DOI: 10.5061/dryad.nzs7h44x1
title: Data from: Leveraging a new branch-based taper curve and form factor from terrestrial laser scanning proxies

description: 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 cylinder-fitting
 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 automatized-techniques, we
 proposed a new branch-based 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 TLS-derived 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 (&lt;10 cm), with R2 of 0.86 and a
 mean relative absolute error of 1.03 cm (29%) when validated with
 field-measured diameters. This approach was also capable of retrieving
 branch diameters for a large percentage of explicitly identified primary
 branches (&gt;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 crown-tops 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 non-destructive TLS
 proxies in tree crowns.
description: Terrestrial laser scanning
 (TLS) was used to acquire point cloud datasets of individual trees during
 the leaf-off 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 comma-delimited 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 cross-sections) at 0.50 m
 intervals along the course of the branch were cross-sectioned 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
 three-dimensional 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) circle-fitting algorithm
 (Fischler and Bolles,
 1981). The package
 ‘TreeLS’ (de Conto,
 2020) in R language
 (RStudio Team,
 2021) was used for RANSAC
 circle-fitting. This served as a non-destructive TLS-based 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 ground-truth 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. TaperCurve-BFF.R is the Rscript
 for the taper curve using the multivariate spline regression model.
 The optimal sub-model was determined
 using the generalized cross-validation (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). MN-QSM-asc.xsct2 and MN-QSM-las.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.
description:   
 
 <strong>Column Name</strong> 
 
 <strong>Description</strong> 
 
 <strong>Unit</strong> 
 <strong>Source</strong> 
 <strong>Calculation or Measurement
 Methods</strong> 
 <strong>Software</strong> 
 
 <strong>Data1.csv</strong> 
 
 Species The
 scientific name of the scanned trees 
 <em> </em> 
 <em> </em> 
 <em> </em> 
 <em> </em> 
 Scan_Code Given code
 during scanning 
 <em> </em> 
 <em> </em> 
 <em> </em> 
 <em> </em> 
 Branch_ID Isolated
 sample branch in each tree. Repetition of similar ID numbers indicates the
 series point slices taken along the corresponding branch.
 
 <em> </em> 
 <em> </em> 
 <em> </em> 
 <em> </em> 
 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 
 <em> </em> 
 <em> </em> 
 <em> </em> 
 <em> </em> 
 BO Branch
 order, where all the analysis was made for primary branches (BO
 01) 
 <em> </em> 
 <em> </em> 
 <em> </em> 
 <em> </em> 
 DBH Branch
 diameter at breast height 
 <em>cm</em> 
 Field Diameter
 tape 
   
 H Height of
 the tree. The vertical distance between the base of the trunk and the
 tree-top 
 <em>m</em> Point
 Cloud 
 <em>Z<sub>max </sub>– Z<sub>min
 </sub></em> R
 Programming Language 
 H1 Crown base
 height. The vertical distance between the base of the trunk and the lowest
 live branch 
 <em>m</em> Point
 Cloud 
 <em>Z<sub>first-live-branch </sub>–
 Z<sub>min</sub></em> 
 CloudCompare 
 H2 Crown
 length. Distance between the base of the lowest live branch and
 tree-top 
 <em>m</em> Point
 Cloud 
 <em>Z<sub>max</sub> –
 Z<sub>first-live-branch</sub></em> or
 <em>H<sub> </sub>–
 H<sub>1</sub></em> 
 CloudCompare 
 CR Crown
 ratio. The ratio of the crown length to the tree height
 
 <em> </em> Point
 Cloud 
 <em>H<sub>2</sub>/H</em>
 
 <em> </em> 
 BH Branch
 base height. Height of the primary branch attachment to the trunk from the
 base of the stump 
 <em>m</em> Point
 Cloud 
 <em>Z<sub>primary-branch-base-point </sub>–
 Z<sub>min</sub></em> 
 CloudCompare 
 BRH Branch
 base relative height. Height of the base of the primary branch relative to
 the tree height 
 <em> </em> Point
 Cloud 
 <em>BH/H</em> 
 <em> </em> 
 <strong>Data2.csv</strong> 
 Species –
 BRH Similar to
 <strong>Data1.csv</strong> 
 <em> </em> 
 <em> </em> 
 <em> </em> 
 <em> </em> 
 BL Branch
 length. The total length of the primary branch 
 
 <em>m</em> Point
 Cloud Manual
 length measurement from laser reflections
 <em> </em> 
 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 
 <em>m</em> Point
 Cloud Manual
 length measurement from laser reflections
 <em> </em> 
 CloudCompare 
 BRL Branch
 relative length. The relative length of each <em>BSL</em> from
 the <em>BL</em> 
 <em> </em> Point
 Cloud Normalized
 in [0 - 1] scale (<em>BSL/BL</em>) 
 
   
 BBD Branch
 basal diameter 
 <em>cm</em> Point
 Cloud Determined
 directly from laser reflections using a circular fit for the cross-section
 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
 non-destructive TLS-based dataset to fit the branch taper curve and
 calculate the branch form factor 
 <em>cm</em> 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 
 <em> </em> Point
 Cloud Normalized
 in [0 -1] scale using the <em>BBD </em>(D-TLS/ BBD)
 
   
 D_TaperModel_Relative Predicted
 relative branch diameter from the taper curve model 
 
 <em> </em> 
 <em>Taper Curve</em> Diameter
 prediction in normalized [0 -1] scale R
 Programming Language 
 D_TaperModel Predicted
 diameters from the taper curve model 
 <em>cm</em> 
 <em>Taper Curve</em> Series of
 diameter depicted from the taper curve regression model
 (D_TaperModel_Relative*BBD) 
   <strong>Data3.
 xlsx</strong> 
 BRL Branch
 relative length (As described and derived in
 <strong>Data2.csv</strong>) 
 <em> </em> 
 <em>Field, Taper Curve, QSM</em>
 
