ISSN 1946-7664. MCFNS 2020
Vol. 12, Issue 0, pp. 0–14
Mathematical and Computational
Forestry & Natural-Resource Sciences

AVAILABLE ONLINE AT HTTP://OPR.MCFNS.COM

Submitted: Oct. 3, 2019
Accepted: Dec. 6, 2019
Published: Preprint, 2020
Last Correction: Feb. 4, 2020

AN INTEGRATED SYSTEM FOR ESTIMATING FOREST BASAL
AREA FROM SPHERICAL IMAGES
H. Wang , J.A. Kershaw , T. Yang , Y. Hsu , X. Ma , Y. Chen
University of New Brunswick, The Faculty of Forestry and Environmental Management, Fredericton, NB, Canada

Abstract. Basal area is one of the most important parameters in forest inventory, but data collection
by traditional methods is often time consuming and labor intensive. This study uses a new, portable,
and relatively inexpensive 360° spherical camera to estimate stand basal area and make permanent
digital forest records. Forty-five plots in Newfoundland and eighty-three plots in New Brunswick wereused to compare traditional field inventory with spherical photo inventory and to analyze potential
factors impacting results. Results showed that (1) photo-estimated basal area is similar to traditional
methods measured by diameter tape and fixed-area plots or by angle gauge counting; (2) better accuracy
and precision can be achieved when adding multiple digital sample locations to avoid effects of hidden
trees caused by nearby trunks; (3) understory tree and shrub density did not significantly influencestem visibility; and (4) differences among different users were tested and shown to not be significant. An
open-source software package was developed to make the implementation of our technique easy and efficient.
Keywords:
sampling

1

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

Introduction

Forests are the dominant terrestrial ecosystem on
Earth and account for three quarters of the gross primary productivity of the biosphere and about 80% of
plant biomass (Pan et al., 2013). In addition to ecosystem services like watershed protection and carbon storage (Chazdon, 2008), the other economic and social
products provided by forests are of great interest to landowners and forest managers (Christensen et al., 1996;
Gillis, 1990). To satisfy the multiple of demands fromforests, advanced tools used to collect data efficiently
are required for making good forest management decisions (Baskerville, 1986; Bettinger et al., 2017; Clutter
et al., 1983). Therefore, coupling advanced technology
with traditional forest inventories to save costs and time,
and to improve accuracy of estimates, are of great importance (Husch, 1980; Iles, 2003; Kershaw et al., 2016).
Forest inventories typically collect measurements on
individual trees (e.g., species, diameter at breast height,
and total height) and use these measures to estimate
stand-level parameters such as density, volume, andbiomass (Kershaw et al., 2016). Stand basal area, defined as the sum of individual tree cross-sectional areas,is one of the most common stand-level parameters es-©

timated in most forest inventories (Iles, 2003; Kershaw
et al., 2016). Basal area is often expressed at breast
height (1.3 m in SI and 4.5 ft in the Imperial system).
Basal area is an important measure of stand densitythat incorporates tree size as well as number (Kershaw
et al., 2016). It is a fundamental component of volume and biomass calculations (Iles, 2003; Jenkins et al.,
2003; Kershaw et al., 2016; Lambert et al., 2005; Slik etal., 2010) and is an important stand characteristic forforest growth models (Lootens et al., 2007; Opie, 1968;
Weiskittel et al., 2011).
When using fixed-area sampling units, basal area iscalculated from individual tree diameter measurements(Kershaw et al., 2016), which can be a time consuming endeavor depending upon tree density and sampling
unit size. Angle count sampling (Bitterlich, 1947, 1984;
Iles, 2003), or horizontal point sampling as it is commonly known (Bitterlich, 1984; Grosenbaugh, 1952; Iles,
2003; Kershaw et al., 2016), is an alternative methodthat measures basal area by counting trees that subtend (i.e., appear as large or larger than) a projected
angle and multiplying by the basal area expansion factor(BAF). The ability to estimate basal area by counting
trees makes angle count sampling a very efficient sam-

Copyright
2020 Publisher of Mathematical and Computational Forestry & Natural-Resource Sciences
Wang et al. (2020) (MCFNS 12(0):0–14). Manuscript Editor: MCFNS Editor

Wang et al. (2020)/Math. Comput. For. Nat.-Res. Sci. Vol. 12, Issue 0, pp. 0–14/http://opr.mcfns.com

