized in [0  1] scale (BSL/BL) 

BBD 
Branch basal diameter 
cm 
Point Cloud 
Determined directly from laser reflections using a circular fit for the crosssection of the points just above the point of attachment to the trunk 
R Programming Language 
D_TLS 
Series of branch diameters along the course of the branch. The diameters served as a nondestructive TLSbased dataset to fit the branch taper curve and calculate the branch form factor 
cm 
Point Cloud 
Determined diameters at 0.50 m intervals along the branch. Circle fitting using the RANSAC algorithm was executed for each thin point slice derived from 0.50 m intervals. 
R Programming Language 
D_Relative 
Relative branch diameter 

Point Cloud 
Normalized in [0 1] scale using the BBD (DTLS/ BBD) 

D_TaperModel_Relative 
Predicted relative branch diameter from the taper curve model 

Taper Curve 
Diameter prediction in normalized [0 1] scale 
R Programming Language 
D_TaperModel 
Predicted diameters from the taper curve model 
cm 
Taper Curve 
Series of diameter depicted from the taper curve regression model (D_TaperModel_Relative*BBD) 

Data3. xlsx 

BRL 
Branch relative length (As described and derived in Data2.csv) 

Field, Taper Curve, QSM 
Normalized in [0  1] scale (BSL/BL) 

Reference Diameter 

cm 
Field 
Field measurements of branch diameters using a caliper 

Predicted Diameter 

cm 
Taper Curve, QSM 
Predicted diameters from the Taper curve and QSM 
R Programming Language; SimpleForest 
Prediction Approach 
The approach of the diameter estimation: Taper curve and QSM model 

Taper Curve, QSM 


Absolute Error (AE) 

cm 
Field, Taper Curve, QSM 


Relative Absolute Error (RAE) 

% 
Field, Taper Curve, QSM 
RAE = Prediction Diameters from Taper Curve or QSM – Reference Diameters/ Reference Diameters * 100 

Data4.csv 

Species_Code; Scan_Code; Species; Branch_Sample 
As described in Data1.csv 




Branch_Volume 
The volume of the branch 
cm^{3} 
Point cloud; Taper Curve 
Calculated based on fitted taper curves. Summation of the volumes calculated at every 0.1 m section 
R Programming Language 
CylinderVolume0.05 
Assuming the volume of the cylinder 
cm^{3} 
Point cloud 
Considering the volume of the cylinder over the length of reference diameter, i.e., from 5% (relative length of 0.05) of the total branch length 
R Programming Language 
CylinderVolume0.10 
Assuming the volume of the cylinder 
cm^{3} 
Point cloud 
Considering the volume of the cylinder over the length of reference diameter, i.e., from 10% (relative length of 0.1) of the total branch length 
R Programming Language 
BFF0.05 
Branch form factor with a reference diameter estimation at 5% if the branch length 

Point cloud; Taper Curve 
Branch_Volume/CylinderVolume0.05 

BFF0.10 
Branch form factor with a reference diameter estimation at 10% if the branch length 

Point cloud; Taper Curve 
Branch_Volume/CylinderVolume0.10 

Point Clouds 

PSP28.asc; PSP28.las; APS30.asc; APS30.las 
Examples of filtered tree point clouds (Platanus species and Acer platanoides) 

Any software used for point cloud visualization  
QSM Scripts 

MNQSMasc.xsct2; MNQSMlas.xsct2 
Examples of QSM scripts

SimpleForest  
Pipeline Model (QSM Cylinders) 


PSP28.ply; APS30.ply 
Examples of the reconstructed branch cylinders (based on the provided QSM Scripts) 
CloudCompare 
Reference
CloudCompare. (2021). CloudCompare Software, 3D point cloud and mesh processing Project, Open Source (Version 2.12.0). https://www.danielgm.net/cc/
Computree. (2021). Computree: a platform for processing 3D point clouds (version 5.0). http://rdinnovation.onf.fr/projects/computree/wiki
de Conto, T. (2020). TreeLS: Terrestrial Point Cloud Processing of Forest Data (R package version 2.0.4.). https://mran.microsoft.com/snapshot/20200216/web/packages/TreeLS/index.html
Fischler, M. A., & Bolles, R. C. (1981). Random Sample Consensus: A Paradigm for Model Fitting with Applications to Image Analysis and Automated Cartography. Communications of the ACM, 24(6), 381–395. https://doi.org/10.1145/358669.358692
Hackenberg, J., Spiecker, H., Calders, K., Disney, M., & Raumonen, P. (2015). SimpleTree —An Efficient Open Source Tool to Build Tree Models from TLS Clouds. Forests, 6(11), 4245–4294. https://doi.org/10.3390/f6114245
RStudio. 2021 RStudio: A language and environment for statistical computing. Boston, MA. https://www.rstudio.com/
SimpleForest. (2021). SimpleForest: a 3D tree modelling software from point cloud data (version 5.3.2). https://www.simpleforest.org/
Trimble Inc., Sunnyvale, CA, U. (2021). Trimble TX5 Scanner: A 3D laser instrument. https://www.laserscanningeurope.com/de/glossar/trimbletx5scanner