ISSN 1946-7664. MCFNS 2021
Vol. 13, Issue 1, pp. 1–14
Mathematical and Computational
Forestry & Natural-Resource Sciences

AVAILABLE ONLINE AT HTTP://MCFNS.COM

Submitted: Dec. 3, 2020
Accepted: Jan. 11, 2021
Published: Mar. 30, 2021
Last Correction: Jan. 11, 2021

ESTIMATING INDIVIDUAL TREE HEIGHTS AND DBHS FROMVERTICALLY DISPLACED SPHERICAL IMAGE PAIRS
H. Wang , T.R. Yang , J. Waldy , J A Kershaw, Jr.
University of New Brunswick, The Faculty of Forestry and Environmental Management, Fredericton, NB, Canada

Abstract. Individual tree parameters, such as diameter at breast height (DBH) and tree height, arefundamental measurements in forest inventory, and often labour intensive and require significant financial
expenditures. Applying digital imaging in forest inventory is an efficient way to decrease the workload. In
this study, spherical images taken using a novel commercial 360◦ camera (Ricoh Theta S) and stereographic
geometry were applied to obtain these parameters directly without stitching multiple images from common
cameras. This technology was validated in both a sparse urban forest (pairwise comparison) and denser
real forest (distributional comparison) in Atlantic Canada. The DBH (r2 > 0.76) and height (Dmax< 0.25, K-S test) showed high correspondence with field measures. The spherical camera represents a
low-cost option to terrestrial laser scanning and has potential to produce more accurate forest-level estimates with quicker field and office processing time than current under-canopy remote sensing technologies.
Keywords:
sampling

1

panorama images; digital camera; forest inventory; remote sensing; horizontal point

Introduction

Forests are the dominant terrestrial ecosystems andaccount for over three quarters of gross primary productivity and plant biomass on the Earth (Pan et al.,2013). They provide many ecosystem services including
watershed protection, soil structure maintenance, andglobal carbon storage. Individual tree stem attributes,
such as diameters, heights and spatial locations, are critical measurements in most forest inventories (Kershaw
et al., 2016), and are the fundamental variables used inallometric equations to estimate biomass, volume, andcarbon (Blake et al., 1991; Hayashi et al., 2015; Lambert
et al., 2005; Smith and Brand, 1983; Xing et al., 2005;
Zianis et al., 2005). How to measure these parametersacross extensive forest areas with high efficiency and low
costs is a continuing challenge for all forest inventory
specialists (Gadow et al., 2009; Husch, 1980).
For under canopy tree measurements, traditional tools
such as diameter tapes and clinometers are widely used.
These basic tools have been modified and digitized tomake field data collection more efficient, including optical callipers, rangefinder dendrometers, and optical forks(Clark et al., 2000a). Although several of these instruments have high accuracy and precision, the high costs
and the continued focus on individual trees limit wide-©

spread use. Hence, many instruments have disappeared
from the market (Clark et al., 2000a; Perng et al., 2018;
Shimizu et al., 2014). Laser and sonic instruments formeasuring tree heights have had greater success thandigital instruments for diameter measurement (Clark etal., 2000a). The success of these instruments over similar ones for DBH measurement is probably due to thedifficulty and time-consuming nature of height measurement using traditional tools. More repeatable measurements and reduced field time has contributed to these
instruments being widely adopted in forest inventory operations.
Photogrammetry has a long history of use in forestry.
Reineke (1940) was among the first to develop the ideaof using terrestrial photos in forest inventory. However,use of photos requires establishing scale. Field measured
distances were commonly used in early studies (Clark etal., 2000a,b). Another popular method to establish scale
was the use of reference targets with known lengths orsizes (poles, tags, or laser facula). These methods havebeen widely applied in photogrammetry studies (Celes
et al., 2019; Dean, 2003; Pengle et al., 2013; Shimizu
et al., 2014; Varjo et al., 2006). Multiple photos withknown shifts in position also can be used to establish
scale stereographically (Clark et al., 1998).

Copyright
2021 Publisher of Mathematical and Computational Forestry & Natural-Resource Sciences
Wang et al. (2021) (MCFNS 13(1):1–14). Manuscript Editor: MCFNS Editor

Wang et al. (2021)/Math. Comput. For. Nat.-Res. Sci. Vol. 13, Issue 1, pp. 1–14/http://mcfns.com

