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ISPRS Journal of Photogrammetry and Remote Sensing 82 (2013) 41–48

Contents lists available at SciVerse ScienceDirect

ISPRS Journal of Photogrammetry and Remote Sensing
journal homepage: www.elsevier.com/locate/isprsjprs

3-D voxel-based solid modeling of a broad-leaved tree for accurate
volume estimation using portable scanning lidar
Fumiki Hosoi, Yohei Nakai, Kenji Omasa ⇑School of Agricultural and Life Sciences, The University of Tokyo, Yayoi 1-1-1, Bunkyo-ku, Tokyo 113-8657, Japana r t i c l e

i n f oArticle history:
Received 4 November 2012
Received in revised form 24 April 2013
Accepted 25 April 2013

Keywords:
Portable ground-based scanning lidar
Solid model
Voxel
Woody material volume

a b s t r a c t
We developed a method to produce a 3-D voxel-based solid model of a tree based on portable scanninglidar data for accurate estimation of the volume of the woody material. First, we obtained lidar measurements with a high laser pulse density from several measurement positions around the target, a Japanesezelkova tree. Next, we converted lidar-derived point-cloud data for the target into voxels. The voxel size
was 0.5 cm  0.5 cm  0.5 cm. Then, we used differences in the spatial distribution of voxels to separate
the stem and large branches (diameter > 1 cm) from small branches (diameter 6 1 cm). We classiﬁed thevoxels into sets corresponding to the stem and to each large branch and then interpolated voxels to ﬁll
out their surfaces and their interiors. We then merged the stem and large branches with the small
branches. The resultant solid model of the entire tree was composed of consecutive voxels that ﬁlled
the outer surface and the interior of the stem and large branches, and a cloud of voxels equivalent tosmall branches that were discretely scattered in mainly the upper part of the target. Using this model,
we estimated the woody material volume by counting the number of voxels in each part and multiplying
the number of voxels by the unit voxel volume (0.13 cm3). The percentage error of the volume of the stemand part of a large branch was 0.5%. The estimation error of a certain part of the small branches was
34.0%.
Ó 2013 International Society for Photogrammetry and Remote Sensing, Inc. (ISPRS) Published by Elsevier
B.V. All rights reserved.

1. Introduction
Trees have important functional roles, including the cycling ofmaterials and energy through photosynthesis and transpiration,
the maintenance of microclimates, and the provision of habitats
for various species (Jones, 1992; Larcher, 2001; Monteith, 1973).
To understand the relationship between these functions andstructure, many structural parameters, including height, stem
diameter, leaf area density, volume, and biomass, have been measured by a variety of methods (Bragg, 2008; Norman and Campbell, 1989; Schnitzer et al., 2006). Recently, the importance of
estimating tree volume or biomass for studies of global climatechange has been recognized, because terrestrial vegetation is amajor carbon storage pool and the carbon stock contained in tree
canopies can be determined from their volume or biomass byusing conversion factors. Thus, a method for accurate determination of the volume or biomass of trees is needed to determine theglobal carbon budget.

⇑ Corresponding author. Tel.: +81 3 5841 5340; fax: +81 3 5841 8175.

The most accurate method of estimating the volume or biomassof trees is to physically sample it (i.e., direct measurement).
However, this method is not practical for most ﬁeld researchbecause it is both labor-intensive and destructive. Alternatively,
satellite-based sensors such as the Landsat Enhanced Thematic
Mapper, Synthetic-Aperture Radar (SAR), and the MODerateResolution Imaging Spectroradiometer (MODIS) have been used
to estimate tree volume or biomass (le Maire et al., 2011; Maselli
and Marta, 2006; Neumann et al., 2012). Although these sensors
are suitable for regional-scale estimation, their resolution andaccuracy are insufﬁcient to provide detailed and accurate volume
estimates at the individual-tree scale.
Recently, light detection and ranging (lidar) with laser scanners
has emerged as a powerful active sensing tool for direct 3-D measurement of tree shapes and structures (Brandtberg et al., 2003;
Côté et al., 2009; Holmgren and Persson, 2004; Hosoi et al.,2010; Hosoi and Omasa, 2006, 2007, 2009, 2012; Hopkinson
et al., 2004; Hyyppä et al., 2001; Kaartinen et al., 2012; Lefsky
and McHale, 2008; Lefsky et al., 2002; Means et al., 1999; Næsset
et al., 2004; Omasa et al., 2000, 2002, 2003, 2007, 2008; Zhao
et al., 2011). Lidar provides accurate 3-D information about trees
by measuring the distance between the sensor and the target.
Large-footprint airborne lidar systems can cover a wide expanse

