Terrestrial laser scanning to reconstruct branch architecture from harvested branches

Quantifying whole branch architecture is critical to understanding tree function, for example, branch surface area controls woody gas exchange. Yet, due to measurement difficulty, branch architecture of small diameter branches (e.g. <10 cm ⌀ ) is modelled, subsampled or ignored. Methods that use terrestrial laser scanning (TLS) are now being widely applied to analyse tree and plot‐level tree architecture; however, resolving small diameter branches in‐situ remains a challenge. Currently, it is suggested that accurate reconstruction of small diameter branches can only be achieved by harvest and measurement in controlled conditions. Here we present a new TLS workflow for rapid and accurate reconstruction of complete branch architecture from harvested branches. The workflow sets out scan configuration, post‐processing (including a novel reflectance filter) and fitting of quantitative structure models (QSM) to reconstruct topologically coherent branch models. This is demonstrated on 595 branches (scanned indoors to negate the impact of wind) and compared with 65 branches that were manually measured (i.e. with measuring tape and callipers). Comparison of a suite of morphological and topological traits reveals a good agreement between TLS‐derived metrics and manual measurements where RMSE (%RMSE) for total branch length = 0.7 m (10%), volume = 0.09 L (43%), surface area = 0.04 m2 (26%) and N tips = 6.4 (35%). Scanning was faster and invariant to branch size compared with manual measurements which required significantly more personnel time. We recommend measuring a subsample of tip widths to constrain the QSM taper function as the TLS workflow tends to overestimate tip width. The workflow presented here allows for a rapid characterisation of branch architecture from harvested branches. Increasing the number of branches analysed (e.g. many branches from a single tree or branches from many species globally) could allow for a comprehensive analysis of the ‘missing link’ between the leaves and larger diameter branches.


| INTRODUC TI ON
Tree architecture is the 3D spatial arrangement, morphology and topology of a tree's leaves, branches and stem (Barthélémy & Caraglio, 2007;Valladares & Lo Niinemets, 2007). An individual tree's architecture is the product of its encoded genome during ontogeny, resulting from both evolutionary and ecological tradeoffs between light capture, water transportation and mechanical self-support. Tree architecture is typically measured manually, for example, with a measuring tape and callipers, either in-situ (Sillett et al., 2015) or after destructive harvest (Bentley et al., 2013;MacFarlane & Kane, 2017;Smith et al., 2014); both are laborious, time-consuming and sometimes dangerous tasks (Smith et al., 2014). In particular, characterising the architecture of small diameter woody components is difficult given their often non-trivial complexity and in-situ location many metres above the forest floor. This has resulted in traits of higher-order branching being modelled, subsampled or ignored Sillett et al., 2015). Capturing and quantifying the architecture of the 'missing link' between larger diameter branches and leaves is key to understanding whole tree function, for example, gas exchange and surface area allometry (Chambers et al., 2004), intra-canopy response to light environments (Barthélémy & Caraglio, 2007) or divergence from theoretical predictions of crown architecture (Bentley et al., 2013).
Sensor-based methods to capture 3D information of smaller objects (i.e. centimetre to decimetre scale) have been developed for a number of disciplines, including agronomy, ecology, industry, cultural heritage, medicine and criminal investigation (Calders et al., 2019;Rahman et al., 2017;Sansoni et al., 2009). Capturing complex 3D plant structure has been demonstrated using techniques such as stereo vision, structure from motion (SfM) (Iglhaut et al., 2019;Moriondo et al., 2016), structured light (Nguyen et al., 2015) and X-ray tomography (Dutagaci et al., 2020). These techniques allow for a larger sample size without the need for subsampling (i.e. whole branch architecture) and can generate a suite of quantitative measurements. However, these techniques often require controlled laboratory or photo studio conditions and/or large pieces of specialist equipment that make them less ideal for capturing data in remote areas, such as forests.
Terrestrial laser scanning (TLS) methods have also shown great promise for capturing tree and branch architecture (Disney, 2019;Malhi et al., 2018). TLS instruments use a laser range finder to measure the distance along with azimuth and zenith angles of an intercepting surface, for example, ground, wood and leaf, in relation to the instrument. Scanning across a panorama or hemisphere, TLS instruments can quickly construct a dense 3D representation (i.e. a point cloud) of an area of interest. TLS methods have been used to measure tree and forest biophysical traits, including volume and biomass (Calders et al., 2015), branching topology and scaling exponents (Lau et al., , 2019Martin-Ducup et al., 2020), leaflevel traits (Boni Vicari et al., 2019) and many others (see review by Calders et al., 2020).
However, using TLS to measure small diameter branching architecture (e.g. <10 cm ∅; Lau et al., 2019;Martin-Ducup et al., 2020) of a tree in-situ still remains a challenge, particularly for large trees or in dense evergreen forests, that is, the tropics.
Factors including occlusion, laser beam divergence, wind effects, liana infestation and under sampling preclude accurate characterisation, particularly towards the top of the canopy (Wilkes et al., 2017). This, in turn, can lead to a miss-characterisation of branch architecture as adjacent branches are either aggregated or ignored. When Lau et al. (2019) compared scanned and manually measured branches, TLS methods were only able to reconstruct 56% of branches with a radius of 5-15 cm. In all but the most ideal circumstance, for example, isolated, low stature trees (Calders et al., 2015;Raumonen et al., 2013) and branch harvesting, remains the only viable option.
The capability of TLS methods to accurately scan and reconstruct harvested branches has been tested previously. For example, Cheng et al. (2007)  Presented here is a scanning and post-processing workflow that is rapid, scalable, transportable to remote areas and is capable of reconstructing whole branch architecture to the branch tip. In all, 595 branches were scanned and reconstructed using this method; the full architecture of 65 branches were measured manually and analogue metrics were compared.  (Graham, 2006).