 Normalized in [0 - 1] scale
 (<em>BSL/BL</em>) 
   Reference
 Diameter 
 <em> </em> 
 <em>cm</em> 
 <em>Field</em> Field
 measurements of branch diameters using a caliper 
 
 <em> </em> Predicted
 Diameter 
 <em> </em> 
 <em>cm</em> 
 <em>Taper Curve, QSM</em> 
 
 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
 
 <em> </em> 
 <em>Taper Curve, QSM</em> 
 
 <em> </em> 
 <em> </em> Absolute
 Error (<em>AE</em>) 
 <em> </em> 
 <em>cm</em> 
 <em>Field, Taper Curve, QSM</em>
 
   
   Relative
 Absolute Error (<em>RAE</em>) 
 <em> </em> 
 <em>%</em> 
 <em>Field, Taper Curve, QSM</em>
 
 RAE = |Prediction Diameters from Taper Curve or QSM – Reference
 Diameters|/ Reference Diameters * 100 
   
 <strong>Data4.csv</strong> 
 
 Species_Code; Scan_Code; Species; Branch_Sample
 
 As described in <strong>Data1.csv</strong>
 
 <em> </em> 
 <em> </em> 
 <em> </em> 
 <em> </em> 
 Branch_Volume The volume
 of the branch 
 <em>cm<sup>3</sup></em>
 
 <em>Point cloud; Taper Curve</em>
 
 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 
 <em>cm<sup>3</sup></em>
 
 <em>Point cloud</em> 
 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 
 <em>cm<sup>3</sup></em>
 
 <em>Point cloud</em> 
 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 
 <em> </em> 
 <em>Point cloud; Taper Curve</em>
 
 Branch_Volume/CylinderVolume0.05 
   
 BFF0.10 Branch
 form factor with a reference diameter estimation at 10% if the branch
 length 
 <em> </em> 
 <em>Point cloud; Taper Curve</em>
 
 Branch_Volume/CylinderVolume0.10 
   <strong>Point
 Clouds</strong> 
 PSP28.asc; PSP28.las;
 APS30.asc; APS30.las 
 
 Examples of filtered tree point clouds<em> (Platanus
 species</em> and <em>Acer platanoides</em>)
 
       Any software used
 for point cloud visualization 
 <strong> </strong><strong>QSM
 Scripts</strong> 
 MN-QSM-asc.xsct2; MN-QSM-las.xsct2
 Examples of QSM scripts
   SimpleForest <strong>Pipeline Model (QSM Cylinders)</strong> <strong> </strong> <br> <strong> </strong>   PSP28.ply; APS30.ply Examples of the reconstructed branch cylinders (based on the provided QSM Scripts) CloudCompare Reference CloudCompare. (2021). <em>CloudCompare Software, 3D point cloud and mesh processing Project, Open Source</em> (Version 2.12.0). https://www.danielgm.net/cc/ Computree. (2021). <em>Computree: a platform for processing 3D point clouds</em> (version 5.0). http://rdinnovation.onf.fr/projects/computree/wiki de Conto, T. (2020). <em>TreeLS: Terrestrial Point Cloud Processing of Forest Data</em> (R package version 2.0.4.). https://mran.microsoft.com/snapshot/2020-02-16/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. <em>Communications of the ACM</em>, <em>24</em>(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. <em>Forests</em>, <em>6</em>(11), 4245–4294. https://doi.org/10.3390/f6114245 RStudio. 2021 <em>RStudio: A language and environment for statistical computing</em>. Boston, MA. https://www.rstudio.com/ SimpleForest. (2021). <em>SimpleForest: a 3D tree modelling software from point cloud data</em> (version 5.3.2). https://www.simpleforest.org/ Trimble Inc., Sunnyvale, CA, U. (2021). <em>Trimble TX5 Scanner: A 3D laser instrument</em>. https://www.laserscanning-europe.com/de/glossar/trimble-tx5-scanner
description: 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 cylinder-fitting 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
 automatized-techniques, we proposed a new branch-based 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
 TLS-derived 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 (&lt;10
 cm), with R2 of 0.86 and a mean relative absolute error of 1.03 cm (29%)
 when validated with field-measured diameters. This approach was also
 capable of retrieving branch diameters for a large percentage of
 explicitly identified primary branches (&gt;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 crown-tops
 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 non-destructive 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 leaf-off 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 comma-delimited 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 cross-sections) at 0.50 m intervals along the course of the branch
 were cross-sectioned 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 three-dimensional 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) circle-fitting algorithm (Fischler and Bolles, 1981). The package
 TreeLS (de Conto, 2020) in R language (RStudio Team, 2021) was used for
 RANSAC circle-fitting. This served as a non-destructive TLS-based 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 ground-truth 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. TaperCurve-BFF.R is the
 Rscript for the taper curve using the multivariate spline regression
 model. The optimal sub-model was determined using the generalized
 cross-validation (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). MN-QSM-asc.xsct2 and MN-QSM-las.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). Computree.
 (2021). Computree: a platform for processing 3D point clouds (version
 5.0). de Conto,
 T. (2020). TreeLS: Terrestrial Point Cloud Processing of Forest Data (R
 package version 2.0.4.).
 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. 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. RStudio. 2021 RStudio: A language and environment for statistical computing. Boston, MA. SimpleForest. (2021). SimpleForest: a 3D tree modelling software from point cloud data (version 5.3.2). Trimble Inc., Sunnyvale, CA, U. (2021). Trimble TX5 Scanner: A 3D laser instrument.