E-mail address: aomasa@mail.ecc.u-tokyo.ac.jp (K. Omasa).
0924-2716/$ - see front matter Ó 2013 International Society for Photogrammetry and Remote Sensing, Inc. (ISPRS) Published by Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.isprsjprs.2013.04.011

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of a forest canopy, allowing the volume or biomass to be estimatedby analyzing the waveforms of the returned laser pulses (Lefsky
et al., 2002; Means et al., 1999). However, the image resolutionof such systems is not ﬁne enough for estimates at the scale ofthe individual tree. In contrast, small-footprint airborne lidar systems can cover a larger forest region with a ﬁne enough resolution
and sufﬁcient accuracy for individual-tree-scale estimates. The volume or biomass of individual trees can be estimated from high-resolution images obtained by such lidar systems with high pulse
repetition frequency through the application of allometric equations that relate the lidar-derived structural parameters to volume
or biomass (Hyyppä et al., 2001; Næsset et al., 2004; Omasa et al.,2003, 2007). Portable on-ground scanning lidar systems have also
been used for tree structural measurements (Côté et al., 2009,2011; Dassot et al., 2011; Delagrange and Rochon, 2011; Hosoi
and Omasa, 2006; Yao et al., 2011). The portability of such systems
and their ability to efﬁciently collect data with very ﬁne spatial resolution and accuracy (sub-millimeter to a few centimeters; Omasa
et al., 2007) are advantageous for tree measurements on the
ground. These systems can be used as an alternative to conventional in situ measurements of tree structure on the ground.
Although the area covered by on-ground systems is not as large
as that of airborne lidar systems, recent advances in lidar technology have increased the measurable range of portable systems toseveral hundred to a thousand meters with a range accuracy of better than 1 cm (Pirotti et al., 2013). Thus, portable scanning lidar
systems are regarded as useful tools for ground-based plot-leveltree measurements. Tree structural parameters such as heightand diameter at breast height (DBH) have been extracted from 3D point cloud images obtained by portable scanning lidar systems
and used along with allometric equations (equations that establish
quantitative relationships between key structural parameters oftrees and other properties) to estimate volume or biomass (Hopkinson et al., 2004; Ku et al., 2012; Omasa et al., 2002; Yao et al.,2011). This method facilitates the estimation of volume or biomass
without complex post-processing of the acquired data, but allometric equations are still required. In addition, allometric equations
can only give a representative estimate based on the structuralparameters, whereas shape and structure vary among individual
trees. Thus, volume and biomass can vary among trees even though
the structural parameters (e.g., height, DBH) input into the allometric equations have the same values. This limitation reduces theaccuracy of volume and biomass estimates obtained by using thesame allometric equations for all individuals of a species.
Portable scanning lidar systems can capture the complex shapeand structure of individual trees as a detailed 3-D point-cloud
image. Thus, 3-D tree models faithfully reproduced from the lidarderived 3-D point-cloud image can be used to estimate the volumeof trees without using allometric equations. Several 3-D tree modeling techniques have been employed for the estimation of individual
tree volume and other structural properties from portable scanninglidar data (reviewed by Dassot et al., 2011). For example, modelingmethods that extract the skeleton of a tree from 3-D point clouddata obtained by portable scanning lidar systems have been used
to reconstruct tree architecture (Bucksch and Lindenbergh, 2008;
Côté et al., 2009, 2011; Delagrange and Rochon, 2011). Côté et al.
(2009, 2011) used such a modeling method to construct 3-D treemodels that faithfully reﬂected the structural and radiative properties of the measured trees. In this modeling, the authors aimed tominimize the occlusion effect (that is, the lack of 3-D point clouddata for parts occluded by other branches, surrounding trees, andunderstory) which causes estimates of tree structural properties
to be inaccurate (Côté et al., 2009, 2011; Dassot et al., 2011; Delagrange and Rochon, 2011; Hosoi and Omasa, 2007). Côté et al. (2009,2011) considered their methodology to be relatively insensitive tothe occlusion effect. Although they also used their model for volume