Many studies focus only on single tree images and individual tree measurements. However, for inventory efficiency, methods to extract estimates for multiple trees
without the need to shift the camera for each tree of interest are required (Perng et al., 2018; Stewart, 2004).
DeCourt (1956) demonstrated how printed photos andmanual processing could be used to estimate basal area
per ha using angle count sampling methods (Bitterlich,1984). With the advent of affordable digital cameras,
Stewart (2004) revived this idea and took a series of 8
photographs to represent the plot, while Fastie (2010)
used ultra-high resolution panoramas stitched from 504
photos to estimate stand basal area. In both studies,
the angle gauge was expressed in terms of pixel widths
and trees with pixel widths greater than the angle gauge
pixel width were counted as ”in”. Dick et al. (2010) useda single row of 24 horizontal photos to map tree locations
from stitched panoramas.
Lu et al. (2019) recently expanded this idea to measuretree diameters at different heights. However, for parameters other than stand basal area based on angle countsampling, all of these studies required scale tags (Dick etal., 2010; Lu et al., 2019) on each tree or measured field
distances and slopes (Lu et al., 2019). Measuring or tagging individual trees is time consuming and costly, and,other than providing a permanent record of field conditions, the photos have no benefit for improving fieldinventory efficiency. In addition, errors resulting fromthe stitching of several digital image cannot be avoided(Dick et al., 2010; Fastie, 2010; Lu et al., 2019; Perng etal., 2018).
Using wide-angle hemispherical lenses has potential
to eliminate errors caused by stitching images and could
potentially simplify calculations. Paired fisheye cameras
have been used to obtain stem diameter, basal area, location mapping and volume without dependence on fieldmeasurements (Rodrı́guez-Garcı́a et al., 2014; SánchezGonzález et al., 2016; Wang et al., 2020). Berveglieri etal. (2017) developed an automated algorithm by matching hemispherical images at different heights to estimate
stem diameters. More recently, the development of affordable 360◦ spherical cameras offer new opportunities
for obtaining optical tree measurements (Perng et al.,2018). Spherical cameras, like the Ricoh Theta S (Ricoh Imaging Company, LTD., 2016), offer an inexpensive
option for obtaining spherical inventory images directly.
The compact size of a spherical camera makes it an easyto-use tool in the forest and can be moved through the
canopy using a height pole to obtain structural estimates
more easily than traditional fisheye cameras and otherdigital cameras.
Structure from motion (SfM) technology enables
three-dimensional (3D) reconstruction from image series
without actual measurements (Fang and Strimbu, 2017;

2

Sanvely et al., 2008). This technique has been applied to
3D reconstruction of individual stems (Larsen, 2006a,b;Miller et al., 2015; Mokroš et al., 2018; Surový et al.,2016), and to stand level forest point cloud development(Forsman et al., 2016; Liang et al., 2014, 2015; Liu etal., 2018). The mapping accuracy from SfM is similar to
TLS (Liang et al., 2014). However, SfM technologies often require walking through sample plots and obtaining
a large number of photos (Berveglieri et al., 2017; Liu etal., 2018). Mulverhill et al. (2019) integrated SfM witha spherical camera to generate 3D plot point clouds andsignificantly decreased the number of photos required for
accurate point cloud rendering. The results showed highcorrespondence with field measured data (Mulverhill etal., 2019). Although the procedures are mostly automatic, the point cloud generation and analyses requires
a high performance computer and complex algorithms(Belton et al., 2013; Liang et al., 2015; Mulverhill et al.,2019). It also might be questioned as to the need to generate a 3D point cloud and then do measurements, whenthose basic measurements often can be done directly on
the images. Based on this, we identified a need for a simplified system for obtaining spherical photos in stereo.
The goal of this study was to develop an approachto obtain such spherical image pairs and apply stereoscopic geometry to estimate diameter and height of individual trees directly without any field measurement
dependency. The specific objectives were to: 1) derive
the geometry for two vertically displaced spherical image pairs to estimate desired tree attributes; 2) validate
the technique in a sparse urban forest setting; and 3)
perform a preliminary field assessment in a real forest
situation.

2

Methods

2.1

Study sites

Urban Site – The University of New Brunswick campus located in Fredericton, New Brunswick, Canada(Fig. 1) was used for validating the approach in an open
situation where visibility was not a substantial issue.
Two ditial sampling points were selected for this phaseof the study. The criteria for sample point selection
included: 1) Open forest conditions with a moderate
number of trees (7-12 trees) with each tree’s tip and baseclearly visible; 2) Individual trees have varying distancesfrom the image sampling points; and 3) Individual trees
have varying diameters and heights.
Forest Site – An early spacing trial located on thewestern side of Newfoundland (NL) Island, near Roddickton, Newfoundland and Labrador, Canada (Fig. 1)
was used for testing the approach in a real forest condition. The spacing trial, with different densities andWang et al. (2021)/Math. Comput. For. Nat.-Res. Sci. Vol. 13, Issue 1, pp. 1–14/http://mcfns.com

3

(b)

(a)
Forest Site
(Roddickton)(c)
Newfoundland(d)Urban Site
(UNB Campus)