pling approach (Bitterlich, 1984; Iles, 2003; Kershaw etal., 2016; Marshall et al., 2004; Yang et al., 2017).
DeCourt (1956) was the first to recognize that it waspossible to conduct angle count sampling using photographs. Grosenbaugh (1963) hinted at this application but did not develop the technique very deeply. Because of the time and costs associated with film-based
imagery, photo-based angle count sampling was not developed any further until the work by Stewart et al.
(2004) who proposed photo-based angle count sampling
using 8 directional photos and developed methods tocorrect for image distortion near the photo edges. Dick(2012), using panoramic stitching software, merged 24
images into a single panorama image and eliminatedthe need for distortion correction. By defining an angle gauge in terms of pixels, Dick (2012) developed asimple photographic angle count method implemented
in ArcGIS (ESRI, Redlands, CA). Independently, Fastie(2010) merged 504 images into an ultra-high resolution
panorama to estimate basal area. Given that angle countsampling was already an extremely efficient inventory
system in the field, these approaches for photo-based
sampling were more curiosities than operational developments.
The main advantage of the photo-based method wasthat basal area estimates could potentially be extracted
from archive photos (Stewart et al., 2004). However,photo-based approaches also suffered from potential
under-estimation bias due to occluded (hidden) trees(Dick, 2010; Zasada et al., 2013). In addition to the hidden trees, other potential impacts such as understory
vegetation, counting dead trees, image resolution, anduser errors were not systematically explored in these previous studies.
Digital technology continues to advance rapidly andstitching packages are now available on many smart
phones.
In addition, the recent development ofconsumer-grade spherical cameras opens the opportunity to obtain panoramic photos from single exposurescontrolled by a smart phone. The ability to rapidly obtain panoramic photos and develop onboard processing
creates an opportunity to revisit the photo-based angle count sampling idea. The goal of this study was
to develop an open-source software package that implements angle count sampling using spherical photos takenfrom a Ricoh Theta S, which is a relatively inexpensive
consumer-grade camera. The specific objectives were:(1) to derive the geometry of applying the angle-countsampling idea to spherical images to obtain basal area
estimates; (2) to assess the precision and accuracy of thisapproach compared to traditional field measured data;(3) to assess the inter-observer variability in implementing this approach; and (4) to assess the effects of understory tree density on the photo-based estimates.

2

Methods and Materials

2.1

Study Sites

1

Data for this study come from two different studies.
The first study was three early spacing trials located inwestern Newfoundland (NL). The NL sites were locatedin the Boreal Forest region (Rowe, 1972) and were dominated by balsam fir (Abies balsamea) with some black
spruce (Picea mariana) and other boreal species. The
trials were established in the early 1980’s. At each site,
there were three replicates of five thinning spacing treatments: Control (no spacing), 1.2 m, 1.8 m, 2.4 m, and
3.0 m average spacing.
The second study was located on the Noonan Research
Forest (NRF) in central New Brunswick, Canada, managed by the University of New Brunswick. The NRF
was located in the Acadian Forest region (Rowe, 1972),
and was composed of a variety of stand types from
relatively pure coniferous stands to mixed hardwoodsoftwood stands. A permanent 100 m by 100 m inventory sample grid was overlaid on the NRF in 1999. The
83 grid intersections within the Femelschlag Research
Study were used in this study.
2.2

Data Collection

2.2.1

Field Data

Only the most recent measurements of the 45 NL plots(3 trials Ö 5 treatments/trial Ö 3 replicates/treatment)
were used in this study (Tab. 1). Plot sizes varied bytreatment with the goal to have approximately 100 trees
per plot at the initial measurement. The plot radii were:Control (no spacing) = 5.2 m; 1.2 m spacing = 7.2 m;
1.8 m spacing = 10.4 m; 2.4 m spacing = 15.0 m; and3.0 m spacing = 18.0 m). On each plot, all trees taller
than 1.3 m were measured for diameter at breast height(DBH, 1.3 m above ground, nearest 0.1 cm) and totalheight (nearest 0.1 m). Field basal area (FBA, m2 /ha)
was calculated using:
2 !

n
X
DBHi
(1)
FBA = ExpF ×
π
200
i=1
where ExpF is the plot expansion factor(ExpF=10000/(πR2 ); R is plot radius in meters).
On the NRF sample points, a 2M BAF (basal areafactor; i.e., each tree tallied represented 2 m2 /ha basal
area) angle count sample was conducted centered at the
83 grid intersections in summer 2018. All trees that
subtended the projected angle were counted and FBA(m2 /ha) was calculated by multiplying the number ofcount trees by the BAF (2 in this case). In addition,
those trees with DBHs smaller than 6 cm were tallied asunderstory trees by height status (less than or greater

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2

Table 1: Average stand-level estimates (standard errors in parentheses) by trial and treatment for the 3 early spacing
trials located within western Newfoundland.
Trial

Year

Treatment

Cormack

2013

Pasadena

2013

Roddickton

2017

no spacing
1.2m spacing
1.8m spacing
2.4m spacing
3.0m spacing
no spacing
1.2m spacing
1.8m spacing
2.4m spacing
3.0m spacing
no spacing
1.2m spacing
1.8m spacing
2.4m spacing
3.0m spacing

