Tree Physiology 26, 1123–1136
© 2006 Heron Publishing—Victoria, Canada
A photographic gap fraction method for estimating leaf area of
isolated trees: assessment with 3D digitized plants
J. PHATTARALERPHONG,1,2,4 J. SATHORNKICH 3 and H. SINOQUET1
1
UMR PIAF INRA-UBP, Site de Crouelle, 234 Avenue du Brézet, 63100 Clermont-Ferrand, France
2
Kasetsart University, Faculty of Science, Department of Botany, Bangkok, Thailand
3
Kasetsart University, Faculty of Agriculture, Department of Agronomy, Bangkok, Thailand
4
Corresponding author ([email protected])
Received July 5, 2005; accepted December 19, 2005; published online June 1, 2006
Summary A method for computing leaf area of isolated trees
from perspective photographs was developed. The method is
based on gap fraction inversion. Photographs are discretized
into picture zones where gap fraction is computed from image
processing. Canopy volume and leaf area density associated
with each picture zone are computed from geometrical considerations and inversion of gap fraction equations. Total leaf area
and the vertical profile of leaf area are computed from the product of associated volume and its density. The method has been
implemented in software called Tree Analyser, written in C++.
The method has been tested by comparison with direct estimation of leaf area of three-dimensional (3D) digitized trees of
walnut, peach, mango, olive and rubber. Estimated leaf area
was sensitive to picture discretization, individual leaf size and
leaf inclination distribution. Optimal size of picture discretization was 17 times projected leaf size. Total leaf area was estimated by using a set of eight photographs taken around the
tree in the main horizontal directions: deviation ranged from
–11% in peach tree to +5% in rubber tree. The method allows
fast and nondestructive monitoring of leaf area of individual
tree canopies. The next version of the method will include the
estimation of 3D leaf area distribution within the canopy.
Keywords: image processing, perspective image, Tree Analyser.
Introduction
Leaf area is an important parameter in tree ecophysiology because it determines the tree’s ability for aerial resource capture
and canopy exchange with the atmosphere. Leaf area can be
directly measured on harvested leaves with a leaf area meter
(Daughtry 1990, Whitford et al. 1995). For trees having a large
number of leaves, the process of leaf collection is time consuming and labor intensive. Moreover, direct methods are destructive and therefore preclude continuous monitoring of
individual leaves during the growing season or year after year.
Indirect methods have been developed that are nondestructive, inexpensive and fairly rapid. They can be classified in two
groups (Jonckheere et al. 2004): indirect contact methods
(e.g., point quadrat and allometric techniques) and indirect
non-contact methods based on the measurement of light transmission or gap fraction through the canopy and inversion techniques (e.g., Lang and Yueqin 1986, Nilson 1999). Several
indirect non-contact instruments including fisheye cameras
and associated software have been developed and tested. However, most of the developed methods, instruments and software
are suitable only for large-scale studies of horizontally homogeneous tree canopies.
Application of indirect methods to isolated tree canopies is
scarce. Van Elsacker et al. (1983) computed total leaf area of
poplar tree canopies from gap fraction measured on perspective images, Koike (1985) derived the two-dimensional distribution of leaf area density in individual trees and forest stands
from fisheye photographs, and Villalobos et al. (1995) used
gap fraction information measured with a canopy analyzer
LAI-2000 (Li-Cor, Lincoln, NE) to derive plant area indices of
isolated olive trees.
In this paper, we describe and test a gap fraction method for
estimating leaf area of isolated trees from a set of digital photographs. In the first step, the crown volume is computed
from the photographic information as an array of three-dimensional (3D) cells, as reported by Phattaralerphong and Sinoquet (2005). Leaf area is then computed from the image gap
fraction information, by using either Beer’s or binomial laws
(Nilson 1971). Datasets of 3D digitized trees were used to test
the method. Such databases include extensive information on
canopy geometry at the leaf scale. On the one hand, total leaf
area at the tree scale, computed from individual leaf areas,
served as a direct estimate of tree leaf area. On the other hand,
3D tree databases allowed us to synthesize photograph-like
images, which can be hemispherical and orthographic (Sinoquet et al. 1998) or perspective (Phattaralerphong and Sinoquet 2005). The virtual tree photographs can, therefore, be
processed to compute an indirect estimate of leaf area, which
can then be compared with the direct estimate. The method
was implemented in software called Tree Analyser, running
under the Windows operating system. The sensitivity of leaf
1124
PHATTARALERPHONG, SATHORNKICH AND SINOQUET
area estimation to picture discretization, voxel size, leaf inclination, leaf size and number of photographs was also determined.
Material and methods
Methodology
The method is based on a set of photographs. The photographs
must be taken so that image processing allows classification of
pixels as vegetation or background in order to binarize the image as in fisheye photographic methods (e.g., Mizoue and
Inoue 2001, Frazer et al. 2001). Each photograph must be documented with the camera parameters: camera angles (elevation (β c ) and azimuth (α c )); camera location defined by horizontal distance (D) from, and height (h c ) above, tree base; and
camera focal length ( f ). Figure 1 shows the rationale underlying the method. Each picture is divided into zones of specified
size (dpx and dpy pixels) where gap fraction (P 0 ) is computed.
The division starts from the top-left of the image (i.e., standard
system coordinate of bitmap image). The gap fraction (P 0 ) is
the ratio of white pixels (non-vegetated pixels) to the total pixels of the picture zone. In the first step, which has been described by Phattaralerphong and Sinoquet (2005), gap fraction
data is used to compute crown volume, represented as an array
of 3D cells called voxels, the size of which is defined by the
user. In the second step, gap fraction data is used to compute
leaf area. For this purpose, each picture zone is associated with
a beam line from the camera location to the central pixel of the
zone. The equation of the line can be computed from the camera parameters and pixel location (see details in Phattaralerphong and Sinoquet 2005). The ray-box intersection algorithm
(Glassner 1989) is then applied to the line equation crossing
the voxel array to compute the path length (L i ) of the beam
within the crown volume. Vegetation volume (V i ) associated
with the beam path in the tree canopy is computed as:
V i = sL i
the bound pixels of the picture zone and camera parameters
(see Phattaralerphong and Sinoquet 2005). In the images, the
perspective effect makes s smaller with decreasing distance
from the camera (Figure 1). Here s is assumed to be the area
projected to the middle plane of the canopy, namely the vertical plane perpendicular to camera azimuth, which includes the
tree base.