Figure 1: The study sites locations (and associated topography) used in this study. (a) a map of Atlantic Canada
showing the urban and forest site locations, (b) and (c) are photos of the two urban sites, and (d) is a cylindricalprojection of one of the forest sites in Roddickton, NL.
different resulting tree sizes, was an ideal field setting
for this test. The site was dominated by balsam fir(Abies balsamea) with minor components of black spruce(Picea mariana) and other boreal species. The trial wasestablished in the early 1980’s (Donnelly et al., 1986).
Five spacing treatments were applied: Control (no spacing), 1.2m, 1.8m, 2.4m, and 3.0m average spacing. Plot
radii varied by spacing treatment (Control (5.2m);1.2m(7.2m); 1.8m (10.4m); 2.4m (15.0m); 3.0m (18.0m)) withthe aim of having about 100 trees per plot at the time oftreatment establishment (Donnelly et al., 1986). At thetime of the initial treatments, the site was a naturally
regenerating even-aged stand. The spacing treatments
produced plots that were single strata with relatively
uniform stand structures within spacing treatments.
2.2
2.2.1

Data collection
Digital image pairs

A Ricoh Theta S (Ricoh Imaging Company, LTD.,
2016) spherical camera was used to capture sphericalimages. Two single spherical images were captured at
1.6m and 2.6m above ground (camera was mounted ona height pole stabilized by a tripod (Fig. 2.a) for each
digital sampling point in both study sites. A bubble
level attached to the tripod was used to ensure relative
level of two images captured at different heights.

On the Urban Site, two independent single digital
sampling points were located strategically among thetrees of interest (Fig. 2.b) to ensure visibility and a variety of camera to tree distances. On the forest site,
three digital sample points per replicate plot were used
(Fig. 2.b). Multiple digital sample points were used tominimize tree occlusion and facilitate measurement of as
many plot trees as possible. Digital sample points werelocated at half the plot radii at azimuths of 0◦ , 120◦ ,and 240◦ . On the forest site, three digital sample points
per replicate plot were used (Fig. 2.b). Multiple digital
sample points were used to minimize tree occlusion andfacilitate measurement of as many plot trees as possible.
Digital sample points were located at half the plot radii
at azimuths of 0◦ , 120◦ , and 240◦ .
Although the spherical camera recorded 360◦ spherical images, the images were stored like a common digital
camera pixel matrix using cylindrical equidistant projections generated automatically by the Ricoh Theta S
onboard software. The resolution of the projected cylindrical images was 5367 pixels in width and 2688 pixels
in height.
2.2.2

Urban site data

The urban site was used to validate the algorithm andmethod. The sampling points were located where alltrees’ bases and tops were clearly visible. For each se-

Wang et al. (2021)/Math. Comput. For. Nat.-Res. Sci. Vol. 13, Issue 1, pp. 1–14/http://mcfns.com(a)Ricoh Theta S
Spherical Camera

2.2.4

(b)
Urban Site

Digital sample location

Figure 2: Digital data collection methods. (a) tripod,
height pole and spherical camera set up for spherical image acquisition at two different heights (1.6m and 2.6m).
(b) Digital sample location designs for the urban areavalidation study and the real forest application. For theurban site, only one location was set. For the forest site,
three locations were established at the midpoint of plot
radius along azimuths of 0◦ , 120◦ , and 240◦ .

lected tree, flagging tape was wrapped around the tree
circumference at breast height (1.3m) to facilitate visibility and a numbered target placed on each tree to facilitate matching field and image measurements. The radial
distance from sampling points to each tree (FieldR) was
measured with a TruPulse laser hypsometer. Generally,
the cross-sections of tree trunks are not perfect circles
and are often elliptical (Kershaw et al., 2016). The diameter projected onto an image may vary substantiallydepending on projection azimuth and tree eccentricity,
therefore, the DBH of each tree was measured using callipers along the tree axis perpendicular to the projection
azimuth (ProjectedDBH) and measured with a diameter tape (FieldDBH). Tree height (HT) was measured in
the field from 2 different perspectives using a TruPulse
laser hypsometer: 1) the height measured at the image
sampling point (ProjectedHT); and 2) from a convenient
and reasonable location from which to clearly see tree tip
and base (FieldHT).
2.2.3