Stand-Level Averages (Standard Errors)
Trees
Basal Area
DBH
Total Height(num/ha)(m2 /ha)(cm)(m)
9974 (1807) 62.39(6.26)
8.97 (0.42)
9.21 (0.92)6239(740) 49.94(9.49) 10.14 (1.60)
8.86 (1.63)
2978(433) 34.41 (10.88) 12.07 (1.64)
8.73 (1.61)
1432(168) 32.38(3.81) 16.98 (0.59) 10.62 (0.54)965(62) 21.54(0.92) 16.86 (0.18)
9.62 (0.23)
6112 (2049) 61.04(9.36) 11.52 (1.27)
9.83 (0.82)3616(863) 67.22(5.07) 15.59 (1.95) 11.37 (1.38)
2611(309) 53.59(7.29) 16.16 (0.16) 10.81 (0.43)
1793(545) 46.18 (10.12) 18.26 (0.86) 11.35 (0.29)1111(61) 36.88(3.04) 20.55 (0.58) 11.60 (0.33)
12775 (2101) 73.19(8.06)
8.59 (0.88)
7.07 (0.62)4987 (1066) 54.62(4.61) 11.94 (1.47)
8.28 (1.28)
2927(247) 40.58(2.86) 13.30 (0.50)
7.94 (0.25)2119(253) 40.40(9.13) 15.50 (0.85)
8.74 (0.67)1253(87) 31.25(2.21) 17.83 (0.41)
9.12 (0.35)

than 1.3 m tall) on a 4 m radius plot centered on thegrid intersections. Species and status (live or dead) also
were recorded for all understory trees.
2.2.2

NL

Image Processing Software

Angle count sampling (Bitterlich, 1947, 1984) is asampling method that uses a horizontally projected angle to select trees for inclusion in the sample (Fig. 2.a).
A basal area expansion factor (BAF) is derived from the

Ricoh Theta S
Spherical Camera

NRF
Extension Rod

Digital Sample Points

For each NL sample plot, three digital sample locations were established at half the plot radius along azimuths of 120°, 240°, and 360° relative to plot center(Fig. 1.a). On the NRF sample points, only one digital
sample location was established at the grid intersection(Fig. 1.a).
A Ricoh Theta S (Ricoh, 2016) spherical camera wasused to capture spherical images. A single spherical image was captured at 1.6m above the ground at each
digital sampling point (Fig. 1.b) and downloaded to asmart phone. Though the spherical camera records a
360° spherical image, the spherical image is projected
into a 2D digital image using cylindrical projection. In
this projection system, the vertical coordinate in the 2D
image and related vertical angle (latitude) in sphericalcoordinates are always consistent no matter how far an
object is from horizontal center. The image resolution
was 5376 pixels in width and 2688 pixels in height.
2.3

(b)

(a)

1.6m
TripodDigital sample location

Figure 1: Digital data collection methods: (a) Digital
sample location design for Newfoundland (NL) and Noonan Research Forest (NRF) (Three locations were established at the midpoint of plot radius along azimuths of
120°, 240°, and 360° in each NL plot, while only one location was set in the center for each NRF plot); (b) tripodand camera set up for spherical image acquisition.
sampling geometry associated with a tree that is at its
limiting distance (Fig. 2.b). Angle count sampling is
a form of sampling with variable probability and is anapplication of selecting sample trees based on probability proportional to size (Grosenbaugh, 1958; Kershaw etal., 2016). Basal area per ha is obtained by counting
selected trees and multiplying by the BAF (Bitterlich,
1947; Kershaw et al., 2016). The key point in applying
this sampling method on a spherical image was determining which trees in an image should be counted ornot. In this study, two different methods for photo angle count sampling were developed and compared.

Wang et al. (2020)/Math. Comput. For. Nat.-Res. Sci. Vol. 12, Issue 0, pp. 0–14/http://opr.mcfns.com

(a)
θ

in

borderinborder

out

BAF

BAF

BAF

1

out

Count

Count

BAF

2

3

𝐷
2

R

(a) Edge Marking

Figure 2: Sample geometry. For angle count sampling:(a) overhead view showing “in”, “border” and “out” tree
(gray circles represent tree trunks); (b) the relationshipbetween horizontal angle (θ), tree diameter (D) and plot(inclusion zone) radius (R). The BAF determines the
fixed horizontal angle θ which was used as the thresholdto determine tree status on the spherical images.

(b) Target Count

Figure 3: Two image processing methods: (a) Edge
marking method: users click on the edges of each tree.
A reference bar (the length is based on BAF=1) is used
to guide users so that every tree does not have to bemarked; the line color indicates tree status based ondesired BAF: black = “in”, gray = “out”); (b) Target
count method: a transparent reference octagon, scaled
to the desired BAF, is provided to mark “in” trees, “out”
trees are those trees smaller than the octagon target andare not marked.

Edge Marking Method

In this method, the horizontal angle of each individual tree trunk at breast height (1.3 m) in the image wasdetermined (Fig. 2.b). This was accomplished by having the user mark the edges of each tree on the image(Fig. 3.a).
The width of each tree trunk was used to calculate
the maximum BAF threshold (maxBAF) at “border”
condition using the following equation:
maxBAF =
100 · sinTW
· 360◦PW

2(2)

where TW was the pixel width of the marked tree; andPW was the total width of the spherical image (PW =5376 in this study).
By calculating maxBAF, the number of count trees
was simply the number of marked trees where maxBAF> desired BAF, and photo basal area (PBA, m2 /ha)
was:
PBA = BAF · count(maxBAF > BAF)
2.3.2

border(Not Count)𝐷/2𝜃= sin( )
𝑅
2

2.3.1

in

out

(b)

θ

3

(3)

Target Count Method

This method was similar to the field angle gauge process. The camera projected a horizontal angle basedon the given BAF onto each tree (Fig. 3.b). To better
visualize the cross-sectional angles of leaning trees, anoctagon shaped target was used as the target threshold.
A tree equal to or greater than the octagon target insize was marked as an “in” tree, otherwise that tree wasconsidered an “out” tree and not counted. The PBA ofthis image was equal to the given BAF multiplied by thecount of “in” trees.