Two models were used to relate gap fraction P 0 to canopy
structure. First, Beer’s law assumes that the leaves are infinitely small and randomly dispersed in the canopy. It can be
written as:
P0 = e – G LAD L
(2)
where G is the projection coefficient of leaf area perpendicular
to the beam direction, LAD is leaf area density (m 2 m – 3 ) in the
canopy volume associated with the beam line and L is the path
length of the beam within the canopy volume. The G function
depends on the distribution of leaf inclination angles and beam
elevation angle. The present method assumes that the leaf angle distribution is known and G is computed after Ross (1981),
assuming uniform distribution of leaf azimuth angles.
Because P 0 , G and L are known, inversion of Equation 2 allows us to derive the unknown LAD value:
LAD = –
ln (P0 )
GL
(3)
Second, the positive binomial law proposed by Nilson
(1971) was used such that the finite area of individual leaves
can be taken into account (see Sinoquet et al. 2005). In the
beam cross section (s), leaves are assumed to be randomly located, so that:
aG ⎞
⎛
P0 = ⎜1 –
⎟
⎝
s ⎠
N
(4)
(1)
where s is the area of the picture zone expressed in metric units
and is regarded as the beam cross section. It is computed from
where a is the mean area of individual leaves and N is the number of leaves in the canopy volume associated with the beam
line. In the present method, a is an input parameter derived
Figure 1. Estimation of leaf area from
an image which was taken with camera
direction (γ c ) pointing to the vertical
axis of the canopy. The image is divided into zones of specified size (dpx
and dpy pixels) and gap fraction (P 0 ) is
computed from the ratio of white to total pixels of the zone. The beam direction (δ), intersected volume (V i ) and
path length (L) associated with each
picture zone are computed from camera
parameters (elevation (β c ), azimuth
(α c ), height (h c ) and distance (D)). Gap
fraction (P 0 ) is inverted to leaf area
density (LAD) and total leaf area is the
sum of the products of LAD and V i.
TREE PHYSIOLOGY VOLUME 26, 2006
LEAF AREA OF ISOLATED TREES FROM PHOTOGRAPHS
from field measurements and N can, thus, be related to leaf
area density LAD as:
N =
LAD sL
a
(5)
Combining Equations 4 and 5 gives:
LAD =
a
⋅
sL
ln (P0 )
aG ⎞
⎛
ln ⎜1 –
⎟
⎝
s ⎠
(6)
If all pixels in the picture zone are black (all pixels are vegetated), P 0 is zero and Equations 3 and 6 do not hold because
ln(0) is undefined. Such pictures zones are called black zones,
and the associated V i is called the black volume. To avoid computing ln(0), black zones are processed with a value called the
minimum gap fraction. The minimum gap fraction is a parameter that can be set in the software. In this study, the minimum
gap fraction was set to 0.001. The amount of black volume and
leaf area associated with black zones is computed and used as
a criterion to assess the suitability of the method for a given set
of photographs.
For each image, total leaf area TLA can be written:
n
TLA =
∑ LAD i V i
(7)
i=1
where LAD i and Vi are leaf area density and canopy volume
associated with each beam i (i = 1,…n), respectively. We have
numerically checked that the summation of Vi equals total
crown volume computed from the sum of vegetated voxel volumes.
In addition, the ray-box intersection algorithm (Glassner
1989) was used to compute the intersection of the beam line
with tree canopy horizontal layers defined by the array of
voxels. Leaf area included in V i associated with beam i was
then distributed in the horizontal layers crossed by beam i, according to the proportion of V i in each horizontal layer and assuming uniform distribution of leaf area density within V i.
The leaf area method has been implemented in Tree Analyser software, written in Microsoft Visual C++.Net 2003
(Microsoft Inc.) and is available at http://www.clermont.inra.fr/piaf/eng/download/download.php.
1125
Field Crops Research Station, Pak Chong, 80 km north-east of
Bangkok, Thailand. The rubber trees and walnut tree were digitized at the leaflet scale, whereas the other trees were digitized
at the leaf scale. The length of every leaf or leaflet was measured before digitizing in order to calculate leaf area from the
allometric relationship between leaf length and leaf area (Sathornkich 2000). The experimental database therefore included seven trees with detailed information on the 3D location, orientation angles, size and shape of all leaves.
The software, Tree Box, written in Microsoft Visual
C++.NET 2003, was used to compute actual canopy structure
parameters from the digitized databases, namely total leaf
area, vertical profile of leaf area, leaf azimuth and leaf inclination distributions. The area of each leaf (a) was calculated
from an allometric relationship with leaf length (l) and width
(w) as:
a = kwl
(8)
where k is an allometric parameter (k = 0.62 for mango and olive, and 0.69, 0.61, 0.64 and 0.73 for peach, rubber
‘RRIT251’, rubber ‘RRIM600’ and walnut, respectively).
Area of each leaf was partitioned into seven sub-areas of
equal size, which were distributed in horizontal layers of
20 cm according to the spatial coordinates computed for seven
points on the leaf surface, namely six margin points and the
leaf center. The vertical profile of leaf area was, thus, calculated for each 20-cm layer (i.e., the same size as the voxels
used in the test) from the sum of the leaf subareas in the layers.
Leaf inclination and azimuth angle distribution were calculated as the proportion of leaf area in 10° and 30° angle classes,
respectively. Table 1 shows canopy structure parameters of the
trees computed from the digitized databases. The trees showed
large variation in canopy size, total leaf area and leaf size. Total leaf area ranged from 0.56 m 2 in Olive 1 to 32.01 m 2 in rubber tree cv. ‘RRIM600’. Leaf or leaflet size ranged from
1.32 cm 2 in Olive 2 to 47.2 cm 2 in walnut tree. In all trees, leaf
inclination (Figure 2A) approximated an unbalanced bell
shape. For each tree, mean leaf inclination was around the
peak of the distribution and ranged from 28° in peach to 45° in
Table 1. Total leaf area, mean leaf area, mean leaf inclination and
mean leaf azimuth of the digitized study trees.
Testing the method
Tree
Digitized trees Three-dimensionally digitized data of mango, olive (Olive 1), peach and walnut trees (Phattaralerphong
and Sinoquet 2005) were used to calibrate and test the method.