Image processing geometry

Forest Site

Height Pole

Tripod4

The general workflow included: 1) determining the
projection algorithm to exchange pixel coordinates in
the cylindrical images to latitude and longitude in spherical coordinates; 2) marking the bases and tips of individual trees on the cylindrical images, applying sphericalgeometry to estimate the distances from digital sampling
points, slope deviations and tree heights; and 3) determining the vertical pixel coordinate (y) for breast height(1.3m) in the cylindrical images, marking the left andright tree trunk edges (horizontal angles) at 1.3m, determining the intersection angles to camera center, andestimating DBHs using spherical geometry.
1) Cylindrical images were converted to spherical images using the methods proposed by Aghayari et al.
(2017). For a given point in cylindrical coordinates(xi , yi ), the transformed spherical angles (longitude andlatitude) were given by:
2π
X
(1)
π
Y
lati = (yi − ) ·2
2Y
where X was the cylindrical image width in pixels (5367
pixels for the images used in this study); Y was the cylindrical image height in pixels (2688 pixels for the images
used in this study); xi was the horizontal pixel coordinate; and yi was the vertical pixel coordinate. Latitudeππangles (lati ) ranged from − (−90◦ ) to(90◦ ) while22Longitude angles (loni ) ranged from 0 (0◦ ) to 2π (360◦ ).
2) As shown in Figure 3.a, after marking the tree tip
and base (the bole at ground level) in both cylindrical images manually, 4 latitudinal angles were calculated
from Equation 1. The elevation difference between sampling point and tree base (∆h) was:loni = (X − xi ) ·Z2 · tan(β1 ) − Z1 · tan(β2 )tan(β1 ) − tan(β2 )and radial distance (R) was then obtained using:
∆h =

(2)

Forest site data

As with the urban site data, DBH (nearest 0.1cm) andHT (nearest 0.1m) of each individual tree in one replicate from the Roddickton spacing trial were measured
using a diameter tape and laser hypsometer. However,the spherical images were acquired for a different study
other than individual tree measurement, and field trees
were not individually identified and tagged in the fieldsuch that they could not be easily aligned on the spherical images. Therefore, comparisons between field measurements and spherical measurements were limited toplot level distributions rather than individual tree levelpairs.

Z1 − ∆htan(β1 )Z2 − ∆hR2 =tan(β2 )R1 =(3)

where Z1 = 1.6m and Z2 = 2.6m (the camera heights inthis study). R was estimated as the average of R1 andR2 .
From Figure 3.b, tree HT was derived using:
HT1 = Z1 − ∆h + R · tan(τ1 )HT2 = Z2 − ∆h + R · tan(τ2 )(4)Wang et al. (2021)/Math. Comput. For. Nat.-Res. Sci. Vol. 13, Issue 1, pp. 1–14/http://mcfns.com

ZZ

P2(0, Z2)

P2(0, Z2)

5

T3

τ2
T2 (R, Z2)

β2

H3

P1(0, Z1)

P1(0, Z1)

β1

τ1

H2
T1 (R, Z1)
H1

X

∆ℎ

X
T0 (R, Δh)

R
(a)

(b)

Figure 3: The distance, slope deviation, and tree height calculation from the vertical projection of the sphericalgeometry: (a) derived distance (R) and slope deviation (∆h) caused by terrain variation derived from the key points
for tree bases. (b) height calculation based on several key points for tree tips and along on the bole.
Tree HT, as defined by these relationships is the perpendicular distance from ground to tree tip, as is typically measured in most forest inventories (Kershaw etal., 2016), rather than stem length. HT was estimatedas the average of HT1 and HT2 .
3) For DBH estimation, it was necessary to locate the
1.3m height on each image. The angle from horizontal
to 1.3m was estimated for each image (Fig. 4.a) using:Li =i
R + DBH
2
cos(γi )(7)

In Figure 4.c, DBH also was represented by the spherical geometry based on the basal area factor derivation(Kershaw et al., 2016):
DBHi = 200 · Li · sin(ωi )(8)Solving Equation 7 and Equation 8, DBH was equal to:
1.3m − (Z1 − ∆h)−1γ1 = tanR
1.3m − (Z2 − ∆h)−1γ2 = tanR

As with the other parameters, γ was estimated as theaverage between gamma1 and γ2 . DBH was then estimated from the tree projection angles for each tree on
each image (Fig. 4.b). Tree projection angles (ω) were
estimated by marking the left (Bl ) and right (Br ) treeedges:

xr,1 − xl,1X
xr,2 − xl,2
ω2 = 360◦ ·X

ω1 = 360◦ ·DBHi =(5)Then distance from camera to the tree center, as shownin Figure 4.c, was the slope distance (L) shown in Figure 4.b:(9)

As with R and HT, DBH was estimated as the average
from the two images: DBH=(DBH1 +DBH2 )/2.
To facilitate extraction of the required image measurements, a graphical interface (Fig. 5) was developedin Python 3.6 (Guido, 2018) to mark key points fortrees and for calculating the required parameters as
illustrated in Figs. 3 and 4. The interface can be downloaded from https://github.com/HowcanoeWang/
Spherical2TreeAttributes/releases.
2.3

(6)

200 · R · sin( ω2i )cos(γi ) − sin( ω2i )2.3.1

Data analysis
Urban data analysis

To validate the accuracy of our approach, a pairwise
linear regression was fitted to the field and image measurements for R, DBH, and HT:
F ield = b0 + b1 · P hoto