estimation, the accuracy of their estimates is not clear because they
did not use ﬁeld data to validate the estimation method. Using amethod different from the tree skeleton extraction method, Omasa
et al. (2008) produced 3-D polygonal surface models of individual
tree canopies from portable scanning lidar data in conjunction withairborne scanning lidar data. Although they were able to estimate
the volume of a part of the stem by this polygonization process, it
was difﬁcult to apply the process to the surfaces of stems andbranches with complex shapes. Thus, the method could not be used
to estimate the volume of the whole tree. Another approach to 3-Dtree modeling based on lidar-derived point-cloud data is voxel representation (Hosoi and Omasa, 2006; Lefsky and McHale, 2008;
Schilling et al., 2012; Vonderach et al., 2012). Hosoi and Omasa(2006) recently proposed a voxel-based method of 3-D modelingthat uses high-resolution portable scanning lidar data (Voxel-based
Canopy Proﬁling method). In this method, lidar data points are converted into voxel elements in a 3-D voxel array to faithfully reproduce the canopy as a voxel model. Although this method has beenused for estimating vertical leaf area density proﬁles rather thanfor volume estimation, several studies have proved the ability of avoxel-based method to accurately estimate tree structural parameters (Hosoi and Omasa, 2006, 2007, 2009, 2012; Hosoi et al., 2010;
Omasa et al., 2007). Lefsky and McHale (2008) also estimated tree
volume in an urban area by 3-D voxel-based modeling using portable scanning lidar data. However, since their method approximates
the shapes of stems and large branches as cylinders, it might notaccurately reproduce their real shapes. In addition, Lefsky and
McHale (2008) did not model small, very thin branches, which area major canopy component, and thus the volumes of the small
branches were not estimated. Moreover, because they did not compare the estimated volume with the actual measured volume, theaccuracy of the method is uncertain. Therefore, accurate tree volume estimation by 3-D tree modeling is still under development.
In the present study, we propose a novel approach to 3-D treemodeling that enables tree volume to be accurately estimated fromportable scanning lidar data. We validate the accuracy of the volume estimates obtained with the model by comparing them withthe actual measured volumes.

2. Materials and methods
2.1. Study site
The study was carried out in a mixed plantation in Ibaraki Prefecture, 40 km northeast of central Metropolitan Tokyo, Japan. The
dominant tree species are Japanese cedar (Cryptomeria japonica[L.f.] D. Don), Japanese red pine (Pinus densiﬂora Siebold & Zuccarini), ginkgo (Ginkgo biloba Linnaeus), and Japanese zelkova (Zelkova serrata [Thunberg] Makino). The understory includes
grasses, forbs, and young evergreen trees such as Camellia japonica
Linnaeus, Ilex integra Thunberg, and Ternstroemia gymnantheraSprague. Tree density in the study area was about 600 trees per
hectare. We established a 32 m2 (4 m  8 m) measurement plotat the site and chose a Japanese zelkova tree (height, 14 m; DBH,
0.25 m) within the plot for measurement. We established a relatively narrow plot and examined only one tree species to establish
the basic processes used in the present modeling approach. Japanese zelkova is a medium to large deciduous tree, and its branches
are numerous, usually ascending strongly from a short trunk toform a high domed crown (MobileReference, 2009). The complicated branch structure makes the zelkova tree an ideal species
for model testing because the present method was designed to offer accurate volume estimation of even a complicated tree. Poles
were placed at each corner of the measurement plot and scanned
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the point cloud image, laser returns from the targeted zelkova tree
could be identiﬁed. Hosoi and Omasa (2007) previously describedthe details of the measurement plot and the Japanese zelkova tree.

on the volume estimation was negligible. We also measured thediameters of the sampled small branches at 100 randomly selected
points with calipers and calculated the mean diameter at thosepoints.