Additional trees were included to validate the method, namely
one olive tree cultivar ‘Arbequina’ (Olive 2) and two rubber
trees cultivar ‘RRIT251’(Sangsing 2004) and ‘RRIM600’. Olive 2 was 16 months old when digitized and photographed in
January 2005 at the Kasetsart University Kampaeng Saen
Campus, Nakorn Prathom, 80 km west of Bangkok, Thailand.
The 3-year-old rubber tree cultivar ‘RRIM600’ was digitized
and photographed in August 2003 in Suwan Wajokkasikit
Height Diameter Total
(m)
(m)
leaf area
(m 2 )
Mean
leaf area
(cm 2 )
Mean leaf
inclination
(°)
Mango
Olive 1
Olive 2
Peach
Rubber
‘RRIT251’
Rubber
‘RRIM600’
Walnut
1.7
2.3
1.4
2.5
3.9
1.7
1.4
0.95
3.0
1.4
6.48
0.83
0.56
28.11
3.61
39.58
1.52
1.32
19.64
40.351
41.74
44.63
45.40
28.52
34.4
5.3
3.9
32.01
26.361
37.07
2.8
1.8
7.35
47.2 1
33.74
1
Mean of leaflet area for walnut and two rubber trees.
TREE PHYSIOLOGY ONLINE at http://heronpublishing.com
1126
PHATTARALERPHONG, SATHORNKICH AND SINOQUET
Figure 2. Leaf inclination (A) and leaf
azimuth (B) distribution of the studied
trees.
olive tree. Almost all of the trees showed uniform distribution
of leaf azimuth except rubber tree ‘RRIT251’ (Figure 2B),
which was grown in a greenhouse where part of the incident
light was intercepted by a wall.
Random canopies Random canopies of mango, Olive 1,
peach and walnut trees were created to eliminate the effect of
nonrandom leaf dispersion in the canopy volume, namely foliage clumping. Random canopies were created by randomly
generating the position of all leaves inside the canopy volume,
as computed from Tree Box software (see Phattaralerphong
and Sinoquet 2005). Other leaf attributes were unchanged, so
that random canopies had the same number of leaves, total leaf
area and leaf angle distributions as the actual tree canopies.
Random canopies added four additional plants to the experimental database when testing the method in a canopy with no
foliage clumping.
Image synthesis Virtual photographs of 3D digitized plants
were synthesized by freeware POV-Ray version 3.5 (Persistence of Vision Development Team, www.povray.org), as pro-
posed by Sinoquet et al. (1998) and Phattaralerphong and
Sinoquet (2005). The parameters of the Nikon CoolPix 885
camera were used. Black and white images of three million
pixels (2048 × 1536, i.e., maximum resolution of the Nikon
CoolPix 885) were synthesized. The camera distances were set
at about twice canopy height. Camera height was fixed at 1.2 m
(i.e., a convenient height for field applications). Focal length
was set so that the entire canopy was visible in the image frame
(Table 2).
Sensitivity analysis The effects of parameters expected to influence leaf area computations were investigated. This included the zone size where gap fraction is computed in the
pictures, the voxel size chosen to represent crown volume and
the canopy attributes used as input parameters in the method
(i.e., leaf inclination distribution and individual leaf size). The
default parameters for the computations are shown in Table 3.
The value of the studied variable in the sensitivity analysis was
changed while the others were set to the default. Picture zone
was changed between 2 × 2 and 300 × 300 pixels. To compare
TREE PHYSIOLOGY VOLUME 26, 2006
LEAF AREA OF ISOLATED TREES FROM PHOTOGRAPHS
Table 2. Camera parameters for each tree used for image synthesis.
Tree
Camera parameters
Distance
(m)
Mango
Olive 1
Olive 2
Peach
Rubber
‘RRIT251’
Rubber
‘RRIM600’
Walnut
Height
(m)
Elevation
(°)
Focal length
(mm)
3.4
4.6
2.8
5.5
7.8
1.2
1.2
1.2
1.2
1.2
0
5
–5
2
13
8
13
9
8
16
10.6
1.2
13.5
12.5
5.6
1.2
3
9
results between species, picture zone was expressed as the ratio
between zone area in metric units at the canopy plane and mean
projected individual leaf area, namely s and aG in Equations
4–6. This ratio was called the picture zone area (PZA). Both
random and actual canopies were tested with Beer’s and binomial models of inversion. Voxel size was varied from 5 to
80 cm. Default distribution of leaf inclination angle was the actual one, described as the fraction of leaf area in nine classes of
10°, and the effect of using predefined leaf angle distributions,
namely conical, erectophile, extremophile, plagiophile, planophile and spherical (de Wit 1965), was studied with each inversion model. In addition, mean leaf inclination when using
conical leaf inclination distribution was varied between ± 20%
of actual mean leaf angle. Finally, input leaf size for the binomial model was varied between ± 50% of actual leaf size.
Validation of the method The best settings found from the
sensitivity analysis were used for the validation of the photographic method. Validation included virtual photographs synthesized from the digitized data of seven trees: mango, two olives, peach, walnut, rubber ‘RRIT251’and rubber ‘RRIM600’.
The total leaf area and the vertical profile of leaf area in 20-cm
layers were compared between values computed from the photographic method and the direct measurements. The number of
Table 3. Default parameter for testing the method. Abbreviation:
LAD = leaf area density.
Parameter
Number of images
Camera distance
Camera height
Camera model
Voxel size
Image resolution
Leaf inclination distribution
Value
8 (N, S, E, W, NE, NW, SE and SW)
About twice canopy height (Table 1)
1.2 m
Nikon CoolPix 885
20 × 20 × 20 cm
2048 × 1536 (3 Mpixels)
Custom (nine classes calculated
from digitized data)
Leaf azimuth distribution
Assumed to be random
Fixed zero gap
0.001
Fixed maximum LAD
30
Gap fraction inversion model Binomial
1127
photographs (n) needed to obtain the mean value of total leaf
area with 5% and 10% error with 95% confidence interval (α =
0.05) was calculated as (see http://www.isixsigma.com/library/content/c000709.asp):
⎛ Z σ⎞
n = ⎜ α /2 ⎟
⎝ E ⎠
2
(9)
where n is the sample size necessary to estimate tree leaf area
with an error less than or equal to ± E with confidence of 1 – α,
Z α/2 is the critical value of α/2 in the right tail of the stand normal distribution and σ is the population standard deviation,
calculated from the results obtained from eight photographs.