(10)

Wang et al. (2021)/Math. Comput. For. Nat.-Res. Sci. Vol. 13, Issue 1, pp. 1–14/http://mcfns.com

Z

6

Z
DBH/2
Bl,1

P2(0, Z2)

Bl,1

γ2

Br,1

Li

P1(0, Z1)

Br,1

γ1

X
Td (R, Δh+1.3) P1

L1

ω1
T0

𝑋
R
T0 (R, Δh)

ω1
P1
(c)

(b)

(a)

Figure 4: DBH calculation using spherical geometry. (a) calculation of the 1.3m height on the images. (b) DBH
boundary marking and distance to tree center derived from stereo coordinates (based on the 1.6m height image as
an example); and (c) geometrically derived DBH.

r Pn
rM SE =2i (Imagei − F ieldi )n
rM SE%rM SE = 100 ·F ieldmean
2.3.2
Figure 5: The graphical user interface used to mark key
point coordinates for individual trees for parameter calculation. The images shown in this figure are from urban
plot B with a steep slope. The yellow line indicates theimage horizon (image equator) of spherical image.

If image estimates were identical to field estimates, thenb0 =0 and b1 =1. The resulting parameter estimates
were tested for these values using t-tests and Bonferroniadjusted α levels (Zar, 2009).
The agreement between field and image measurements
were also evaluated by root mean square error (rMSE)
and root mean square error expressed as a percentage ofmean (%rMSE):

(11)
(12)

Forest data analysis

The images from the Roddickton spacing trials wereoriginally taken for area-based estimation, not individual tree measurement, so the trees were not tagged.
Instead of using pairwise statistical tests, we focusedon distributional statistics at the plot level to compare
DBH and HT estimates. The two-sample KolmogorovSmirnov (K-S) test (Hodges, 1958) which tests whether
two samples were drawn from the same continuous distribution, was used here. Our null hypothesis was thatthe field measured samples and image measured samples were identically distributed. The alternative hypothesis was that they were not identically distributed.
We assume that equal distributions convey a level ofconfidence that our technique was measuring DBH andHT correctly. This assumption ignores potential bias intree visiblity in the images and repeat observation of thesame trees across the three ditial sampling points.

Wang et al. (2021)/Math. Comput. For. Nat.-Res. Sci. Vol. 13, Issue 1, pp. 1–14/http://mcfns.com

3

Results

3.1

Urban forest validation

Figure 6.a shows the relationships between field measured distance (FieldR) and image estimated distance(ImageR). While the ImageR was slightly overestimatedcompared with FieldR, the simple linear regression(Tab. 1) showed no significant differences (p > 0.05)
from the hypothesized parameter estimates and had ahigh r2 and low root mean square error (rMSE). ImageHT was not significantly different (p > 0.05) from
ProjectedHT (Fig. 6.b), which is the field measured
height at the digital sample points; however, ImageHT
was significantly different (p < 0.05) from FieldHT,
which is the field measured height from a point wheretree tips can be clearly observed. As FieldHT increased,
there was a trend of increasing overestimation associated with ImageHT (Fig. 6.c). The significance of thesetrends was confirmed by the linear regressions (Tab. 1.).
For DBH estimation (Fig. 6.d-e), the b0 s and b1 s were
not significantly different from 0 and 1, respectively,(p > 0.05) for both ProjectedDBH (measured by calipers
along the tree axis perpendicular to the projection azimuth) and FieldDBH (measured by diameter tape).
The high r2 s (0.96) and low rMSEs (around 2.4) confirmed strong linear relationships between image measured DBHs and field measured DBHs. The percentage
root mean square errors (%rMSE) without unit concern
in Table 1 demonstrated that the both DBH (FieldDBH and ProjectedDBH) was estimated more consistently than the FieldHT, but similar to ProjectedHT.
3.2

Field forest test

The distributional comparisons between field measured attributes and image estimated attributes for the7

Roddickton, NL spacing trial are shown in Figure 6 andthe K-S test results are given in Table 2. With the exception of the 1.2m spacing treatment, the number ofmeasurable trees on the images were lower than the number of trees measured on the actual field plots (Tab. 2),
despite having 3 digital sample points per plot.
The results obtained in the forest situation were different from what were observed in the urban setting. With
the exception of the Control spacing treatment (S00),
all image HT distributions were not significantly different (p > 0.05) from field distributions (Fig. 7.f-j andTab. 2). On the other hand, only the 3.0m spacing (S30)
produced DBH distributions that were not significantly
different from field distributions (Fig. 7.e and Tab. 2).
These results are the opposite of what was observed in
the Urban situation where DBH was estimated consistently more accurately than HT (Fig. 6.d-e and Tab. 1).