2.3.3

Software ImplementationAn
opensourcesoftwarepackage,
Panorama2BasalArea, was developed in Python
3.6 (Guido, 2018) to implement the angle count sampling workflows described above. It included the plot
photo management, tree trunk edge marking and octagon threshold counting, individual tree management,
and PBA data export (Fig. 3). When using the edge
marking method, a reference scale bar was provided.
Trees which were narrower than the reference scalebar (BAF=1) were ignored in order to reduce theworkload associated with edge marking (Fig. 3.a).
For the target marking method, a reference octagon
scaled to a given BAF was provided. Only those
trees equal to or larger than the reference octagon
were marked (Fig. 3.b). The source code for thissoftware package can be downloaded from: https://github.com/HowcanoeWang/Panorama2BasalArea.
It was also packaged as an executable app for Windows platforms: https://github.com/HowcanoeWang/
Panorama2BasalArea/releases.

Wang et al. (2020)/Math. Comput. For. Nat.-Res. Sci. Vol. 12, Issue 0, pp. 0–14/http://opr.mcfns.com

2.4
2.4.1

Data Analysis
Influence of Number of Digital Sample
Points

Hidden trees blocked by closer trees or understory vegetation create a potential for underestimating PBA. One
possible way to deal with the hidden tree problem wasto use multiple sample points in one plot. While hidden trees result in underestimation, errors in marking
tree edges and judging octagon thresholds could resultin over- or under-estimation relative to field basal area
(FBA). To test the influence of multiple digital sample points and the effects of two tree marking methods
on PBA estimates, three separate analyses were undertaken: (1) PBA estimated from one central digital sample point on the 83 NRF sample points; (2) PBA estimated on the NL plots using three individual (off-center)
digital sample points; and (3) PBA estimated from theaverage of the three digital sample points on each NL
plot. For each analysis, a simple linear regression was
fitted to the FBA – PBA data:
FBA = b0 + b1 · PBA(4)

If PBA was the same as FBA, then b0 = 0 and b1 = 1.
The resulting parameter estimates were tested for thesevalues using t-tests and Bonferroni-adjusted alpha levels(Zar, 2009).
2.4.2

Influence of Choice of BAF

As BAF increases, the distance a tree of a certain diameter can be from plot center decreases (Fig. 2). The
expected number of counted trees also decreases. Bothfactors should result in a lower probability of hidden
trees (i.e., fewer hidden trees). On the other hand, as
photo BAF increases so does variation between sample
points. The trade-off becomes one of under-estimation
versus increased sampling error. The optimal compromise is to use a BAF that reduces the number of hidden
trees without appreciably increasing sample variation.
To test this idea, BAFs ranging from 2 to 15 were applied
to calculate PBA, and then compared to FBA using theedge marking method (edge marking was used because
the user only needs to mark trees once to determine all
BAFs, whereas target counting requires multiple runs
through the images). The difference between FBA andPBA were compared using bean plots, and variance andbias were visually analyzed.
2.4.3

Inter-Observer Variation

To examine inter-observer variability, 15 images fromthe three NL sites (one replicate from each trial) and5 images from the NRF plots were selected as test images. These 20 images were used for the edge marking

4

method. For the target count method, horizontally mirrored images were used. In total, there were 40 tests
images given to 7 individuals. Everyone had different
random orders for these images. The volunteers weretrained how to use the software in both modes and theninstructed to mark each image in the order given. Interobserver differences between PBA and FBA at BAF=2
for both modes were tested using linear mixed effects(LME) models. The fixed effects were PBA (covariate)
and marking mode, whereas the random effects included
the observer and image order.
2.4.4

Effects of Understory Density

Understory vegetation may limit sight distances in thefield as well as in photos. In the field there are a variety
of techniques the field observers can use to determine
tree count when visibility is low. On photos, these options are not available. To test whether understory vegetation influenced PBA estimates, the difference between
FBA and PBA (FBA – PBA) was graphed versus understory density, and a locally weighted scatterplot smoothing (LOWESS) regression was used to assess trends in
differences over understory density. Understory density
was separated into two height classes: HT ≤ 1.3 m andHT > 1.3 m, and evaluated by height class and total
understory density.