Two trees were photographed with a real camera for method
validation with real photographs (Figures 3A and 3B). The
rubber ‘RRIM600’ was photographed with a Nikon CoolPix
885 with a resolution of 2048 × 1536 (3.1 Mpixels). Olive 2
was photographed with a Minolta DiMAGE A2 with a resolution of 2560 × 1920 (5 Mpixels). Both cameras were placed on
a tripod and equipped with inclinometer, tubular level vials
and compass. Camera height relative to the tree base was recorded. A red cloth was used as background for convenient
separation between plant and background pixels in image processing (Andrieu and Sinoquet 1993). Photographs were taken
in eight directions around the tree in the main horizontal directions. Exact camera inclination and azimuth angles were recorded with the inclinometer and compass fixed on the tripod.
The focal length of each photograph was stored automatically
in EXIF data (Exchangeable Image File format for Digital Still
Cameras, Japan Electronic Industry Development Association
(JEIDA), Japan) in the digital image file.
All photographs were processed manually to black and
white bitmap files using GIMP for Windows Version 2.2.9
(GNU Image Manipulation Program, http://www.gimp.org).
First, the red background was removed using the “Select regions by color” tool. Then the other parts such as main stem,
main branches and unwanted objects in the photographs were
removed using the “Eraser” tool. The photographs were then
converted to “Gray Scale” mode and were adjusted with the
“Brightness–Contrast” tool until the color of leaves in photographs was black and the background was white. Finally, the
photographs were converted to black and white (index color
conversion) without dithering and saved as Bitmap files (Figures 3C and 3D). Two other sets of photographs (Figures 3E
and 3F) were synthesized from the digitized data with the
same camera parameters, as in the actual photographs, to compare virtual and real photographs. Leaf area was computed
from the actual photographs with Tree Analyzer using the best
setting found in the sensitivity analysis.
Results
Sensitivity analysis
Effect of picture discretization The degree of picture discretization, namely the size of picture zones used to compute gap
fraction, had a large effect on leaf area computations, for both
TREE PHYSIOLOGY ONLINE at http://heronpublishing.com
1128
PHATTARALERPHONG, SATHORNKICH AND SINOQUET
Figure 3. Representative photographs of Olive 2 (left) and
rubber ‘RRIM600’ (right),
comparison between real photographs (top), actual photographs after image binarization
(middle) and synthesized images from the digitized data
(bottom).
gap fraction inversion models and for both randomized and actual distribution of leaf area in canopy volumes (Figures 4
and 5). Picture zone area (PZA) was expressed in units of individual leaf area projected onto a plane perpendicular to the
beam direction, namely aG. By using Beer’s law, the larger the
picture zone, the smaller the estimated tree leaf area (Figure 4).
The effect was very sensitive in the case of a small PZA. In the
case of randomized canopies, the range of PZA, where estimated leaf area of all tree canopies was within a ± 10% range of
actual leaf area (PZA10%), was between 11 and 208 (Figure 4A). In the case of actual canopies, i.e., showing nonrandom distribution of leaf area within the canopy volume, the
range of PZA 10% was much smaller, namely between 14.6 and
20.1 (Figure 4B). This was mainly owing to the behavior of the
peach tree which showed the highest small-scale leaf clumping
(Sinoquet et al. 2005). By disregarding the peach tree canopy,
PZA 10% would be between 14.6 and 80. By using the binomial
model of gap fraction inversion, estimated leaf area as a function of PZA showed an asymmetric bell-shaped line: it was first
underestimated for small picture zones, then showed a peak
and finally decreased for large picture zones (Figure 5). The
values of PZA 10% were mainly located after the peak. As for
Beer’s law, the range of PZA 10% was much larger for random
canopies (i.e., between 6.5 and 227) than for actual canopies
(i.e., between 11.8 and 22.5), and range reduction for actual
canopies was mainly due to the peach tree. The range of
PZA10% obtained with the binomial model were, however,
slightly larger than those computed from the inversion of
Beer’s law. Finally, a PZA value of 17 was found to be the best
for estimating leaf area with the two inversion models.
The smaller the PZA, the larger the amount of black zones,
and consequently, the larger the fraction of black volume and
leaf area computed from black zones (Figure 6). For PZA values of 1, the fraction of black volume could reach 27% in the
peach tree canopy, and associated fraction of leaf area was
larger (up to 91%) because black zones were obviously dense.
This shows that a too small PZA is unsuitable in this kind of inversion method. Conversely, PZA of 17 showed negligible
TREE PHYSIOLOGY VOLUME 26, 2006
LEAF AREA OF ISOLATED TREES FROM PHOTOGRAPHS
1129
Figure 4. Effects of picture zone area (PZA) on leaf area estimated
from Beer’s model on a random canopy (A) and on an actual canopy (B).
Figure 5. Effects of picture zone area (PZA) on leaf area estimated
from binomial model on a random canopy (A) and on an actual canopy (B).
fractions of black volume and associated leaf area for all canopies, except the peach tree (2% black volume, 5% leaf area associated with black volume).
At small PZA values, the two inversion models behaved differently. The smaller the PZA, the higher the leaf area estimated from Beer’s model, as a result of the averaging properties of the exponential function (Equation 3). In contrast, leaf
area estimated from the binomial model tends to 0 when PZA
tends to 1. This is because ln (1 – aG / s ) in Equation 4 tends to
–∞ when PZA tends to 1; thus, the binomial model cannot be
used with PZA ≤ 1.
size were much smaller: for 20-cm voxels, computation time
ranged from 8 min for the olive trees to 14 min for the peach
tree.