2.2. Portable ground-based scanning lidar measurements
In this study, only the volume of woody material, in the form ofstems and branches, was quantiﬁed, because the method to estimate the quantity of leaves (i.e., leaf area density or leaf area index) has been already reported (Hosoi and Omasa, 2006, 2007,2009, 2012; Hosoi et al., 2010; Omasa et al., 2007). Thus, the measurements were made in January 2010, during leaf-off conditions,with a portable ground-based scanning lidar system (LPM-25HA,RIEGL, Austria). This portable lidar system can obtain the distanceto the surface of an object between 2 and 60 m from the sensor bymeasuring the time elapsed between the emitted and returned laser pulses (the ‘‘time of ﬂight’’ method). A rotating mount driven
by built-in stepper motors panned and tilted the lidar head with
0.009° accuracy, and the distance to each sample point was computed with an accuracy of ±8 mm. The target was scanned fromsix surrounding positions (similar to the previous setting describedby Hosoi and Omasa, 2007). The central scan angle of the laser
beams from the zenith was 57.8°, and the average distance of thelidar sensor from the targeted zelkova tree was about 10 m. The
mean laser beam diameter and mean laser beam pitch (i.e., themean of the distances between the centers of adjacent laser
beams) in a plane perpendicular to the direction of the laser beam
were both 12 mm at the distance of the target. This pitch value
indicates that the laser pulse density (i.e., the number of incident
laser pulses per unit area of a plane perpendicular to the directionof the laser pulse) was high.
2.3. Direct measurement of the tree volume
Immediately following the lidar data collection, we directly
measured the volumes of the stem, part of a large branch, andsome of the small branches. In this study, we deﬁned brancheswith a diameter of more than 1 cm as ‘‘large branches’’ and all others as ‘‘small branches,’’ because 1 cm is the approximate spatial
resolution of the lidar system. First, we chose a continuous partof the target tree that included the stem and part of a large branch(as illustrated in the results section) for direct measurement. Next,
we obtained clay molds of the outer shape of 0.30-m-long sectionsof the stem and branch between heights of 0.00 and 7.80 m atintervals of 0.30 m by pressing oil-based clay around each section.
Then, we carefully removed the mold by making two cuts, longitudinally along the stem or the large branch, to retain the outer shapeof that section. The mold was sufﬁciently thick (about 5 cm) to prevent deformation; thus, it preserved the outer shape of the stem orbranch. We then photographed the inside of the clay mold of eachsection to obtain a cross-sectional image of the shape of that partof the tree at the height of the section. By referring to a scale included in each photograph, we determined the actual area (m2)of each pixel in the photograph, and we calculated the area ofthe cross-section by counting the number of pixels in the crosssection and multiplying it by the actual per pixel area. Then, by
multiplying the cross-sectional area by 0.30 m (the measurement
interval), we obtained the volume of each 0.30-m section of thestem and branch. For direct measurement of small branches, weused a cherry picker to cut out small branches that were distributed on the tree between heights of 10.00 and 11.00 m. Altogether,
we cut out about 400 samples of small branches. We then submerged these small branches, which were each about 1 m long,in a water tank and obtained their volume by measuring theincrease in the water volume. Since the volume was quickly
measured, the inﬂuence of water permeation into the branches

2.4. 3-D modeling using the obtained lidar data
2.4.1. Registration and voxelization
The 3-D modeling procedure is diagrammed in Fig. 1. We registered the 3-D point cloud data obtained at the six measurement
points by the portable ground-based lidar systems into a common
coordinate system by using the iterative closest-point algorithm(Besl and McKay, 1992). The error of the registration was within
2 cm. We then converted all points in the registered data set intovoxel coordinates (Hosoi and Omasa, 2006). For the voxelization(i.e., conversion of the lidar-derived point-cloud data into volume
elements in a 3-D array set in the computer memory), it is important for the voxel size to be determined appropriately; it must be
small enough to adequately represent the lidar data as voxels.
Therefore, we based the voxel size on the diameter of the small
branches of the target tree because they are the thinnest parts ofthe target. The small-branch diameters were less than the lidar’slaser beam pitch. Thus, a certain portion of a small branch hit by
one laser beam was recorded as a lidar data point, and the portionof the small branch hit by one laser beam could be considered to bea cylinder with its height equal to the laser beam diameter (Fig. 2).
We calculated the volume of the cylinder from the mean laser
beam diameter (1.2 cm) and the mean small-branch diameter(0.37 cm; obtained as described in Section 2.3 of the Methods) tobe 0.13 cm3. Then we chose the voxel size so that its volume would
be approximately the same as that of the cylinder, that is,
0.5 cm  0.5 cm  0.5 cm. We thus produced our initial 3-D voxel-based model of the zelkova tree using voxels of that size.

Lidar measurements
3-D point cloud images
Registration
Voxelization
Separating the stem andlarge branches

Stem and large branchesi.
ii.

Small branches

Surface generation
Classification of voxels
by grid tracking
Contour interpolation
Internal filling
3-D solid model
VolumeFig. 1. Schematic diagram of 3-D voxel-based solid tree modeling from portablescanning lidar measurements.

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Lidar
Small branch

Laser beam

Volumelabeled (a certain value was given to each cell as its attribute value), thus producing a set of labeled cells corresponding to the stemor to a large branch. Next, scanning of the grid was repeated, skipping already labeled cells, and the ﬁrst-encountered ﬁlled andunlabeled cell was treated as the next starting cell. The same procedure was applied to the other ﬁlled cells, with different labels
being used to discriminate the stem and each large branch(Fig. 3B: (a), (b), and (c)). In this way, we classiﬁed the voxels included in the cells into sets, each of which corresponded either
to the stem or to a speciﬁc large branch.