| Branch harvesting and processing
Trees were selected using the protocol described by  where species that contributed maximally to plot basal area were selected (up to 80%), then for each identified species three to five individuals were sampled. The aim was to collect a minimum of two branches per tree: a branch from the sunlit part of the canopy and another from a shaded region (immediately below the sunlit canopy). Branches were harvested using a variety of techniques dependent on forest type and personnel (Table 1). The size of harvested branches was determined by the harvesting method and the size of the tree. Ideally branches had a length of >1 m and included >2 branch furcations. Harvested branches were stripped of all leaves, flowers and fruits before measurement.

| Scanner and branch setup
A RIEGL VZ-400 terrestrial laser scanner (RIEGL Laser Measurement Systems GmbH) was used for all scans. In all, 1-6 branches (dependent on branch size) were arranged in a group, orientated so that they would not touch each other or the ground, and scanned simultaneously ( Figure 1). Branches were secured in the end of metal tubing and placed in buckets of sand to minimise movement. Fiducial markers (akin to QR codes) were placed on the floor to allow identification of each branch in post-processing (Wilkes, 2021). The markers include a pattern of four retroreflective stickers (10 mm ∅) which were used to co-register scans.
Between four and six scan positions (collectively known as a project), located around the branches (Figure 1b), were used to capture each set of branches. At each position, a single scan was performed where the scanner rotation axis was approximately perpendicular to the ground plane. A 100 • × 80 • field of view was captured at an TA B L E 1 Description of plots and number of branches measured. Country codes are Australia (AUS), Brazil (BRA) and Malaysia (MAL). Pole refers to either a pole-lopper or a pole with a snagging hook, B&A refers to a bow and arrow. 'Full' refers to complete manual measurement of branch architecture whereas 'Tips' refers to measurement of a subsample (N = 5) of tip-widths, see Section 2.5 for more details  laser pulses were fired. The VZ-400 beam has an exit diameter of 0.007 m and a beam divergence of 0.35 mrad; branches were at a maximum distance of 5 m from the scanner, and at this distance maximum cross-sectional beam diameter is ∼0.01 m.
The scanning area needed to be large enough to allow easy movement around the branches and minimum distance between the scanner and target (for the RIEGL VZ-400, this is 0.5 m). It should be noted, owing to the restricted scanning field of view, large or featureless areas required additional 'features' (e.g. furniture in the scanning field of view) to assist with registration. Initially, scanning was performed outside but it became clear that branch tips would oscillate even with very low wind speeds; therefore, scanning was moved to an indoor space.