Effect of voxel size In the range of 5 to 80 cm, voxel size had
no effect on estimated leaf area (Figure 7A). In contrast, voxel
size greatly influenced computation time, especially for small
voxel sizes (Figure 7B). For a voxel size of 5 cm, computation
time ranged from 1 h for the olive trees to 15 h for the peach
tree. Three-dimensional reconstruction of the canopy volume
was the most time consuming process because of the large
number of voxels in the case of small voxel size (e.g., for the
peach canopy processed with voxels of 5 cm, volume reconstruction took 98% of total computation time). For voxels
larger than 20 cm, differences in computation time due to voxel
Effect of leaf inclination Estimation of leaf area was highly
sensitive to leaf inclination distribution (Figure 8). The actual
leaf inclination distribution generally gave the best estimation,
with the lowest root mean square error (RMSE), namely 6% of
actual leaf area (Table 4). The conical distribution (i.e., all
leaves at measured average leaf inclination) led to slightly underestimated leaf area and slightly higher RMSE of 7%. However, the difference in estimated leaf area by using either the
actual or the conical leaf angle distribution was insignificant
(P = 0.49). Other theoretical leaf angle distributions globally
resulted in larger RMSE (Table 4), namely from 16 to 37%. For
a given tree, the suitability of a given theoretical distribution
obviously depended on its approximation to the actual distribution, e.g., the plagiophile distribution for the mango tree. Conversely, the erectophile and spherical distribution led to large
underestimation of tree leaf area because none of the studied
tree canopies showed this kind of leaf angle distribution. Estimated leaf area was also sensitive to the mean leaf inclination
used in the conical distribution (Figure 9). For all plants, the
TREE PHYSIOLOGY ONLINE at http://heronpublishing.com
1130
PHATTARALERPHONG, SATHORNKICH AND SINOQUET
Figure 6. Effects of picture zone area
(PZA) on black volume (A and B), leaf
area associated with black volume
from Beer's model (C and D) and from
binomial model (E and F) for a random
canopy (left) and an actual canopy
(right).
larger the leaf inclination, the smaller the estimated tree leaf
area. Changing mean leaf inclination within ± 20% around the
measured value led to an estimated leaf area ranging from +25
to –17% of actual leaf area.
Effect of leaf size Estimation of leaf area was shown to be
less sensitive to leaf size than to leaf inclination. Changing leaf
size within ± 50% caused estimated leaf area to range between
+5 to –12% of actual tree leaf area. A greater effect was found
when leaf size was underestimated (Figure 10).
Validation
Figure 11 shows the comparison of total leaf area for seven
trees: (1) the direct computation from the digitized database;
and (2) the 8-photograph method parameterized after the sensitivity analysis, i.e., using the binomial model, voxel size of
20 cm, PZA of 17 projected leaf size and conical leaf angle
distribution with actual mean inclination angle. For virtual
photographs, there was good correlation between the direct
and photographic method (R 2 = 0.986). The mean estimated
values from photographs ranged from +5% of actual leaf area
in rubber ‘RRIM600’ to –11% in peach tree. Standard deviations of the estimated value calculated from the eight photographs ranged from 1.5% in peach to 11.1% in rubber
‘RRIT251’. Computations from real photographs showed larger errors, with leaf area overestimation of +9.3% and +13.4%
for Olive 2 and rubber tree ‘RRIM600’, respectively (Figure 11). The finding that virtual photographs led to a better estimation of leaf area than real photographs indicates that the
overestimation found with actual photographs must be related
to image processing, especially the problem of separating pixels between leaves and other organs.
The photographic method was also able to satisfactorily render the vertical profiles of leaf area, as computed in 20-cm layers (Figure 12). The RMSE ranged from 0.006 m 2 in Olive 2 to
0.45 m 2 in peach tree. In particular, the shape of the profile, the
value and altitude of maximum leaf area density were correctly estimated.
The number of photographs required to get the mean within
the range of 5 and 10% error with 95% confidence (α = 0.05) is
TREE PHYSIOLOGY VOLUME 26, 2006
LEAF AREA OF ISOLATED TREES FROM PHOTOGRAPHS
1131
Figure 8. Leaf area estimated with different leaf angle distributions
(Actual = nine classes of leaf angle from digitized data).
Discussion
Figure 7. Effects of voxel size on estimated leaf area (A) and computation time (B). The computation was done on a personal computer
with CPU Intel Pentium III 1.0 GHz.
shown in Figure 13. For 10% error, the number of pictures
ranged from one picture for Olive 1, peach and walnut to nine
pictures for Olive 2. For 5% of mean error, the number of picture ranged from one picture for peach to 36 pictures for
Olive 2. The larger number of photographs required for Olive 2 was a result of the low leaf area and the inclination of the
canopy (Figure 3). The rubber ‘RRIT251’ required a large
number of photographs (21 pictures) because of its nonuniform leaf azimuth distribution (Figure 2B). This simple analysis shows that eight pictures are generally enough to get the
mean error within 5%.
We developed a photographic method to estimate leaf area of
isolated tree canopies based on inversion of a gap fraction
model—a model that has been widely used in studies on horizontally homogeneous canopies. Unlike the few proposed
methods for estimating leaf area of isolated plants, our method
includes computation of tree crown shape and uses standard
photographs taken in horizontal directions. We have conducted a sensitivity analysis of the method, and tested the
method on various tree canopies from 3D digitized databases
and on two additional sets of actual photographs. We have previously discussed the use of virtual experiments for estimating
crown volume from photographs (Phattaralerphong and Sinoquet 2005).
Previous methods proposed for estimating leaf area of isolated plants from a gap fraction inversion model assume the
canopy fit a parameterized shape (semi-ellipsoid in Van Elsacker et al. 1983, ellipsoid in Villalobos et al. 1995). Here canopy
volume is computed from a set of eight photographs: volume
computations have been satisfactorily validated against direct
measurements of canopy volume by Phattaralerphong and
Sinoquet (2005). The sensitivity analysis showed that the computation of leaf area is insensitive to voxel size, whereas canopy volume computation is highly sensitive to voxel size
owing to the fractal nature of tree crowns (Zeide and Pfeifer
Table 4. Root mean square error (RMSE) in percentage of actual leaf area for each model of leaf inclination. Nine classes of leaf inclination were
analyzed.
RMSE%
Custom
Conical
Erectophile
Extremophile
Plagiophile
Planophile
Spherical
Walnut
Olive
Peach
Mango
Mean
4.09
5.63
8.29
7.09
6.27
3.66
7.77
11.35
5.59
7.09
35.55
23.52
53.23
23.88
34.05
9.84
10.20
31.54
13.40
16.25
19.92
5.21
39.67
5.83
17.66
28.75
54.60
1.94
61.29
36.64
31.81
17.46
48.54
16.55
28.59
TREE PHYSIOLOGY ONLINE at http://heronpublishing.com
1132
PHATTARALERPHONG, SATHORNKICH AND SINOQUET
Figure 9. Sensitivity of estimated leaf area to leaf angle for a conical
leaf angle distribution.
