ArticlePDF Available

Abstract and Figures

Background Plant density and its non-uniformity drive the competition among plants as well as with weeds. They need thus to be estimated with small uncertainties accuracy. An optimal sampling method is proposed to estimate the plant density in wheat crops from plant counting and reach a given precision. ResultsThree experiments were conducted in 2014 resulting in 14 plots across varied sowing density, cultivars and environmental conditions. The coordinates of the plants along the row were measured over RGB high resolution images taken from the ground level. Results show that the spacing between consecutive plants along the row direction are independent and follow a gamma distribution under the varied conditions experienced. A gamma count model was then derived to define the optimal sample size required to estimate plant density for a given precision. Results suggest that measuring the length of segments containing 90 plants will achieve a precision better than 10%, independently from the plant density. This approach appears more efficient than the usual method based on fixed length segments where the number of plants are counted: the optimal length for a given precision on the density estimation will depend on the actual plant density. The gamma count model parameters may also be used to quantify the heterogeneity of plant spacing along the row by exploiting the variability between replicated samples. Results show that to achieve a 10% precision on the estimates of the 2 parameters of the gamma model, 200 elementary samples corresponding to the spacing between 2 consecutive plants should be measured. Conclusions This method provides an optimal sampling strategy to estimate the plant density and quantify the plant spacing heterogeneity along the row.
This content is subject to copyright. Terms and conditions apply.
Liu et al. Plant Methods (2017) 13:38
DOI 10.1186/s13007-017-0187-1
A method toestimate plant density
andplant spacing heterogeneity: application
towheat crops
Shouyang Liu1*, Fred Baret1, Denis Allard2, Xiuliang Jin1, Bruno Andrieu3, Philippe Burger4, Matthieu Hemmerlé5
and Alexis Comar5
Background: Plant density and its non-uniformity drive the competition among plants as well as with weeds. They
need thus to be estimated with small uncertainties accuracy. An optimal sampling method is proposed to estimate
the plant density in wheat crops from plant counting and reach a given precision.
Results: Three experiments were conducted in 2014 resulting in 14 plots across varied sowing density, cultivars and
environmental conditions. The coordinates of the plants along the row were measured over RGB high resolution
images taken from the ground level. Results show that the spacing between consecutive plants along the row direc-
tion are independent and follow a gamma distribution under the varied conditions experienced. A gamma count
model was then derived to define the optimal sample size required to estimate plant density for a given precision.
Results suggest that measuring the length of segments containing 90 plants will achieve a precision better than 10%,
independently from the plant density. This approach appears more efficient than the usual method based on fixed
length segments where the number of plants are counted: the optimal length for a given precision on the density
estimation will depend on the actual plant density. The gamma count model parameters may also be used to quan-
tify the heterogeneity of plant spacing along the row by exploiting the variability between replicated samples. Results
show that to achieve a 10% precision on the estimates of the 2 parameters of the gamma model, 200 elementary
samples corresponding to the spacing between 2 consecutive plants should be measured.
Conclusions: This method provides an optimal sampling strategy to estimate the plant density and quantify the
plant spacing heterogeneity along the row.
Keywords: Wheat, Gamma-count model, Density, RGB imagery, Sampling strategy, Plant spacing heterogeneity
© The Author(s) 2017. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License
(, which permits unrestricted use, distribution, and reproduction in any medium,
provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license,
and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (
publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
Plant density at emergence is governed by the sowing
density and the emergence rate. For a given plant den-
sity, the uniformity of plant distribution at emergence
may significantly impact the competition among plants
as well as with weeds [1, 2]. Plant density and uniformity
is therefore a key factor explaining production, although
a number of species are able to compensate for low plant
densities by a comparatively significant development
of individual plants during the growth cycle. For wheat
crops which are largely cultivated over the globe, tillering
is one of the main mechanisms used by the plant to adapt
its development to the available resources that are partly
controlled by the number of tillers per unit area. e till-
ering coefficient therefore appears as an important trait
to be measured. It is usually computed as the ratio of the
number of tillers per unit area divided by the plant den-
sity [3]. Plant density is therefore one of the first variables
measured commonly in most agronomical trials.