4Discussion

The goal of this study was to examine the potentialof using spherical images to estimate individual tree diameter and height. This method was applied in an open
urban setting and in a real forest situation. Our results observed a good correspondence with field measured data in the urban area, while the real forest results
were mixed.
Our urban site validation showed that correspondence
between image measured and field measured DBHs washigh for both ProjectedDBH (measured by caliper at
image view angle) and for FieldDBH (measured withdiameter tape) (Fig. 6.). However, for the real forest
test, the results were not as positive. Distributions ofimage derived DBHs were consistently larger than distributions of field measured DBHs (Fig. 7.). For height
estimation, the urban forest study showed a high corre-

Table 1: Simple linear regression results between photo estimates and field measurements. The linear model is
Y = b0 + b1 ∗ X, if Photo measured (X) is the same as Field measured (Y), then b0 = 0 and b1 = 1. In table header,
YRange is the range of Y values = (min, max); Param. = Parameter; Est. = Estimate; SE = Standard Error; rMSE
= root Mean Square Error; %rMSE = root mean square error expressed as a percentage of mean.
X
ImageRY
FieldRYRange( 2.7, 27.7)

ImageHT

ProjectedHT( 9.4, 25.6)

ImageHT

FieldHT( 9.4, 23.1)

ImageDBH

ProjectedDBH(12.3, 69.6)

ImageDBH

FieldDBH(12.8, 69.6)

Param.
b0
b1
b0
b1
b0
b1
b0
b1
b0
b1

Est.
-0.180
1.058
0.653
0.990
3.954
0.692
-1.246
1.039
0.116
0.999

SE
0.542
0.039
0.743
0.052
1.245
0.087
1.546
0.044
1.578
0.044

p-value
0.743
0.153
0.390
0.851
0.005
0.002
0.430
0.378
0.942
0.963

r2
0.974

rMSE
0.153

%rMSE
7.111

0.949

0.971

6.794

0.762

1.627

12.074

0.966

2.398

7.167

0.962

2.448

7.321

Wang et al. (2021)/Math. Comput. For. Nat.-Res. Sci. Vol. 13, Issue 1, pp. 1–14/http://mcfns.com

8

Table 2: Summary of KS-Tests for real forest validation. Plot radii varied by spacing treatment (Control (S00,
5.2m);1.2m (S12, 7.2m); 1.8m (S18, 10.4m); 2.4m (S24, 15.0m); 3.0m (S30, 18.0m)).
Plot
S00

Field Tree #94

Image Tree #
63

S12

56

92

S18

103

60

S24

137

96

S30

122

59

spondence with ProjectedHTs measured from the digital sampling point; however, correspondence was not ashigh with heights measured from locations where treetips were clearly visible (FieldHT). However, surprisingly, in the forest situation, image measured heights(ImageHT) were distributed similarly (based on K-S test
Dmax values) to field measured heights (FieldHT) for all
spacings except S00 (the control plots).
There are several possible explanations for the reversed results observed between the two study areas.
First, the urban trees were substantially larger (bigger
DBHs and taller heights) than the forest trees. The urban tree HTs ranged from 10m to 25m (Fig. 6.b), and theurban DBHs ranged from 15cm to 70cm (Fig. 6.d), while,the forest trees had a DBH range from 5cm to 25cm withlarge variation within and between the different spacing
treatments (Fig. 7.a-e). Only the 3.0m spacing treatment had low variability within treatment, and this was
the treatment that had DBH distributions that were notsignificantly different (p > 0.05) from the field DBH distributions. In contrast to the generally higher variability
in DBHs, the forest trees had much lower HT variability
within and between the spacing treatments with mostfield and image-estimated HTs below 15m (Fig. 7.f-j).
Tree density probably played an important role for thediffering results observed between the urban and forest
study sites. In the urban setting, the trees were wellspaced and the boles clearly distinguishable against abackground of grass (visibility was further enhanced by
the use of flagging tape). In the forested situation, especially for plots with narrower spacings, the tree trunks
often overlapped in the background making it very difficult to clearly distinguish the tree edges. The smaller
trees were most likely easier to be missed when marking trees for measurement and single pixel width errors
had greater impacts. If the trunk edges were not clearly
distinguishable, those trees were not marked on the im-