1991, Sinoquet et al. 2005). These observations imply that leaf
area estimation is likely to be insensitive to canopy volume,
which may justify previous leaf area estimation methods in
which it is assumed that the canopy fits an approximate shape.
The use of a set of photographs taken in horizontal directions has advantages and shortcomings. It is easy to set the
camera in the field compared with using some other elevation
angle, and it is probably the reason why the method satisfactorily computed the vertical profiles of leaf area distribution
(Figure 12). Because the method computes leaf area associated with any beam traced from the camera to the canopy, but
Figure 10. Sensitivity of leaf area computed from the binomial model
to leaf size.
Figure 11. Comparison of total leaf area obtained by the direct method
and the photographic method based on eight photographs with optimal parameters (binomial model, voxel size 20 cm, PZA equal to 17
and conical leaf angle distribution based on mean leaf angle as input).
Symbols: 䊊 = photographic method using virtual images of the 3D
plants; and 䊉 = photographic method using actual tree photographs.
disregards changes in leaf area density along the beam path, it
is unable to compute the distribution of leaf area density in the
canopy, namely a value of leaf area density per voxel. However, the beams are mostly close to horizontal; therefore, the
chance of any beam crossing a single 20-cm horizontal layer is
likely to be high, and the leaf area associated with any beam is
likely to be the leaf area associated with a given horizontal
layer. This makes possible the computation of the vertical profiles of leaf area. In contrast, computing the vertical profiles of
leaf area would be impossible with the proposed inversion
method if the beams were not mostly horizontal. Our method
is particularly suitable for estimating the vertical distribution
of leaf area of small trees at large distances from the tree
trunks, i.e., by using a large focal length that ensures less deviation in beam horizontality. The use of photographs taken in
horizontal directions also provides an unbiased estimation of
canopy shape and volume. Canopy volume is computed as the
intersection of cones originating from the camera as defined
by the plant silhouette projected on the photographs (Shlyakther et al. 2001). Use of a set of photographs taken obliquely
around the tree (i.e., with the camera pointing upward) would
result in a canopy volume having some empty space at the top
of the canopy, and consequently lead to overestimation of
canopy volume.
Use of photographs taken horizontally makes the method
highly sensitive to leaf inclination (Figures 8 and 9). This is a
shortcoming because it means that accurate measurement of
leaf inclination angles is critical. Usually leaf area methods
based on gap fraction inversion are rather insensitive to leaf inclination, which is why estimation of leaf angles from gap
fraction methods is difficult (Lang 1986). Our method uses
gap fraction information in a single direction, whereas stan-
TREE PHYSIOLOGY VOLUME 26, 2006
LEAF AREA OF ISOLATED TREES FROM PHOTOGRAPHS
1133
Figure 12. Vertical profile of leaf area
in 20-cm layers for each plant: comparison between the photographic method
(solid line) and the direct method (dotted line).
Figure 13. Number of photographs required to obtain the estimated
leaf area within the range of 5 and 10% error with 95% confidence
(α = 0.05).
dard methods (e.g., based on fisheye photographs) use information from all directions of the sky hemisphere. For example,
the pioneer formula proposed by Miller (1967) integrates directional gap fraction over the range of zenith angles in order
to remove the effect of leaf inclination—namely the G-function (Ross 1981)—from the leaf area equation. In our method,
the G-function is involved in LAD computations by both the
Beer’s and binomial models (Equations 3 and 6). Sensitivity to
leaf angle could be minimized by using directional photographs with a 32° view angle, i.e., the special angle where the
G-function is known not to depend on leaf inclination (e.g.,
Ross 1981), but this would be accompanied by all of the shortcomings associated with non-horizontal photographs. For horizontal photographs, sensitivity to leaf angle is expected to increase with decreasing leaf inclination angle, i.e., when the
G-function diminishes and finally tends towards 0 for horizontal leaves. This is because G tending to 0 makes the denominator in Equations 3 and 6 also tend to 0. The method with horizontal photographs is, therefore, expected to be more difficult
TREE PHYSIOLOGY ONLINE at http://heronpublishing.com
1134
PHATTARALERPHONG, SATHORNKICH AND SINOQUET
to apply to planophile canopies; however, the tree species we
studied showed no difference in method sensitivity to leaf inclination angle (Figure 9) in the range of mean inclination
angles they displayed (30–45°; Table 1). We computed the
G-function without considering the hypothesis of uniform distribution of leaf azimuth angle or azimuth variations. This
assumption was suitable for all plants, except rubber tree
‘RRIT251’, but led to large between-photograph variance in
leaf area estimates (Figure 13).
In addition to sensitivity to leaf inclination angle, our photographic gap fraction method showed high sensitivity to the
picture discretization used to compute gap fraction (Figures 4
and 5). This behavior has never been reported in other indirect
methods applied to isolated plants (Van Elsacker et al. 1983,
Koike 1985), but it has been observed in horizontally non-homogeneous canopies (Lang 1986). Here we faced the same dilemma as Lang (1986) faced when averaging directional gap
fraction data along transects in row canopies: if the integration
length is too small, a number of averaged gap fraction data are
set to 0 and cannot be used in the gap fraction inversion
method; and if the integration length is too large, gap fraction
averaging smooths small-scale variation in gap fraction as a
result of variations in leaf area density.
In the photographic method, we invoked the notion of black
zones, i.e., pictures zones where the gap fraction is zero, to
deal with the lower limit of the picture zone. The canopy volume associated with black zones was used as a criterion to assess the suitability of the method when applied to a given set of
photographs. The fraction of black volume increased as the
picture zone decreased (Figure 6). Moreover, at a given picture
zone, the densest peach tree canopy showed the largest fraction of black volume of the study trees. All remote sensing methods, whether based on gap fraction or reflectance measurements, face problems with dense canopies
because the measured signals saturate (cf. for example, Andrieu and Baret 1993). When using large picture zones, leaf
area computed from the photographic method was underestimated (Figures 4 and 5). Because the relationship between gap
fraction and leaf area density is nonlinear, gap fraction averaging follows the Jensen’s inequality (Davis and Marshak 2004),
e.g., exp(– x i ) ≤ exp(– x i ) for Beer’s law. Inverting the gap
fraction results in leaf area underestimation due to neglecting
variations in optical density (Figures 4 and 5). This underestimation occurs with both actual and uniform distribution of leaf
area density within the crown volume: in the case of random
canopies, changes in optical density are caused by variations
in beam path length within the canopy volume; and in the case
of actual canopies, nonuniform distribution of leaf area density causes a second source of variation in optical density. A
compromise was found at a PZA of around 17 times projected
individual leaf areas that allowed both a small fraction of black
volume and estimated leaf area within ± 10% of the actual
value (Figures 4 and 5).