Crops are generally sown in rows approximately evenly
spaced by seedling devices. Precision seedling systems
mostly used for crops with plants spaced on the row by
Open Access
Plant Methods
1 INRA, UMR-EMMAH, UMT-CAPTE, UAPV, 228 Route de l’aérodrome CS
40509, 84914 Avignon, France
Full list of author information is available at the end of the article
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Page 2 of 11
Liu et al. Plant Methods (2017) 13:38
more than few centimeters (e.g. maize, sunflower or soy-
bean) distribute seeds relatively evenly along the row.
Conversely, for most crops with short distances among
plants on the row, e.g. wheat, barley or canola, seeds are
distributed non-evenly along the row. is can be attrib-
uted both to the mechanisms that free, at a variable fre-
quency, the seed from the seed tank, and the trajectory
of the seed that may also vary in the pipe that drives it
from the seed tank to the soil. Further, once reaching
the soil, the seed may also move with the soil displaced
by the sowing elements penetrating the soil surface.
Finally, some seeds may abort or some young plants
may die because of pests or too extreme local environ-
mental conditions (excess or deficit of moisture, low
temperature etc.). e population density and its non-
uniformity are therefore recognized as key traits of inter-
ests to characterize the canopy at the emergence stage.
However, very little work documents the plant distribu-
tion pattern along the row, which is partly explained by
the lack of dedicated device for accurate plant position
measurement [4]. Electromagnetic digitizers are very low
throughput and not well adapted to such field measure-
ments [5]. Alternatively, algorithms have been developed
to measure the inter-plant spacing along the row for
maize crops from top-view RGB (Red Green Blue) images
[6, 7]. Improvements were then proposed by using three
dimensional sensors [810]. However, these algorithms
were only validated on maize crops that show relatively
simple plant architecture with generally fixed inter-plant
spacing along the row.
Manual field counting in wheat crops is still exten-
sively employed as the reference method. Measurements
of plant population density should be completed when
the majority of plants have just emerged and before the
beginning of tillering when individual plants start to be
difficult to be identified. Plants are counted over ele-
mentary samples corresponding either to a quadrat or
to a segment [11]. e elementary samples need to be
replicated in the plot to provide a more representative
value [12]. For wheat crops, [3] suggested that at least
a total of 3m of rows (0.5m segment length repeated 6
times) should be counted, while [13] proposed to sam-
ple a total of 6m (segments made of 2 consecutive rows
by one meter repeated 3 times in the plot). [14] pro-
posed to repeat at least 4 times the counting in 0.25m2
quadrats corresponding roughly to a total of 6.7m length
of rows (assuming the rows are spaced by 0.15 m). In
this case, quadrats may be considered as a set of con-
secutive row segments with the same length when the
quadrat is oriented parallel to the row direction or with
variable lengths when the quadrat is oriented differently.
Although these recommendations are simple and easy to
apply, they may not correspond to an optimal sampling
designed to target a given precision level. ey may either
provide low precision if under sampled or correspond to
a waste of human resources in the opposite case.
e sample size required to reach a given precision of
the plant density will depend on the population density
and the heterogeneity of plant positions along the row
that may be described by the distribution of the distances
between consecutive plants. is distribution is more
likely to be skewed, which could be described by an expo-
nential distribution or a more general one such as the
Weibull or the gamma distributions. Fitting such random
distribution functions provides not only access to the
plant density at the canopy level, but also to its local vari-
ation that may impact the development of neighboring
plants as discussed earlier.
e objective of this study is to propose an optimal
sampling method for plant density estimation and to
quantify the heterogeneity of plant spacing along the row.
For this purpose, a model is first developed to describe
the distribution of the plants along the row. e model
is then calibrated over a number of ground experiments.
Further, the model is used to compare several plant
counting strategies and to evaluate the optimal sampling
size to reach a given precision. Finally, the model was also
exploited to design a method for quantifying the non-
uniformity of plant distribution.
Field experiment
ree sites in France were selected in 2014 (Table1): Avi-
gnon, Toulouse and Grignon. A mechanical seed drill
was used in the three sites, which represents the stand-
ard practice for wheat crops. In Grignon, five plots were
sampled, corresponding to different cultivars with a sin-
gle sowing density. In Toulouse, five sowing densities were
sampled with the same “Apache” cultivar. In Avignon,
four sowing densities were sampled also with the same
Table 1 The experimental design in2014 overthe three sites
Sites Latitude Longitude Cultivar Density (seedsm2)
Toulouse 43.5°N 1.5°E Apache 100, 200, 300, 400, 600
Grignon 48.8°N 1.9°E Premio; Attlass; Flamenko; Midas; Koréli 150
Avignon 43.9°N 4.8°E Apache 100, 200, 300, 400
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Page 3 of 11
Liu et al. Plant Methods (2017) 13:38
Apache” cultivar. All measurements were taken at around
1.5 Haun stage [15], when most plants already emerged
and were easy to identify visually. is stage is reached
approximately 10–14days after the germination for wheat
in France [3]. A total of 14 plots are thus available over the
3 sites showing contrasted conditions in terms of soil, cli-
mate, cultivars, sowing density and sowing machine, with
however a fixed row spacing of 17.5cm. All the plots were
at least 10m length and 2m width.