Factor
DBH
HT
DBH
HT
DBH
HT
DBH
HT
DBH
HT

KS Value
0.42620.25180.36020.2096
0.25890.11260.26000.13930.15550.1188p-value<0.0010.0134<0.0010.079
0.00970.6697<0.001
0.19820.25730.5774ages. Given that we had three digital sampling points
per forest plot, larger trees were probably more visible
across multiple images as well, further contributing to
the bias toward larger trees. For example, consider S00
and S12 field distributions which showed an abundanceof very small trees (Fig. 7.a-b) - these two plots had
the worst performance for DBH estimation and had thelargest distributional differences in the upper DBH range(Fig. 7.a-b). Because we did not attempt to eliminate
repeated measures of trees across the three digital sampling points, this probably contributed significantly tothe overestimation problem observed in this study. Furthermore, the problem with hidden trees, which exists
in all panoramic images (Dick et al., 2010) and affects
smaller trees more frequently, was an additional sourceof bias in this study.
The uniformity in the field height distributions(Fig. 7.) negated any visibility bias for the image height
distributions. In addition, the shorter conifer trees in
the forested situation, with their cone-shaped crowns,
made it easier to identify the real tree tip. As Kershaw
et al. (2016, p. 117) pointed out, there is a tendency tooverestimate the height of large, flat-crowned trees using
the tangent method.
The irregularity in tree cross-sectional shape did notappear to be a problem in this study, at least in the
Urban setting (Fig. 6.). Stem irregularities can cause
errors in image derived DBH estimates (Perng et al.,2018). Several studies have addressed this issue by either taking photos at different angles around the stem,or constructing 3D models (Larsen, 2006a) or even generating 3D point clouds to assess stem geometric structure (Liang et al., 2014; Mokroš et al., 2018; Ringdahl
et al., 2013; Surový et al., 2016). Though these methods produce small errors (2.2 ± 3.0cm; Ringdahl et al.
(2013)) and low rMSEs (2.39cm for Liang et al. (2014),
1.87cm for Surový et al. (2016), and 1.27cm for MokrošWang et al. (2021)/Math. Comput. For. Nat.-Res. Sci. Vol. 13, Issue 1, pp. 1–14/http://mcfns.com

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Figure 6: Comparisons between field measurements
and image estimates: (a) radial distance (R); (b) digital image height (ImageHT) compared to field heightmeasured HT at the digital sampling points (ProjectedHT); (c) digital image height (ImageHT) comparedto field height measured from locations where tree tips
are clearly visible (FieldHT); (d) digital image DBH(ImageDBH) compared to projected DBH measured bycalipers (ProjectedDBH); and (e) digital image DBH(ImageDBH) compared to DBH measured by diametertape (FieldDBH).
et al. (2018)), the computation requirements limit theirwide-scale application in forest inventories. Our results
show, if accounting for optical fork effects (Grosenbaugh,1963), the errors can be decreased to acceptable levels.
In our case, errors were 2.4 ± 1.6cm. Similarly, Celes
et al. (2019) reported an uncertainty of approximately±1cm and Lu et al. (2019) had errors within ± 6cm withthe assistance of field reference targets, while Perng et al.
(2018), using similar geometry had a rMSE of 13.19cm.
Decreasing spatial grain with distance is a problem
associated with all remote sensing techniques (including
LiDAR). Remote sensing is driven by reflection point

Figure 7: Field measured distributions versus image estimated distributions for DBH and HT by spacing treatment: (a) and (f) Control; (b) and (g) 1.2m Spacing; (c)and (h) 1.8m Spacing; (d) and (i) 2.4m spacing; and (e)and (j) 3.0m Spacing.

values that are averaged over the photon footprint. One
point (or pixel) represents an increasing area with increasing distance from digital sampling point. The effects of distance from digital cameras (Dick, 2012; Wang,2017) and spherical cameras (Wang, 2019; Wang et al.,2020) has been well analyzed. Decreasing accuracy withincreasing distance is a limitation of any light-based sensor (Clark et al., 2000a). This issue is exacerbated if theobjects of interest are smaller (Reu et al., 2014).
The primary advantage of a spherical camera over acommon camera is that we obtain the whole 360◦ plot ina single image from a single shutter trigger. The image
is derived from two fixed fisheye lenses and stitched using the camera’s onboard software. Obtaining the wholeplot in one image saves a lot of time acquiring images,
stitching them together and analyzing images. In order to take a 360◦ plot using images from a common
camera, a heavier tripod with a stabilized rotary table
is required to be transported in the forest. At least 15
images are needed to ensure enough overlap between images (Dick, 2012) which requires more field time and office time stitching the photos together.If heights are re-Wang et al. (2021)/Math. Comput. For. Nat.-Res. Sci. Vol. 13, Issue 1, pp. 1–14/http://mcfns.com