3

Results

3.1

Influence of different digital sample locations

Figure 4 shows the relationship between FBA and
PBA by tree marking method and digital sample location type. With the exception of edge marking withthree individual digital sampling points (Tab. 2 (e)),
all slope coefficients (b1 ) were not significantly different
from 1.0, indicating that photo bias does not increase
with increasing basal area. Results were not as consistent when examining the intercept terms. For both
marking methods, when using a single digital sample
location at plot center (Tab. 2 (a) and (d)), the intercept values were significantly different from 0 and almost
double the intercept values (b0 ) obtained using multiple
digital sampling points. For the multiple digital sampling points, only the intercept term for edge marking
was significantly different from 0 (Tab. 2 (e)). Both intercepts for the average of three digital sampling points
were negative, though not significantly different from 0(Tab. 2 (c) and (f)).
In terms of goodness of fit, the edge marking techniques generally had higher r2 values and lower root
mean square error (rMSE) values, indicating a stronger
linear relationship between FBA and PBA (Tab. 2). All

Wang et al. (2020)/Math. Comput. For. Nat.-Res. Sci. Vol. 12, Issue 0, pp. 0–14/http://opr.mcfns.com

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Figure 4: Comparisons between photo-estimated basal
area (PBA) and field measured basal area (FBA) bydigital sample location type (one center versus three individuals versus mean of three individuals) and two tree
marking method (target counting (left panels) versusedge marking (right panels)). The one center estimates(a and d) were from the Noonan Research Forest (NRF),
whereas the three estimates per plot (b and e) and meanof three estimates (c and f) were from the Newfoundland(NL) spacing trials.

regressions indicate an under-estimation of FBA, except
at the very lowest FBA values, when averaging acrossmultiple digital sampling points. Under-estimation wasconsistent with the hypothesis of visibility bias resulting from occluded (hidden or missing) “in” trees. It was
expected that the visibility bias would increase with increasing FBA; however, that was not generally observedin this study (Tab. 2 and Fig. 4).
3.2

Effects of BAF Choice

It was hypothesized that increasing BAF would result in fewer hidden trees and less user error in marking edges, and that PBA would become closer to FBA;

however, that was not what was observed in this study.
Figure 5 shows the effects of increasing BAFs on PBA
estimation. For the NRF plots, the mean differences between FBA and PBA decreased slightly, but remained
positive (indicating underestimation) across all levels of
BAF. For the NL plots, the deviations decreased, butwere essentially 0 across all levels of BAF. The NRF
only had one central digital sample location, while NL
had three sample locations (Fig. 1.a). The additional
digital sample points capture a greater range of the plot
variation and reduce the effects of hidden trees. One issue noted on several of the NRF plots was the presenceof a tree very close to plot center. Large trees can block
significant view angles on plots. Increasing BAF does
not compensate for these situations. On the other hand,
multiple digital sample locations minimized these effects
by locating the camera at different positions within theplot.
For both NRF and NL sites, variation in the differences between FBA and PBA increased with increasing
BAF (Fig. 5). Smaller plots are inherently more variable, and this was an expected outcome. It was expectedthat there would be an optimal BAF that minimized differences without substantial increases in variation. This
was not observed in this study. It should be notedthat this inference was only based on the edge marking method because of the ease of changing BAF (edges
only have to be marked once to determin all BAFs). Results for target counting were not undertaken because
counts would have to be made independently for each
BAF tested, requiring a significant increase in image
processing time.

NL

Basal Area Difference (m2/ha)

5

NRF

40
20
0
−20
−40

2

3

4

5

6

7

8

9

10 11 12 13 14 15

Basal Area Factor (m2/ha)

Figure 5: The influence of photo basal area factor (BAF)
choice on the basal area difference (field basal area –photo basal area, m2 /ha) for Newfoundland (NL) andNoonan Research Forest (NRF). The black solid line is
the mean for each location and the gray dashed line indicates perfect fit.

Wang et al. (2020)/Math. Comput. For. Nat.-Res. Sci. Vol. 12, Issue 0, pp. 0–14/http://opr.mcfns.com

3.3

Inter-observer consistency

Comparisons between FBA and PBA across the sevenvolunteers are shown in Figure 6. Most users consistently underestimated FBA with both marking methods,
with edge marking resulting in greater underestimation
than target counting (Fig. 6., Column 1). While differences between users were observed (Fig. 6., Columns2-7), on average, user estimates were comparable (i.e.,
LOWESS lines were very close to the 1:1 line). Target counting was generally more consistent than edge
marking among different users and generally resulted insimilar estimates across users (Fig. 6).
Figure 7 shows the two plots with the least and greatest deviations between users. For the least deviation
plot, though different users did not mark exactly thesame points across different trees, the edge positions, aswell as the dark gray targets for “in” trees, were almost
identical across users. The simple forest structure facil-

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6

itates tree marking and results in lower variability between users. However, it was a different story for the plot
with the greatest deviations. Neither the “out” trees nor
the “in” trees have similar positions. Trees were very
dense with smaller diameters, resulting in many “border” trees: small deviations in edge marking resulted
in changes in “in” and “out” status. This problem wasfurther compounded by the fact that edges of each tree
were difficult to distinguish.
To statistically assess the effects of tree marking methods, different users and image order (i.e., familiarity withusing the software), a linear mixed effects (LME) model
was fitted to the data. The full model was:
FBA = PBA + Marking + (User) + (Order) + e(5)where (User) and (Order) indicate random effects. A
backwards selection method was used to test significanceof random effects. For the full model, the standard deviations associated with the random effects were: 2.1879

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Figure 6: Comparisons between field basal area and photo basal area by two marking methods (edge marking versus
target counting) among seven different users. The locally weighted scatterplot smoothing (LOWESS) regression lines
show the trends between field measure and photo.