Image processing
A Sigma SD14 RGB camera with a resolution of 4608
by 3072 pixels was installed on a light moving platform
(Fig.1). e camera was oriented at 45° inclination per-
pendicular to the row direction and was focused on the
central row from a distance of about 1.5m (Fig.1). e
50mm focal length allowed to sample about 0.9m of the
row with a resolution at the ground level close to 0.2mm.
Images were acquired along the row with at least 30%
overlap to allow stitching. A series of 20 pictures was col-
lected that correspond to three to five rows over about
5m length. e images were stitched using AutoStitch
html) [16]. For each site, one picture was taken over a
reference chessboard put on the soil surface to calibrate
the image: the transformation matrix derived from the
chessboard image was applied to all the images acquired
within the same site. It enables to remove perspective
effects and to scale the pixels projected on the soil sur-
face. e image correction and processing afterwards
was conducted using MATLAB R2016a (code available
on request). Coordinates of the plants correspond to the
intersection between the bottom of the plant and the soil
surface (Fig. 2). ey were interactively extracted from
the photos displayed on the screen. For each of the 14
plots, the coordinates of at least 150 successive plants
from the same row were measured along (X axis) and
across (Y axis) of the row. It took between 15 to 30min to
extract the plant coordinates, depending on the density.
e precision on the coordinates values along the row is
around 1.5mm as estimated by independent replicates
of the process over the same images. Some slightly larger
deviations are observed marginally in case of occlusions
by stones or straw in the field.
e coordinates
of plant n (noted
) along the
row axis allow to compute the spacing
e actual plant density
expressed in plants per square meter horizontal ground
(plants m2) was computed simply as the number of
plants counted on the segments, divided by the product
of the length of the segments and the row spacing.
Development andcalibration ofthe plant distribution
Distribution ofplant spacing
e autocorrelation technique was used to explore the
spatial dependency of spacing between successive plants:
the linear correlation between
where m
is the lag is evaluated. Results illustrated in Fig.3 over the
Fig. 1 The moving platform used to take the images in the field in
Fig. 2 Extraction of plants’ coordinates from the image
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Page 4 of 11
Liu et al. Plant Methods (2017) 13:38
Toulouse site show that the autocorrelation coefficient of
inter-plant distance is not significant at 95% confidence
interval. e same is observed over the other 13 plots
acquired. It is therefore concluded that the positions
among plants along the row direction are independent:
each observation ∆x could be considered as one inde-
pendent realization of the random variable ∆X.
e distribution of the plant spacing is positively
right-skewed (Fig. 4). A simple exponential distribu-
tion with only one scale parameter was first tentatively
fitted to the data using a maximum likelihood method.
However, the Chi square test at the 5% significance level
showed that the majority of the 14 plots do not fol-
low this simple exponential distribution law. Weibull
and gamma distributions are both a generalization of
the exponential distribution requiring an extra shape
parameter. Results show that Weibull and gamma dis-
tributions describe well (Chi square test at the 5% sig-
nificance level successful) the empirical distributions
over the 14 plots (Fig.4; Table2). However, the gamma
distribution will be preferred since it provides generally
higher p value of Chi square test (Table2) [17]. Besides,
the tail of the Weibull distribution tends toward zero
less rapidly than that of the gamma distribution:
Weibull may show few samples with very large values
[18], increasing the risk of overestimation for the larger
plant spacing. e gamma distribution was therefore
used in the following and writes [19]:
x|a, b
where a and b represent the shape and scale param-
eters respectively. e expectancy
and variance
are simple expressions of the two parameters:
As a consequence, the coefficient of variation
is a simple function of the shape
Modeling the distribution ofthe number ofplants perrow
e plant density evaluated over row segments needs to
account for the uncertainties in row spacing. e vari-
ability of the row spacing is of the order of 10mm as
reported by [20] which corresponds to CV=6% using a
typical row spacing of 175mm. For the sake of simplic-
ity, the variability of row spacing will be neglected since
it is likely to be small. Further, it is relatively easy to get
precise row spacing measurements for each segment
and to actually account for the actual row spacing val-
ues. Considering a given row spacing, the plant density
depends only on the number of plants per unit linear row
length. Estimating the number of plants within a row seg-
ment is a count data problem analogous to the estimation
of the number of events during a specific time interval
[19, 21]. Counts are common random variables that are
assumed to be non-negative integer or continuous values
Fig. 3 The autocorrelation of the spacing among plants along the
row direction illustrated with sowing density of 300 seeds m2
observed over the Toulouse experiment. The lag is expressed as the
number of plant spacing between 2 plants along the row direction
(X axis). Lags 1–20 are presented. The upper and lower horizontal line
represent the 95% confidence interval around 0
Fig. 4 Empirical histogram of the spacing along the row (gray bars).