quired then multiple rows of images must be acquired bytilting the camera at increasing angles, increasing fieldtime, stitching time and analysis time; however, very
high resolution images are produced (Fastie, 2010). The
trade-offs between field time and increased image resolution versus accuracy of resulting image measurements
needs more evaluation. Based on a preliminary study using a common digital camera to measure DBH (Wang,2017), the higher resolution images showed improved accuracy (42% of trees within ± 0.5cm and 25% within ±0.5cm to 1.0cm), while the accuracy for this study was
2.4cm (based on rMSE, Table 1),
The advantages of a spherical camera over a laser
scanner include both the instrument costs and data acquisition time. For spherical images, field time is around
5-10 minutes per plot, and around 4-5 minutes for processing each image pair (about 1-2 mins to align thepaired images, and about 3 mins to click the key points
for all trees and processing the measurements. Adapting
an hierarchical subsampling scheme could significantly
reduce processing time without substantially reducing
accuracy (Dai, In review). TLS technology continues
to improve and both fixed-base and mobile scanners
are available, Using a FARO (FARO Technologies, Inc.
Florida, U.S.) X330 Scanner, three in-plot scans required
about 45 minutes, and 2-3 hours for software stitching
the three scans together. Point cloud processing cantake up to 5 hours depending upon which tree measures
are required and what algorithms used without any real
gains in accuracy over what we obtained here (Gollob
et al., 2019). As a benchmark comparison, field measurement of plot trees can range from about 20 minutes
to 2-3 hours depending on plot size, plot type, and thedifferent tree measurements required.
The manual clicking of key points, as implemented
in this study, introduces the possibility of inter-observer
errors and biases. Based on our previous application of
spherical images implementing angle count sampling on
spherical images (Wang, 2019; Wang et al., 2020), interobserved differences were affected by the complexity ofspherical images. For images obtained in sparse forests
with bigger trees and clear trunk boundaries, the consistency was higher than dense forest images. This is likely
to be an issue with the clicking for DBH and HT measurements developed here. Automatic detection algorithms may help decrease the subjectivity, but, as figure
1.d shows, this is a complicated common computer vision task requiring thousands of annotated training images for deep learning based algorithms to be effective,
and is far beyond the scope of this study.
One of the biggest limitations for applying sphericalimages to whole plot measurement is tree visibility, notonly for small trees far away from plot center with very
narrow view angles, but also for trees occluded by larger

10trees near plot center. Non-detection bias is a significant
concern with any remote sensing technology, Multiple
scans from different locations within plots can reduce
occlusion (Ritter et al., 2013). Instead of basing areabased estimates on fixed area sampling methods, angle
count sampling (Wang et al., 2020) is a powerful sampling technique that could eliminate or minimize nondetection biases. By controlling the basal area factor,
the visibility issue can be controlled (Dick, 2012; Wanget al., 2020). Multiple digital sampling points, as implemented in this study, can reduce the number of hidden
trees, though this introduces the unavoidable duplicate
marking of some trees with potential bias toward larger
trees (Figure 7).
The projection distortion produced by the cylindrical projection of the spherical images is another factor
limiting the current method. Trees very close to camera
location become very distorted making the tree tips very
difficult to determine. This issue limits the applicability of subsampling schemes like big-BAF sampling (Iles,
2012) because this method inherently selects trees thatare closer to the digital sampling point. Finally, we only
tested and validated our approach in a conifer dominantforest with tree heights around 15m. It may difficult toapply in forests with taller trees or composed of dense
broad leaved species. Conditions which are likely to result in increased distortion issues.
One of the key next steps is to replicate the measurement protocols used in the urban setting in aforested situation where field and image measurements
are matched. This will help eliminate some of the uncertainty we obtained in our forested test. Time-motion
studies comparing field measurement times with image
measurement times would also provide additional insight
into gains in measurement efficiency and accuracy associated with this technique.

5

Conclusion

Though using camera photos in forest inventory has along history and earlier studies have tried diverse methods to estimate typical forest attributes, the use of vertical paired spherical cameras (Ricoh Theta S) and stereoscopic geometry to calculate attributes directly has notbeen explored. Our results show this novel technology can achieve good correspondence with field measured tree metrics in simple urban conditions (sparseand big trees). For complex and dense forest conditions,it achieved moderate correspondence, as measured by
the K-S two-sample distribution test for DBH and HT
estimation. The spherical camera represents a low costalternative to terrestrial laser scanning for the estimation of DBHs, heights, and possibly stem form. Field
work is greatly reduced and data processing is much sim-

Wang et al. (2021)/Math. Comput. For. Nat.-Res. Sci. Vol. 13, Issue 1, pp. 1–14/http://mcfns.com

pler. Integration into a hierarchical subsampling design
is likely to be the most efficient use of the methods developed in this study

Acknowledgements
The authors declared no Conflict of interest. And
this work was partly supported by the National Science and Engineering Research Council of Canada, Discovery Grants program, the Province of Newfoundlandand Labrador Centre for Forest Science and Innovation Contribution Agreement, and the New Brunswick
Innovation Foundation Research Assistant’s Initiativeand Graduate Scholarships programs. The authors also
thank Yang Zhan, Rongrong Gu, Zizhen Gao and Luji
Xiong for their volunteer work to collect field data in the
Urban Site.

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