| Co-registration of scan projects
Co-registration of scans in a project is a two-step process (coarseand fine-registration) that produces a 4 × 4 roto-transformation matrix for each scan position. When applied, a scan is rotated into a common, arbitrary coordinate system (nominally referenced to the first scan position). Co-registration of a project was done using

| Filtering points
Terrestrial laser scanning data invariably contain points that are erroneous or is not required, that is, ℬ � = ℬ + where ℬ is the branch point cloud and is to be filtered. There are a number of sources of , for example, neighbouring objects that were not correctly clipped, that may have to be rectified manually. Two sources of that required an analytical approach to filter were: Source 1 errors were filtered using the 'deviation' field so that where is the centroid of the footprint and is the standard deviation.
The effective laser footprint cross-sectional area was determined by constraining F * to 1∕e 2 ; therefore, the integral of F is The branch model G is represented by a cylinder with axis centred on zero and infinite length. It is approximated from Figure 2 that a branch is a Lambertian scatter where reflectance decreases with increasing incidence angle. Therefore, G can be modelled using Lambert's cosine law, where reflectance is proportional to the cosine of the incidence angle and the surface normal.
where R is the radius of the modelled branch.
The convolution of F and G is calculated to compute reflectance, this is then transformed to give in units of dB.
As surface scattering characteristics are likely to differ along a branch, ℬ ′ is first voxelised with a voxel length of 0.01 m. F I G U R E 2 Point reflectance for a branch cross-section. (a) a cross-section of a branch section where points are coloured by scan position (SP 1-5) or if they are filtered (grey), (b) point clouds coloured by reflectance (grey points were filtered) where points clouds have been rotated towards the scanner (grey dashed line approximate branch axis) and (c) mean reflectance as a function of surface normal (coloured by scan position; see panel (a)) where normals have been calculated from a local neighbourhood of points, also include is curve representing Lambert's Cosine Law Finally, a nearest neighbour analysis was conducted to remove spatial outliers which were generally artefacts from filtering processes

| Quantitative structure models
Methods to parameterise unordered points include fitting a plane to or enclosing points in a geometric primitive (e.g. a cylinder), this allows computation of a surface normal or volume, respectively . In the case of tree point clouds, methods have been developed to segment into a set of spatially separate clusters  (Åkerblom, 2017), was applied to smooth variations in cylinder radius caused by residual point cloud noise.
Where possible, branch tip widths were measured (see Section 2.5) and used to weight the polynomial functions that constrain cylinder radius; where this was not possible, tip width was determined by an unweighted taper function.

| Manual measurement of branches
To compare QSM modelled branch morphology and topology, a subset of branches (Table 1) were measured manually with a measuring tape and callipers (Bentley et al., 2013). For each branch, starting from the base (the point at which the branch was harvested), the length to the first node and distal radius was measured. Distal radius measurements were done with digital callipers where major and minor axes were measured at the base and below the furcation point. The internode was labelled and measurement moved onto the daughter internodes, this continued until all internodes had been measured; whether an internode was a tip (or broken) was also recorded. Parent-daughter internode connections were recorded to allow for a connected graph to be generated, analogous to a QSM.
See Appendix S2 for more details on manual measurements.

| Number of branches scanned and measured
A total of 595 branches were scanned of which 15 were discarded from further analysis owing to data quality issues, for example, a branch moving between scans. The full architecture of 99 branches

| RE SULTS AND D ISCUSS I ON
Presented here is a method to reconstruct branch morphology and topology of harvested branches using a TLS-based workflow.
Capturing this information across a single harvested tree, a single species across a plot or pan-tropically, for example, will allow for a greater understanding of branch architecture, for example, describing the major axes of architecture variation . The workflow has been designed to give the best possible reconstruction of woody branch architecture, hence the requirement to remove leaves and scan in controlled environments.
Therefore, the results (e.g. accuracy of reconstruction) may not be directly transferable to in-situ scanning of branches; however, scanning branches pre-and post-harvest or scanning harvested branches leaf-on and -off may provide a reference for in-situ reconstruction.