The solid (respectively dashed) line represents the fitted gamma (resp.
Weibull) distribution. Case of the sowing density 300 seeds m2
observed over the Toulouse experiment. a and b represent the shape
and scale parameters respectively
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Page 5 of 11
Liu et al. Plant Methods (2017) 13:38
representing the number of times an event occurs within
a given spatial or temporal domain [22]. e gamma-
count model suits well our problem with intervals inde-
pendently following a gamma distribution as in our case.
e probability,
, to get n plants over a segment
of length l, writes (Eqs.58 were cited from [19, 21]):
where N1 is the number of plants over the segment
of length l, and
n, l
is the incomplete gamma
where Γ is the gamma Euler function. e expectation
and variance of the number of plants over a segment of
length l is given by:
1IGa, l
bfor n=0
a·n, l
a·n+a, l
for n=1, 2,
a·n, l
a·n, l
(2n 1)IGa·n, l
a·n, l
Finally, the expectation and variance of the plant den-
sity, D1, estimated over a segment of length l can be
expressed by introducing the row spacing distance, r,
assumed to be known:
e expectation,
, converges toward the actual
density of the population when 1.
e transformed gamma-count model allows evaluating
the uncertainty of plant density estimation as a function
of the sampling size. e uncertainty can be characterized
by the coefficient of variation (CV) as follows:
Several combinations of values of a and b may lead to
the same plant density, but with variations in their dis-
tribution along the row (Fig.5). e fitting of parameters
a and b over the 14 plots using the transformed gamma-
count model (Eq.9) shows that the shape parameter, a,
varies from 0.96 to 1.39 and is quite stable. Conversely,
the scale parameter, b, appears to vary widely from 0.96
to 6.38, mainly controlling the plant density (Fig. 5).
Since the CV depends only on the shape parameter a
(Eq.4), it should not vary much across the 14 plots con-
sidered. is was confirmed by applying a one-way analy-
sis of variance on the CV values of the 14 plots available
(F = 1.09, P = 0.3685): no significant differences are
Table 2 Parameters ofthe tted distributions
Sites Sowing density
(seedsm2)Cultivar Gamma Weibull
a b p value ofChi
square test a b p value ofChi
square test
Avignon 100 Apache 1.14 6.38 0.27 7.44 1.07 0.29
200 Apache 1.25 4.04 0.62 5.29 1.13 0.05
300 Apache 0.99 2.53 0.38 2.51 1.00 0.56
400 Apache 0.96 1.50 0.22 1.39 0.94 0.57
Toulouse 100 Apache 1.07 5.01 0.12 5.32 0.99 0.10
200 Apache 1.39 1.95 0.17 2.86 1.15 0.12
300 Apache 1.21 2.28 0.94 2.89 1.12 0.94
400 Apache 1.24 1.37 0.51 1.76 1.10 0.40
600 Apache 1.16 0.96 0.37 1.14 1.09 0.21
Grignon 150 Premio 1.12 3.37 0.70 3.85 1.06 0.68
150 Attlass 1.13 2.48 0.69 2.87 1.05 0.67
150 Flamenko 1.11 3.3 0.92 3.75 1.05 0.92
150 Midas 1.24 3.03 0.21 3.92 1.12 0.24
150 Koréli 1.15 2.89 0.24 3.48 1.15 0.18
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Page 6 of 11
Liu et al. Plant Methods (2017) 13:38
observed. is result may be partly explained by the fact
that the same type of seed drill was used for all the three
Optimal sample size toreach a givenprecision forplant
density estimation
e transformed gamma-count model provides a con-
venient way to investigate the effect of the sampling size
on the precision of the density estimates. e precision
will be quantified here using the coefficient of varia-
tion (CV). e sample size can be expressed either as a
given length of the segments where the (variable) num-
ber of plants should be counted, or as a (variable) length
of the segment to be measured corresponding to a given
number of consecutive plants. e two alternative sam-
pling approaches will be termed FLS (Fixed Length of
Segments) for the first one, and FNP (Fixed Number of
Plants) for the second one.