Wang et al. (2020)/Math. Comput. For. Nat.-Res. Sci. Vol. 12, Issue 0, pp. 0–14/http://opr.mcfns.com

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Figure 7: Two plots with the smallest (a) and largest (b) variance among seven users by two tree marking methods(edge marking versus target counting). PBA means photo-based basal area and FBA means field-based basal area.
The FBA of (a) is 30 m2 /ha, and FBA of (b) is 55.2 m2 /ha. The small dots are the tree edges that users marked.
The black small dot with connected lines means this tree is counted as an “in” tree, while the light gray small dotsmeans it is an “out” tree in edge marking mode. The dark gray octagon is the “in” tree marked in target counting
mode.

Wang et al. (2020)/Math. Comput. For. Nat.-Res. Sci. Vol. 12, Issue 0, pp. 0–14/http://opr.mcfns.com

8

Table 2: Simple linear regression results for field basal area versus photo basal area by digital sample point type.
The linear model is FBA=b0 + b1*PBA, if PBA is the same as FBA, then b0=0 and b1=1
Digital sample points type

Parameters(a) One center estimate

b0
b1
b0
b1
b0
b1
b0
b1
b0
b1
b0
b1

(b) Three individual estimates(c) Mean of three estimates
Edge Marking(d) One center estimate(e) Three individual estimates(f) Mean of three estimatesfor User and 0.7292 for Order (residual standard error
was 3.7051). The model was refitted with Order excluded and a log likelihood test performed. The p-value
associated with dropping Order was 0.926, indicatingthat image order was not a significant random effectinfluencing deviations from FBA. Similarly, User was
subsequently dropped, and the p-value was 0.081. So,
while more significant than image order, differences between users were still not significant at α = 0.05. The
final reduced model only included the fixed effects PBA(covariate) and Marking (method). Both factors weresignificant: PBA (p < 0.001) and Marking (p < 0.01).
The root Mean Square Error was 10.6129 and the Fvalue associated with PBA was 320.87 (p < 0.001) andfor Marking Method was 9.913 (p = 0.002).
3.4

Understory density effects

Effects of understory density on PBA estimates for
the NRF plots are shown in Figure 8. Based on the
LOWESS trend lines, understory density did not posea large visibility bias in this study. Except for a single
plot with very high understory density (> 30000 trees
per ha), the trend lines remained around 15 m2 /ha, indicating little impact of understory density on FBA. The
value of 15 is very close to the intercept coefficient estimated above (Tab. 2), and the results here show thatthe variation in FBA - PBA (Fig. 8) was not due tounderstory vegetation.

4

Discussion

Our results show that spherical images from a
consumer-grade 360° camera can efficiently and effectively estimate basal area using photo-based angle-countEstimate
19.74
0.84
4.44
0.99
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0.11
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4.09
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2.91
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0.09

p-valuer2

rMSE<0.001
0.150
0.152
0.868
0.282
0.063
<0.001
0.093
0.013
0.048
0.355
0.158

0.41

9.27

0.61

9.66

0.75

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0.44

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0.60

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7.30

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Figure 8: Effects of understory density on the basal area
difference (field basal area – photo basal area, m2 /ha) in
the NRF plots as determined by two marking methods(target counting (left panels) versus edge marking (rightpanels)). (a) and (d) are total understory trees, (b) and(e) are understory trees whose height smaller than 1.3m, while (c) and (f) are those understory trees greaterthan 1.3 m.

sampling. While underestimation was consistently observed, the trend did not appear to be related to amountof basal area per ha present, understory vegetation, norinter-user variability. As a result, underestimation could
be easily corrected using some form of double sampling(Dai, 2018; Dick, 2012) with ratio correction.
In this study, two photo processing methods wereused: the edge marking method and the octagon target
counting method. The resulting PBA estimates were
acceptable for both methods. The advantage of edge

Wang et al. (2020)/Math. Comput. For. Nat.-Res. Sci. Vol. 12, Issue 0, pp. 0–14/http://opr.mcfns.com