Determined voxel

Fig. 2. Determination of voxel size. The voxel dimensions were selected so that thevolume of one voxel would be the same as the volume of the portion of a small
branch irradiated by one laser beam.

2.4.2. Separating the stem and large branches from small branches
After the initial voxelization of the target, we needed to separate the voxels of the stem and larger branches from those of thesmall branches for further characterization (‘‘Separating the stem
and large branches’’ in Fig. 1). First, we manually picked several
voxels corresponding to the stem or large branches from the voxelized 3-D model. We used these as starting points for separating
the stem and large branches from small branches. Then, we categorized voxels neighboring these initial voxels within a certain
distance (in this case, 1 cm) as stem or large-branch voxels. The
categorized voxels then became new initial (starting) points andthe above searching procedure was repeated. This procedure wasiterated until no more voxels could be categorized as stem or large
branches. Then, we categorized all of the remaining voxels as
small-branch voxels.
2.4.3. Surface generation
We applied a surface generation procedure to the voxels categorized as stem or large-branch voxels (‘‘Surface generation’’ inFig. 1). The voxels converted from the lidar data on the surfacesof the stem and large branches were not adjacent because the laser
beam pitch (mean = 1.2 cm) was larger than the pitch of the voxel
array (0.5 cm). The surface generation procedure interpolated
additional voxels between the initial voxels of each one-voxelthick horizontal layer of the voxelized model to obtain a continuous closed curve representing the exterior surface of the stemand each large branch by the following two steps (Fig. 3).
2.4.3.1. Classiﬁcation of voxels into sets, each representing either thestem or a large branch, by grid tracing. To generate the surfaces, weﬁrst classiﬁed the voxels within a horizontal layer into sets, each
one corresponding to the stem or to a large branch. To do this,
we ﬁrst superimposed a grid on each horizontal voxel layer. We
chose the grid size (2 cm  2 cm) to be larger than both the original
voxels and the laser beam pitch (Fig. 3B). We then ﬁlled (labeled)each cell of the grid that included at least one voxel and used
Moore’s neighbor-tracing algorithm to connect adjacent ﬁlled cells
to trace the approximate contour of the exterior surface of the stemor large branch (Ghuneim, 2009). In this method, cells in each rowof the grid, starting from the top row and proceeding to the bottomrow, were scanned from the leftmost to the rightmost. Then, theﬁrst-encountered ﬁlled cell was treated as a starting cell and theeight neighboring cells were examined in a clockwise direction until another ﬁlled cell was encountered; this encountered cell wasthen treated as the next cell in the contour. These steps wererepeated until the starting cell was again encountered. This procedure yielded a closed curve outlining the stem or a large branch.
During this procedure, the starting cell and each selected cell were

2.4.3.2. Contour interpolation. We next applied a contour interpolation procedure to each set of classiﬁed voxels (Fig. 3C) within ahorizontal layer. Here, we no longer used the superimposed gridcells (2 cm  2 cm) described above. To generate contours of theexterior surfaces of the stem and each large branch composed ofconsecutive voxels, gaps (empty voxels) between voxels in a voxel
set were ﬁlled by linear interpolation. First, voxels that should not
be included in a contour were excluded as noise (Fig. 3C). We
judged whether a voxel was noise by calculating the mean (dm)and standard deviation (r) of the distance between each voxel
and the centroid of the voxel set. We regarded voxels at a distanceof more than dm + 3r as noise and excluded them from the set.
Next, we calculated the angle between the x-axis and each line segment connecting a voxel with the centroid of the voxel set. We
then sorted the angles in ascending order to determine the tracking
order of each voxel. Then, to generate the contour, we picked a certain tracked voxel and then ﬁlled the empty voxels between thatvoxel and the next ﬁlled voxel in the tracking order by linear interpolation (Fig. 3C). We repeated this procedure until all voxels composing the contour of the exterior surface of the stem or large
branch had been ﬁlled (that is, until a continuous contour composed of consecutively ﬁlled voxels had been generated). This procedure was applied to each classiﬁed voxel set within a horizontal
voxel layer and repeated from the lowest to the highest horizontal
layer, thus generating exterior surfaces of the stem and each large
branch composed of consecutive voxels.
2.4.4. Interior ﬁlling and generation of the 3-D voxel-based solid modelWe ﬁlled the interiors of the stem and each large branch byscanning between the voxels of a contour in both the x and y directions (Fig. 3D). For instance, for a scan in the x direction, we pickeda starting voxel near the lower left of the contour and traced a linein the positive x direction from the starting voxel to the voxel on
the opposite side of the contour. The ﬁrst voxel was equivalent
to the minimum and the last voxel to the maximum x-coordinate
value along the scan line, and all empty voxels between the starting and ending voxels were labeled. We repeated this procedure
for each voxel along the contour in both the x and y directions.
Then, we regarded those voxels that had been labeled twice (thatis, by both the x- and y-direction scans) as interior voxels of that
contour and ﬁlled them. We applied this interior ﬁlling procedure
to the stem and all large branches within each horizontal voxel
layer, from the lowest to the highest horizontal layer. In thisway, we ﬁlled both the surfaces and interiors of the entire stem
and all large branches with consecutive voxels. We then produced
a 3-D voxel-based solid model of the whole target tree by merging
the ﬁlled stem and large branches with the voxels previously categorized into small branches (Section 2.4.2).
2.5. Estimation of woody material volume from the 3-D solid model
We calculated the volume of the woody material from the generated 3-D voxel-based solid model. This model was composed ofconsecutive voxels that ﬁlled the outer surfaces and the interiorsof the stem and large branches, and a cloud of voxels equivalentAuthor's personal copy