Lang (1986) concluded that mean leaf length should be
10 leaf widths, when directional gap fraction is measured from
sunbeam transmission, i.e., mimicking an orthographic camera with parallel beams. Although the values are difficult to
compare, mainly because of leaf length versus leaf area integration, the larger integration proposed by Lang may indicate
that integration area depends on the focal length used to take
the photographs. The range of suitable PZA was larger for random canopies and when using the binomial model because it
explicitly takes into account leaf size. As previously reported
for other gap fraction methods, foliage clumping made our
method less accurate (e.g., Stenberg et al. 1994). Although
picture discretization allowed leaf clumping to be taken into
account, the gap fraction equations were unable to deal with
leaf clumping at the local scale in the random canopies. This
was especially evident in the case of the peach tree, which
showed small-scale leaf clumping (Sinoquet et al. 2005). Including a leaf clumping parameter in Equations 3 and 4 does
not seem an appropriate way to account for small-scale clumping in the photographic method because such a parameter is be
expected to change with PZA. Another way would be to combine the PZA averaging method with the theory of gap size
distribution (Chen and Cilhar 1995), as recently proposed by
Leblanc et al. (2005) for retrieving leaf area index of boreal
forest canopies from fisheye photographs.
Several additional difficulties arise when using the photographic method with actual plant photographs. First, the user
must set up the camera and control the camera parameters. For
this purpose, electronic distance meter, compass and inclinometer may help. Second, photograph quality should be good
enough to allow accurate separation between vegetation and
background. Taking the photographs with a red cloth as a
background makes the pixel separation easier (Andrieu and
Sinoquet 1993) because of high radiation absorption by the
leaves in the red wavelengths. Taking photographs in overcast
conditions, as for fisheye photographs but for different reasons, is recommended because (1) it avoids shadow cast by the
tree onto the background; and (2) it reduces the effect of specular reflection and thus, leaf brightness on the photograph.
Even with these precautions, processing the photographs for
pixel separation may be difficult, especially for hairy or waxy
leaves that do not show high greenness, e.g., olive trees in this
study. Finally, a general problem with all photographic methods is the separation between leaves and woody parts, which is
critical when foliage density is low (e.g., olive trees in this
study). This is the reason why several authors have proposed
using plant area index (PAI) instead of leaf area index (LAI)
and expressing leaf area as a fraction (α) of plant area. Values
of α have been tabulated for some boreal species (Chen et al.
1997). Pixels of the branch cannot usually be totally removed
from the photographs because of the overlap between
branches and leaves, which results in higher overestimates in
real photographs than in virtual photographs. These problems
could be decreased by taking high-resolution photographs
with the least pixel compression. Many of these difficulties
could also be minimized if automatic processing of the image
were developed, as for processing fisheye photographs (e.g.,
Jonckheere et al. 2005).
Finally, unlike canopy volume calculations (Shlyakther et
al. 2001, Reche et al. 2004), the computation of leaf area from
the photographic method was found insensitive to the number
TREE PHYSIOLOGY VOLUME 26, 2006
LEAF AREA OF ISOLATED TREES FROM PHOTOGRAPHS
of photographs. For all trees, except rubber tree ‘RRIT251’
which shows crown asymetry and Olive 2 with low leaf area, a
set of eight photographs was sufficient to get the confidence
interval within ± 5% of the mean value (Figure 13).
In conclusion, we have developed a photographic gap fraction method for estimating total leaf area of isolated trees. The
method has been implemented in Tree Analyser software. The
method has been tested by comparing leaf area computed from
the photographs with that of 3D digitized plants. Satisfactory
estimation of total leaf area has been found by using a set of
eight photographs taken around the tree in the main horizontal
directions. The method is fast and nondestructive, allowing
monitoring of leaf area of individual tree canopies. For field
applications of actual photographs, it is necessary to define the
best image resolution and find the proper way to separate target tree pixels from the background (Mizoue and Inoue 2001),
as in processing fisheye photographs (e.g., Frazer et al. 2001,
Jonckheere et al. 2005). Further development of the method
will include the estimation of the spatial distribution of leaf
area within the canopy, namely leaf area density in each voxel
as required in 3D turbid medium models based on canopy
discretization into voxels (e.g., Myneni 1991, Sinoquet et al.
2001).
Acknowledgments
The authors are grateful to D. Combes (INRA-Lusignan, France),
P. Kasemsap, S. Thanisawanyangkura and N. Musigamart (Kasetsart
University, Bangkok, Thailand), K. Sangsing (Surat Thani Rubber
Research Center, Thailand) for assistance with tree digitizing, and to
the POV-Ray Team who provided POV-Ray freeware and its documentation. Rubber tree digitizing was supported by project “3D Plant
Structure Simulation Model Development for Rubber Tree” and olive
tree digitizing was supported by project “Ecology, Growth and Productivity of Olive under Tropical Condition” funded by Kasetsart
University Research and Development Institute (KURDI). Peach tree
digitizing was supported by project “Production Fruitière Intégrée”
funded by INRA. The peach tree was made available by CTIFL,
Balandran.
References
Andrieu, B. and F. Baret. 1993. Indirect methods of estimating crop
structure from optical measurements. In Crop Structure and Light
Micromate: Characterization and Applications. Eds. C. VarletGrancher, R. Bonhomme and H. Sinoquet. INRA Editions, Paris,
pp 285–310.
Andrieu, B. and H. Sinoquet. 1993. Evaluation of structure description requirements for predicting gap fraction of vegetation canopies. Agric. For. Meteorol. 65:207–227.
Chen, J.M. and J. Cihlar. 1995. Plant canopy gap-size analysis theory
for improving optical measurements of leaf area index. Appl. Optics 34:6211–6222.