marking was that different BAFs can be assessed without re-marking, but this is generally only useful for big
BAF sampling (Bell et al., 1983; Iles, 2003; Marshall etal., 2004) or for research situations where one is interested in effects of different BAFs (as in this study). Allusers in this study felt the target counting was morefamiliar (more similar to the process they used in thefield) and more repeatable than edge marking. Difficulties recognizing tree edges, especially in dense forest
conditions, along with twice the number of mouse clicks
for each tree, could potentially cause higher user errors.
The octagon target count method avoided potential edge
marking errors and only required one click; however, repeated marking for different BAFs would be required.
It was expected that visibility bias would increase withincreasing basal area because of an increasing number ofhidden trees; This was not observed in this study. There
are several potential explanations for this result. First,
and most likely, the results obtained here were the compensatory effects of underestimation caused by hidden
trees coupled with overestimation caused by increaseduser error as field basal area increased. In this study,
the plots with the highest basal areas were generallycomposed of very dense small stems, especially on the
NL sites. With many small trees in an image it can bedifficult to distinguish multiple overlapping small trees
from one larger individual tree. With the edge marking method, it can be very difficult to clearly see thetree edges due to the resolution and exposure conditions(Fig. 7.b). Secondly, the plots with very high basal areas also had a significant number of dead trees present.
While care was exercised in determining live/dead trees
and in avoiding marking dead trees, this could have increased counts on the higher basal area plots. Both factors may have also contributed to the lack of improvement in PBA estimates with increasing BAF.
Multiple digital sampling locations within plots
greatly decreased effects of hidden trees and any user
errors. In several individual images there were nearby
tree trunks which occluded large portions of the plot
radial view. The potential for hidden trees in these situations was quite large. The multiple digital sample
locations minimize this issue by providing multiple plot
viewpoints, as well as capturing more of the local spatial variability. Hidden trees cannot be observed using
any remote sensing technique and represent a difficult
problem to deal with (Ducey et al., 2013, 2011; Zasadaet al., 2013). When carrying out field measured angle
count sampling, it is possible for the observer to lean
left and right or even to slightly change their location
to identify hidden trees. Distances from plot center anddiameters of hidden trees also can be measured to determine if hidden trees are count trees or not. This is
not possible with photographic or other remote sensing

9

methods (Fastie, 2010). Building a model to correct for
hidden tree effects can be very complex and should take
into account stand density, distance from tree to sensor,
the thickness of each tree trunk, and so on (Zasada etal., 2013). Such model-based approaches are inherently
more variable and require substantial field data to calibrate (Ducey et al., 2013). A simpler method is to use
double sampling with ratio correction (Dai, 2018; Dick,2012) or some form of distance sampling correction (Kershaw, 2010). We have shown another alternative, whichis to simply add additional digital sampling locations
within a plot, which is often the solution employed withterrestrial LiDAR scanning (Seidel et al., 2012; Wallace
et al., 2017). Limiting plot size (or in this case increasingBAF) is another way to decrease effects of hidden trees(Dick, 2010; Zasada et al., 2013); however, this did notseem to be effective in this study. While multiple digital sample locations improve PBA estimation, it greatly
increases field acquisition time. Given that angle countsampling is already an efficient method to implement in
the field, multiple images would likely require more field
effort. Double sampling with ratio correction is most
likely to be the most efficient method for dealing withhidden trees (Dai, 2018; Dick, 2012).
It is very important to determine an appropriate BAF
for angle-count sampling (Bitterlich, 1984; Iles, 2003;
Yang et al., 2017). Choice of BAF greatly influences
variability, which in turn, influences sample size requirements, numbers of trees counted per plot, and ultimately
inventory costs (Iles, 2012; Yang et al., 2017). We foundthat BAF could be increased to about 5 without substantially increasing variability. Yang et al. (2017) obtained similar results for the entire NRF. The increased
BAF had the added effect of slightly reducing visibility bias; thus a trade-off between visibility bias andplot variation needs to be considered when implementing
photo-based angle count sampling.
In this study, understory vegetation did not seem toinfluence visibility bias. Concerns about effects of understory vegetation has been mentioned by many photobased forest inventory studies (Dick, 2010; Fastie, 2010;
Perng et al., 2018; Stewart, 2004), but none of thesestudies verified this effect experimentally. We found thatdifferent understory tree densities had no significant impact on the differences between FBA and PBA. This wascontrary to our expectations. A possible explanation forthis phenomenon is that most of the understory vegetation in the study plots were shorter than 1.3 m in height.
Additional advantages in our study include very flat terrain and the ability to view up the stem and visualize
stem size when taller understory vegetation blocked theview.
Variability between different users is a very important consideration when choosing measurement meth-Wang et al. (2020)/Math. Comput. For. Nat.-Res. Sci. Vol. 12, Issue 0, pp. 0–14/http://opr.mcfns.com