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(A)

(B)
(a)

(b)

(C)

(c)

(D)
Y
X

Noise

X

Centroid

Fig. 3. Generation of the exterior surface contours of the stem and large branches. (A) Original voxels (dark gray in the print version, red in the online version) within ahorizontal layer obtained by conversion of the lidar data points. (B) A grid was overlaid on a one-voxel-thick horizontal layer, and voxel sets (a), (b), and (c), corresponding to
the contours of the stem and each large branch (hatched or gray colored in the print version, light blue, yellow, and pink colored in the online version), were identiﬁed byconnecting cells using a neighbor-tracing algorithm. (C) Contours of the stem and of large branches were ﬁlled by interpolating voxels (light gray) between the original voxels(dark gray in the print version, red in the online version). Original voxels too far from the centroid of each voxel set were excluded as noise. (D) Interior voxels were identiﬁed
and ﬁlled by scanning in the x and y directions from voxels on the contour.

to small branches that were discretely scattered in mainly theupper part of the target. By using the model, we could easily estimate the woody material volume of any part of the tree by
counting the number of voxels within the part and then multiplying the number of voxels by the unit voxel volume(0.5  0.5  0.5  0.13 cm3). In the present study, we calculated
the volumes of the stem and large and small branches within each
1.00-m-thick horizontal layer to determine the vertical distribution of volume within the target. Then, we summed the volumes
in each layer to obtain the total stem and large-branch volume,the total small-branch volume, and the whole woody material volume. Also, to validate the volume estimation, we extracted the partof the tree chosen for direct measurement (see Section 2.3) fromthe model and determined its volume separately. Then we compared the model estimation with the directly measured volume
to obtain the estimation error.
3. Results
The 3-D voxel-based solid model of the zelkova tree generated
from the 3-D point cloud data obtained by the portable scanninglidar system faithfully reproduced each part of the target becauseof the ﬁne resolution of the lidar image and appropriate settingof the voxel size (Fig. 4B). The small branches were well separated

from the stem and large branches, and a cross-sectional view of thestem shows that both the outer surface of the model and its interior are composed of consecutively ﬁlled voxels (Fig. 4C).
Examination of the estimated volume at each height (Fig. 5)
showed that the volume of the stem and large branches increased
as the height decreased, reaching its maximum in the lowest
height interval (Fig. 5). Conversely, the volume of the small
branches increased with height and reached its maximum value
at 12.00 m. As a result, between heights of 0.00 and 9.00 m, mostof the total volume was accounted for by the stem and large
branches, but above 9.00 m height, most of the volume was insmall branches. In the whole target, the volume of the stem
and large branches was 0.417 m3, and that of the small branches
was 0.135 m3, for a total volume of 0.552 m3 for the wholetarget.
Direct stem and branch measurements (Fig. 6A) and model-estimated stem and branch volume demonstrated strong agreement(Fig. 6B). The mean absolute percentage error, obtained by calculating the absolute percentage error in each height interval andthen averaging them, was 6.8%. The error of the total volume ofthe part, obtained by summing the volumes of each height interval,
was 0.5%. The estimated percentage error corresponding to thesampled part of the small branches, obtained by comparing theestimated volume with the directly measured value, was 34.0%.