Chen, J.M., P.M. Rich, S.T. Gower, J.M. Norman and S. Plummer.
1997. Leaf area index of boreal forests: theory, techniques, and
measurements. J. Geophys. Res. 102:29429–29443.
Daughtry, C.S.T. 1990. Direct measurement of canopy structure. Remote Sens. Rev. 5:45–60.
1135
Davis, A.B and A. Marshak. 2004. Photon propagation in heterogeneous optical media with spatial correlations: enhanced meanfree-paths and wider than exponential free-path distributions.
J. Quant. Spectros. Radiat. Transfer 84:3–34.
Frazer, G.W., R.A. Fournier, J.A. Trofymow and R.J. Hall. 2001. A
comparison of digital and film fisheye photography for analysis of
forest canopy structure and gap light transmission. Agric. For.
Meteorol. 109:249–263.
Glassner, A.S. 1989. An introduction to ray tracing. Morgan Kaufmann Publishers, San Francisco, CA, 119 p.
Jonckheere, I., K. Nackaerts, B. Muys and P. Coppin. 2005. Assessment of automatic gap fraction estimation of forests from digital
hemispherical photography. Agric. For. Meteorol. 128:243–250.
Jonckheere, I., S. Fleck, K. Nackaerts, B. Muys, P. Coppin, M. Weiss
and F. Baret. 2004. Review of methods for in situ leaf area index
determination: Part I. Theories, sensors and hemispherical photography. Agric. For. Meteorol. 121:19–35.
Koike, F. 1985. Reconstruction of two-dimensional tree and forest
canopy using photographs. J. Appl. Ecol. 22:921–929.
Lang, A.R.G. 1986. Leaf area and average leaf angle from transmittance of direct sunlight. Aust. J. Bot. 34:349–355.
Lang, A.R.G. and X. Yueqin. 1986. Estimation of leaf area index from
transmission of direct sunlight in discontinuous canopies. Agric.
For. Meteorol. 37:229–243.
Leblanc, S.G., J.M. Chen, R. Fernandes, D.W. Deering and A. Conley. 2005. Methodology comparison for canopy structure parameters extraction from digital hemispherical photography in boreal
forests. Agric. For. Meteorol. 129:187–207.
Miller, J.B. 1967. A formula for average foliage density. Aust. J. Bot.
15:141–144.
Mizoue, N. and A. Inoue. 2001. Automatic thresholding of tree crown
images. J. For. Plann. 6:75–80.
Myneni, R.B. 1991. Modeling radiative transfer and photosynthesis in
three-dimensional vegetation canopies. Agric. For. Meteorol. 55:
323–344.
Nilson, T. 1971. A theoretical analysis of the frequency of gaps in
plant stands. Agric. Meteorol. 8:25–38.
Nilson, T. 1999. Inversion of gap frequency data in forest strands.
Agric. For. Meteorol. 98–99:437–448.
Phattaralerphong, J. and H. Sinoquet. 2005. A method for 3D reconstruction of tree crown volume from photographs: assesment with
3D-digitized plants. Tree Physiol. 25:1229–1242.
Reche, A., I. Martin and G. Drettakis. 2004. Volumetric reconstruction and interactive rendering of trees from photographs. ACM
Transactions on Graphics (SIGGRAPH Conference Proceedings)
23:1–10.
Ross, J. 1981. The radiation regime and architecture of plant stands.
Dr. W. Junk Publishers, The Hague, The Netherlands, 391 p.
Sangsing, K. 2004. Carbon acquisition and plant water status in
response to water stress of rubber (Hevea brasiliensis Muell. Arg.).
Ph.D. Thesis, Kasetsart Univ., Thailand, 130 p.
Sathornkich, J. 2000. Leaf area estimation of rubber tree. M.S. Thesis, Dept. Botany, Kasetsart Univ., Thailand, 15 p.
Shlyakhter, I., M. Rozenoer, J. Dorsey and S. Teller. 2001. Reconstructing 3D tree model from instrumented photograph. IEEE
Comput. Graphics Appl. 21:53–61.
Sinoquet, H., S. Thanisawanyangkura, H. Mabrouk and P. Kasemsap.
1998. Characterization of the light environment in canopies using
3D digitising and image processing. Ann. Bot. 82:203–212.
Sinoquet, H., G. Sonohat, J. Phattaralerphong and C. Godin. 2005.
Foliage randomness and light interception in 3-D digitized trees: an
analysis from multiscale discretization of the canopy. Plant Cell
Environ. 28:1158–1170.
TREE PHYSIOLOGY ONLINE at http://heronpublishing.com
1136
PHATTARALERPHONG, SATHORNKICH AND SINOQUET
Sinoquet, H., X.L. Roux, B. Adam, T. Ameglio and F.A. Daudet.
2001. RATP: a model for simulating the spatial distribution of radiation absorption, transpiration and photosynthesis within canopies:
application to an isolated tree crown. Plant Cell Environ. 24:
395–406.
Stenberg, P., S. Linder, H. Smolander and J. Flower-Ellis. 1994. Performance of the LAI-2000 plant canopy analyzer in estimating leaf
area index of some Scots pine stands. Tree Physiol. 14:981–995.
Van Elsacker, P., H. Keppens and I. Impens. 1983. A simple photographical method for analysing the radiation interception by an individual tree. Agric. Meteorol. 29:285–298.
Villalobos, F.J., F. Orgaz and L. Mateos. 1995. Non-destructive measurement of leaf area in olive (Olea europaea L.) trees using a gap
inversion method. Agric. For. Meteorol. 73:29–42.
Whitford, K.R., I.J. Colquhoun, A.R.G. Lang and B.M. Harper. 1995.
Measuring leaf area index in a sparse eucalypt forest: a comparison
of estimates from direct measurement, hemispherical photography,
sunlight transmittance and allometric regression. Agric. For.
Meteorol. 74:237–249.
de Wit, C.T. 1965. Photosynthesis of leaf canopies. Agric. Res. Rept.
No. 663. Center for Agric. Publ. and Doc., Wageningen, 57 p.
Zeide, B. and P. Pfeifer. 1991. A method for estimation of fractal dimension of tree crowns. For. Sci. 37:1253–1265.
TREE PHYSIOLOGY VOLUME 26, 2006