| Harvesting, scanning and manual measurement
Harvesting of branches is a laborious process requiring either large infrastructure or skilled personnel. Branch harvesting technique differed between location (Table 1) where climbers and the canopy crane resulted in the highest success rate while also allowing access to sunlit branches even in very tall trees (>60 m). Ground-based techniques were less successful leading to fewer (often larger) branches. Preparing branches for measurement, for example, removing leaves, can also be time-consuming; however, this can be combined with complementary leaf trait analysis.
Scanning branches was a far quicker process than manual measurement. Typically, 3-6 branches could be set-up and scanned in <30 min (10 min to set-up and 20 min to scan), whereas manual measurement required a two-person team per branch and a single branch may have taken >1 day to measure, that is, scan time is independent of branch size, whereas time to manually measure full architecture is not. Registering ∼200 projects in RiScan Pro was time-consuming; however, once this was semi-automated (using the fiducial marker reflective dots as tie points) projects could be registered in ∼15 min.
We recommend that a subsample of tip widths (N ≈ 5) is measured with callipers to constrain the QSM taper function. This additional step improves the morphological representation of branches and leads to smaller errors in volume and surface area estimates (Figures 7 and 8).

| Post-processing of point clouds
Filtering ℬ ′ , as described in Section 2.4.1, removed ∼ 64 % ± 10 % of points, where mean | ℬ | was ∼210,000 points. Fitting QSMs to ℬ ′ without specifying tip width in the taper function significantly increases branch volume (bias = 171%) when compared to ℬ with measured tip widths constraining the taper function (Figure 7a).
Branch volume decreases when applying either filtering or tipwidth correction; however, volumes are still larger than their fully processed counterparts where bias is 83% and 13%, respectively (Figure 7b,c). QSMs fitted to ℬ ′ without specifying tip width decreases the number of internodes detected (bias = 1.8 internodes), particularly for shorter branches. As expected, specifying tip width F I G U R E 5 Examples of (a) an unfiltered branch point cloud (ℬ ′ ), (b) a filtered branch point cloud (ℬ) and (c) the resulting QSM. Points are coloured by reflectance in (a). In (b), points are coloured by unique cluster , large points are cluster centroids that act as the start and end points of cylinders and arrows are the axis of the QSM cylinders determined by a graph where their direction is towards the base of the branch. The QSM in (c) is coloured by unique internode has no impact on QSM topology derived from ℬ ′ (Figure 7f). QSMs derived without a constrained taper function produces tend to overestimate smaller tip widths by 2-5 mm and underestimate tip width >3 mm (Figure 7g,i). There is an apparent good agreement between manually measured and QSM metrics derived from ℬ (cf. Figure 8) suggesting that filtering and a constrained taper correction are necessary post-processing steps.
The model developed in Section 2.4.1 estimates branch diameter from max where predicted and observed max follow a similar trend of decreasing max with decreasing branch radii (see Appendix S1).
Observed max is lower than the reflectance model would predict indicating that the branch surface is more attenuating of the laser pulse than predicted. results. However, full waveform data were not collected for this experiment.