ods. While a few photo forest mensuration studies
have shown that they can achieve small differences between field measured data and photo measured data
(Clark et al., 2000; Fastie, 2010; Rodrı́guez-Garcı́a etal., 2014), none, to our knowledge, have systematicallytested the repeatability and reproducibility among different users. Our repeatability test, given by seven volunteers, showed: (1) Random effects of image processing order (familiarity of software) and different users did
not have significant impacts on photo estimation; (2) the
denser the plot, the more differences between users due
to manual identification and selection by mouse clicking;and (3) using octagon target counts did not require identifying tree edges and resulted in lower underestimation
than edge marking.
Many studies have focused on individual tree measurements, before summarizing these measures into standlevel attributes. Some studies use scale tags placed oneach tree or measured field distances and slopes (Dick,
2010; Lu et al., 2019). These methods require measuring
or tagging individual trees, which is time-consuming andcostly and/or requires multiple images for each tree ofinterest (Perng et al., 2018; Stewart et al., 2004). These
techniques have limited benefit for improving inventory
efficiency. In addition, errors resulting from stitching
several digital photos together cannot be avoided (Dick,
2010; Fastie, 2010; Lu et al., 2019; Perng et al., 2018).
Structure from Motion (SfM) is an “automatic” merging
technology which enables 3D reconstruction from photoseries without actual measurements (Fang and Strimbu,
2017; Sanvely et al., 2008). Several studies have used thistechnique to reconstruct individual tree stems (Miller etal., 2015; Mokroš et al., 2018; Surový et al., 2016), or todevelop stand level point clouds (Forsman et al., 2016;
Liang et al., 2014, 2015; Liu et al., 2018). However, thisautomatic technology requires obtaining a large numberof photos (Berveglieri et al., 2017a; Liu et al., 2018) andhigh performance computers and complex algorithms to
conduct analysis (Belton et al., 2013; Liang et al., 2015;
Mulverhill et al., 2019). In addition, the point clouds require subsequent measurement to produce the tree andstand attributes. Our method simply extracts the standlevel basal area directly from the photos.
The method we have proposed here has several advantages. First, using a consumer-grade spherical camera
is a very cost-effective (around $400 CDN) and timeefficient (less than 1 minute per photo) method. The
produced image is automatically merged into the camera, eliminating the often time-consuming task of acquiring and stitching multiple photos from different view
radii (Dick, 2010; Fastie, 2010) or placing reference scale
objects in the field (Dean, 2003; Perng et al., 2018; Varjo
et al., 2006). Keeping permanent digital records for forest plots provides the opportunity for making new retro-10spective measurements. This aspect is likely to become
more advantageous as novel technology develops in the
future (Iles, 1994). Finally, quantification of differencesamong users is difficult to assess and correct with mostfield measurement techniques. The software developed
here keeps a record of individual markings (Fig. 7) that
could be used as a comparison reference for correcting
photo-based samples.
This study also had some limitations. The camera elevation was not exactly at the definition of breast height(1.3 m). When selecting tree trunks for marking and estimating basal area at breast height, we used the equatorial plane of the spherical camera rather than calculating
1.3 m height on tree trunks based on stereoscopic principles (Perng et al., 2018; Rodrı́guez-Garcı́a et al., 2014;
Sánchez-González et al., 2016). Also, merging two hemispherical lenses into spherical image sometimes caused
the joint region fuzzy or blurred, makes tree trunk identification more difficult. Variable sunlight conditions canresult in inconsistent exposure levels across the sphericalimage. Underexposure makes trunks in the far distancedark and hard to distinguish while overexposure flashes
out trunk edges. Our terrain was relatively flat. In
steeper terrain, different methods for identifying breast
height on trees will be required. This is a more complicated problem than is currently implementing in ourlab. Finally, all images were marked manually, which
is time consuming and prone to user error. Automatic
image processing and 3D reconstruction is a rapidly developing area (Hapca et al., 2007). It may prove feasible
to automatize the process described here by applying
computer vision and developing algorithms similar to
our manual selection methods (Berveglieri et al., 2017b;
Sánchez-González et al., 2016). Another possibility is
to use Structure from Motion (SfM) techniques (Sanvely et al., 2008) to obtain point clouds from different
camera views (Forsman et al., 2016; Liang et al., 2014;
Mokroš et al., 2018; Surový et al., 2016); however, as
mentioned above, point cloud development obviates thesimplicity of the methods developed here – other thanclicking trees, no measurements were required. Last but
not least, as Iles (2018) pointed out, using attributes
easily obtained by novel technologies (lead by LiDAR)
to build models to avoid messy field inventory may be
tempting. But using sample to correct initial estimate
rather than creating a correction model is still important.

5

Conclusion

Spherical photos are suitable for estimating standbasal area based on modified angle-count sampling
methods. Adding multiple digital sample locations candecrease effects of visibility bias. Careful selection of

Wang et al. (2020)/Math. Comput. For. Nat.-Res. Sci. Vol. 12, Issue 0, pp. 0–14/http://opr.mcfns.com

BAF can somewhat reduce visibility bias without substantially increasing variation. Variability among different users did not seem to be a significant problem in implementing photo angle counts. Though limited by occasionally fuzzy joint regions and extreme sunlight conditions, this novel method could still be a cost-effective
and efficient method to increase field sample sizes and toprovide permanent forest records for future use. Effects
of understory vegetation and sloping terrain needs to be
examined beyond the range of conditions encountered inthis study. Future research should focus on other forest
attribute extraction, such as height and diameter andautomatic image processing.

6

Acknowledgements

Funding for this project was provided in part by
the National Science and Engineering Research Council of Canada Discovery Grants program, the Provinceof Newfoundland and Labrador Centre for Forest Science and Innovation Contribution Agreement, and the
New Brunswick Innovation Foundation Research Assistants Initiative and Graduate Scholarships programs.
The authors also thank the labmates, collaborators, andsummer field crew who helped make this project possible: Emily Loretta Nicholson, UNB; Dr. Mike Lavigne,
Gretta Goodine, and Rodney Foster, Atlantic Forestry
Research Centre, Natural Resources Canada; We also
thank Yang Zhan, Wushuang Li, Shun-Ying Chen, andYunjia Dai for their volunteer work in software testingand inter-observer error analysis.

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