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A

B

C

Fig. 4. The 3-D voxel-based solid model of the zelkova tree generated from the 3-D point cloud data obtained by portable scanning lidar. (A) A point cloud image of a group of
zelkova trees before voxelization. Area enclosed by dashed lines is the target tree within the measurement plot (the evergreen understory is colored green in the online
version). (B) The 3-D model of the target tree: small branches are white. The upper-right ﬁgure is a close-up view of small branches in the model. (C) Stem and large branches
only. In the cross-section of a part of the stem, the interior voxels are colored white.

14.00
12.00
Small branches

Height (m)10.00

Stem and large branches
Total

8.00
6.00
4.00
2.00
0.00
0.00

2.00

4.00

6.00

8.00

10.00

Volume (×10-2 m3)
Fig. 5. The estimated volume of the stem and large branches, the estimated volumeof the small branches, and the estimated total volume, derived from the voxelbased solid model by counting voxels in each 1.0-m height interval.

4. Discussion
Our results demonstrated that a 3-D voxel solid tree model
based on portable scanning lidar data can accurately capture thecomplex structure of an individual tree. In this method, we usedlidar data obtained by fully illuminating the target withhigh-pulse-density laser beams emitted from multiple measurement positions surrounding the target to reproduce the complex
shape of the target with consecutive voxels, thus producing an
accurate model. No approximation of tree shape is required by thismethod, such as the approximation of the stem and large branch as
cylinders in some previously proposed volume estimation methods(Côté et al., 2009, 2011; Delagrange and Rochon, 2011; Lefsky and
McHale, 2008). Such approximation causes errors when the shapesof the stem and large branches are complex, whereas the present
method can accurately estimate the volumes of stems and large
branches with complex shapes that are quite different fromcylinders. The accuracy of the model based on the present method
also depends on the voxel size used. In particular, because small
branches are very thin, the estimation of their volume might include an error if the voxel size is not ﬁne enough. In a recent study,
Vonderach et al. (2012) estimated tree volume by counting thenumber of voxels after using portable scanning lidar data tovoxelize the target trees. However, they used larger voxels(1 cm  1 cm  1 cm) so that the voxels would be adjacent. As
Vonderach et al. (2012) noted, the use of large voxels caused thevolume of small branches in particular to be overestimated andalso was less suitable for expressing the complex shapes of thestem and branches. Here, we chose the voxel size so that thevolume of a voxel would be the same as that of the portion of asmall branch hit by a single laser beam. This smaller voxel size prevented the overestimation reported by Vonderach et al. (2012) andallowed the complex shape of the target tree to be faithfully reproduced. Although we directly measured the diameters of small
branches by destructive sampling for voxel size determination,easier measurement methods need to be devised to improve thegeneral applicability of our method to various species.
Previous studies have used voxel representations of a tree canopy for estimating leaf area density proﬁles by the Voxel-based
Canopy Proﬁling method, in which voxels are used to trace laser
beams for calculating the contact frequency of laser beams on
the canopy (Hosoi and Omasa, 2006, 2007, 2009, 2012; Hosoi
et al., 2010; Omasa et al., 2007). In contrast, in this study, we usedvoxels to reproduce the woody material of the target tree as a solid
model for estimating woody material volume, so the present method should be distinguished from the Voxel-based Canopy Proﬁling
method.
In the voxelization process, voxels belonging to the stem andlarge branches needed to be separated from those of the small
branches because additional procedures must be applied to obtainthe volumes of the stem and large branches. We used the difference in spatial distribution between the voxels of the stem andlarge branches and those of the small branches to achieve this separation. Because the stem and large branches are wider than thelaser beam’s pitch, the voxels on their surfaces are arranged
relatively regularly according to the laser beam pitch. As a result,voxels corresponding to the stem and large branches can beextracted by searching for voxels within a certain distance (here,
set to 1 cm, which is approximately equivalent to the laser beam
pitch) from initial voxels picked from the stem and large branches.

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47

F. Hosoi et al. / ISPRS Journal of Photogrammetry and Remote Sensing 82 (2013) 41–48(A)(B) 8.00
Directly measured
7.00

Estimated

6.00

MAPE = 6.8%

7.80 mHeight (m)

5.00

4.00

3.00

2.00

0.30 m

1.00

0.00
0.00

0.50

1.00

1.50

2.00

2.50

Volume (×10-2 m3)
Fig. 6. Comparison of the woody material volume estimated from the voxel solid model and the directly measured volume for each 0.30-m height interval. (A) The part of thetarget tree chosen for direct measurement (gray part in the print version, brown part in the online version). (B) Vertical distributions of the estimated and directly measured
volumes. MAPE, mean absolute percentage error.