| Branch architecture comparison
TLS-derived QSMs can characterise branch morphology and reconstruct topology accurately (Figures 6 and 8). Reconstructed total branch length is the most accurately reconstructed metric with a bias of 1.3% and RMSE of 10% when compared to manually measured branches ( Figure 8a); an inability to reconstruct to the very tip may lead to a slight underestimate (Figure 8f). Regarding topology, TLS methods tend to overestimate the number of tips (bias = 0.03 tips, Figure 8d), particularly for smaller branches, but underestimate the number of internodes (bias = − 4.1 internodes, Figure 8f) due to the inability to resolve more ramified branching structures. Surface area (RMSE = 26%, bias = 9.9%, Figure 8c) and volume (RMSE = 43%, bias = 11.4%, Figure 8b) are overestimated by TLS methods owing to a tendency to F I G U R E 7 A comparison of QSM morphological (volume a-c and tip width g-i) and topological metrics (N internodes d-e) derived from unfiltered point clouds and without specifying tip width in the taper correction (left), unfiltered with a specified tip width (middle) and filtered point clouds without specifying tip width (right). All are compared to QSMs derived from filtered point clouds where tip width has been specified in the taper correction overestimate branch radius even after taper correction. Inflation of radius towards the ends of the branches leads to a disproportionate overestimation in total volume, this is due to a compounding effect of many smaller internodes; radius inflation towards the base does not generally lead to an overestimation of total volume (Figure 9).
Although a concerted effort was made to remove noise from the branch point clouds, over inflation of branch radius was still prevalent. Taper functions can reduce overestimation, particularly towards branch tip; however, these are often data driven or require additional manual measurements (such as manual tip width measurements used here). More sophisticated taper functions with a physiological basis could improve volume and surface area estimates. Use of a cylinder as a geometric primitive may also not be most suitable candidate (although see Åkerblom et al., 2017). The mean ratio between major and minor axes as measured with callipers was 0.9, suggesting an elliptical primitive is more suitable. Using only the major axis when calculating volume results in a 6% overestimation of manually measured volume, compared to using major and minor axes. Furthermore, cylinder fitting to a point cloud cluster (i.e. c ∈ C) is naive in that a cylinder is fit to all points without regard for scan position (distance and viewing geometry) or a point quality weighting. A more intuitive cylinder fitting method may consider fitting iteratively to points from sequential scan positions or weighting points by an estimate of point quality. Artificial inflation of branch radius may have implications for whole tree volume and surface area estimates that are yet to be fully considered and should be investigated further.
A comparison radius and length scaling exponents generated from TLS and manual measurements are presented in Figure 10 (see Appendix S2 for methods used to calculate exponents). Both manually measured and TLS-derived radius exponents tended to be slightly greater than theoretical predictions, for example, West et al. (1999), whereas length exponents were less than predicted values. Similar results were presented by Bentley et al. (2013) and Lau et al. (2019) for branch level exponents measured across whole trees. Branches with a greater number of internodes (larger circles in Figure 10) tend towards the WBE scaling exponent value. Both TLS modelled and manually measured median length scaling exponents are <0 suggesting that, for the majority of branches, internode length increases towards branch tips. For branches with fewer internodes (smaller circles in Figure 10b), this could be caused by harvesting points not being located at a furcation.
It should be noted that metrics presented here were for comparison with manual measurements, that is, the suite of metrics Additionally, branch models could have further uses, for example in radiative transfer modelling to better characterise branch architecture when simulating forest scenes .

| Other scanning methods
Although the scanner used here was a high specification time-offlight instrument, we suggest that the scanning and processing workflows are applicable to other TLS systems with only minor modifications. Phase shift laser scanners tend to have a smaller beam divergence (Abegg et al., 2020); however, they are often single return which may preclude scanning multiple branches at once.
Other sensor methods may also become viable as technology improves (e.g. miniaturisation and ruggedness), in particular hand-held SfM and structured light systems where resolution is only limited by pixel size (Reichert et al., 2016;Wilkes et al., 2020).

| CON CLUS IONS
This paper presents a workflow to rapidly characterise the architecture (topology and morphology) of harvested branches using a TLS-based workflow. This involves branches being harvested and F I G U R E 9 Analysis of radius measurements (top row), radius residuals (row 2), volume residual (

CO N FLI C T O F I NTE R E S T
The authors declare there are no conflicts of interest.

PE E R R E V I E W
The peer review history for this article is available at https://publo ns.

DATA AVA I L A B I L I T Y S TAT E M E N T
The three branches presented in Figure 6 are available to download from Wilkes et al. (2021)