In contrast, because the diameter of a small branch is smaller thanthe laser beam’s pitch, voxels on small branches are not regularly
distributed regardless of the laser beam pitch. The nearest-neighbor distances of most of these voxels were larger than those of
the stem and large branches, so most small branch voxels were
not extracted along with the stem and large branch voxels.
To classify the voxels within a horizontal layer into sets so thateach set would correspond to the stem or to a large branch, weutilized the contours of the stem and large branches. Those voxels
included in the same contour were judged as belonging to thesame stem or branch. To support this judgment, we applied aneighbor-tracing algorithm (Ghuneim, 2009) to each horizontal
layer of voxels. This algorithm requires consecutively connected
pixels on a closed curve, but the equivalent voxels on each of thesurface contours of the stem and large branches were not consecutively connected. To satisfy this requirement, therefore, we
overlaid a grid on each horizontal layer. Since the size of the cells
in the grid was larger than the laser beam’s pitch, neighboring cells
were consecutive, allowing application of the neighbor-tracing
algorithm and classiﬁcation of the voxels.
We then used linear interpolation to label all voxels along theexterior surface contours of the stem and each large branch.
Although each contour was a curved line, linear interpolation could
reproduce the contour because of the high laser pulse density of
the lidar measurements. We obtained this high density by adjusting the laser beam pitch and by taking measurements from several
points around the target. As a result, many voxels lay on each contour and distances between neighboring voxels were short. Thus,
lidar measurements must be made with high laser pulse density
for accurate 3-D modeling of a tree. It might be difﬁcult to obtainan adequately high laser pulse density, depending on the conditions at the study site. In that case, the voxels would be sparsely
distributed along each contour and a non-linear interpolation
method, for example, spline interpolation, might be more appropriate than linear interpolation.
The estimation error for the small branches was higher thanthat for the stem and large branches. In the upper part of the target,

where there were a great many, intricately branched small
branches, some small branches were probably not illuminated by
the laser beams because they were obstructed by other small
branches. The obstruction effect is a major problem with the other3-D tree modeling methods based on portable scanning lidar data
(Dassot et al., 2011). For example, underestimation of tree biomassby the tree skeleton extraction method has been attributed to partial occlusion of the inner parts of branches within the crown (Delagrange and Rochon, 2011). In addition, because the small
branches are very thin, the intensity of some of the returned laser
beams might have been too low to be detected by the lidar sensor.
This loss of information about the small branches probably increased the error. A different laser beam diameter setting or theuse of additional measurement positions might improve the accuracy of our method. Multi-return or waveform-recording groundbased lidar systems (Strahler et al., 2008; Yao et al., 2011) mightalso be able to extract more information about the small branches.
In this study, we aimed to establish the basic principles of solid
tree modeling based on lidar-derived data. Therefore, we targeted a
relatively narrow area that included just one tree and used a portable scanning lidar with a relatively short measurable range. The
present method could be applied to a larger area that includes
more trees by using a portable scanning lidar with a longer measurable range and by establishing more measurement positions.
Although the multiple scans needed in the present method may
cause the measurement time to be long, the measurement time
could be shortened by using one of the currently available portablescanning lidars capable of high-speed scanning.
The solid model obtained with our method faithfully retains
spatial information contained in the raw 3-D point cloud data provided by the portable scanning lidar. Thus, it would also be possible to extract other structural parameters besides woody material
volume, such as tree height and stem diameter, from the lidarderived 3-D point cloud data by using previously proposed
methods (Hopkinson et al., 2004; Omasa et al., 2002). This
characteristic is an important advantage of our method overconventional tree modeling methods.

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F. Hosoi et al. / ISPRS Journal of Photogrammetry and Remote Sensing 82 (2013) 41–48

5. Conclusions
In this study, we demonstrated a method to produce a 3-D voxel-based solid model of the tree from portable scanning lidar datathat allows accurate volume estimation. The present method utilizes almost all spatial information contained in the lidar-derived
3-D point cloud data to model the complex shape of the target.
One advantage of this volume estimation method compared withother methods that use allometric equations or approximationsof stem and branch shapes is that no allometric equations areneeded and shapes are not approximated. By using the model,
the woody material volume of not only the whole target tree but
also of any part of the target tree can be directly calculated easily
and accurately by counting the number of corresponding voxels
and multiplying the result by the per-voxel volume. The overall
accuracy of the volume estimation results using the model was satisfactory, as conﬁrmed by comparing the volume estimates withdirectly measured volumes. Future studies should investigate theapplicability of the method to larger regions with different
conditions and species, using portable scanning lidar systems withdifferent performance and considering measurement settings suchas the number of scans and the distance between the target andlidar positions.

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