When considering the FLS approach, the sample size is
defined by the length of segment, L, where plants need to
be counted. e optimal L value for a given target preci-
sion quantified by the CV will mainly depend on the cur-
rent density as demonstrated in Fig.6a: longer segments
are required for the low densities. Conversely, shorter
segments are needed for high values of the plant density
to reach the same precision. e scale parameter, b, that
controls the plant density drives therefore the optimal
segment length L (Fig.6a). Counting plants over L=5m
(500cm) provides a precision better than 10% for den-
sities larger than 150 plants·m2 for the most common
conditions characterized by a shape coefficient a >0.9.
ese figures agree well with the usual practice for plant
counting as reviewed in the introduction [3, 13, 14].
Increasing the precision quantified by the CV will require
longer segments L to be sampled (Fig.7a).
When considering the FNP approach, the sample
size is driven by the number, N, of consecutive plants
that defines to a row segment whose length need to be
Fig. 5 Relationship between parameters a and b of the gamma-
count model for a range of plant density (from Eqs. 6, 7, 9). The lines
correspond to, 100, 150, 200, 300, 400 and 600 plants m2. The dots
color corresponds to the experimental sites
Fig. 6 a The optimal sampling size length (the horizontal solid lines, the length being indicated in cm) used in the FLS approach as a function of
parameters a and b to get CV = 10% for the density estimation. b Idem as on the left but the sample is defined by the number of plants to be
counted (the vertical solid lines with number of plants indicated) for the FNP approach. The gray dashed lines correspond to the actual plant density
depending also on parameters a and b. The row spacing is assumed perfectly known and equal to 17.5 cm. The gray points represent the 14 plots
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Page 7 of 11
Liu et al. Plant Methods (2017) 13:38
measured. e simulations of the model (Fig.6b) show
that N is mainly independent from the plant density.
For the 14 plots considered in this study, segments with
70<N<110 plants should be measured to reach a pre-
cision of CV =10%. e shape parameter a influences
dominantly the sample size: more heterogeneous dis-
tribution of plants characterized by small values of the
shape parameter will require more plants to be counted
(Fig. 6b). To increase the precision (lower CV), more
plants will also need to be counted (Fig.7b).
e sampling approach FLS (Fixed Length of segments)
is extensively used to estimate the plant density. e
600cm segment length recommended by [13, 14] agrees
well with our results (Figs.6a, 7a) demonstrating that a
precision better than 10% is ensured over large range of
densities and non-uniformities. e optimal sampling
length (FSL) and optimal number of plants sampled
(FNP) was computed for other precision levels for a range
of plant densities (Table3). Results show that the FNP
method provides very stable values of the sampling size:
it is easy to propose an optimal number of consecutive
plants to count to reach a given precision. Conversely, the
optimal length of the segment used in the FSL approach
varies strongly with the plant density (Table3): the FLS
approach when applied with a segment length chosen a
priori without knowing the plant density will result in a
variable precision level.
Sampling strategy toquantify plant spacing variability
onthe row
e previous sections demonstrated that the scale and
shape parameters could be estimated from the observed
distribution of the plant spacing. However, the measure-
ment of individual plant spacing is tedious and prone to
errors as outlined earlier. e estimation of these param-
eters from the variability observed between small row
segments containing a fixed number of plants will there-
fore be investigated here. is FNP approach is preferred
Fig. 7 The optimal sampling length for the FLS approach (a) and the number of plants for the FNP approach (b). The dominant parameter is used
(the scale parameter for FLS and the shape coefficient for FNP). The precision is evaluated with the CV = 5, 10, 15 and 20%
Table 3 Optimal sampling size forFSL and FNP overdierent densities (100, 150, 200, 300, 400 and600 seeds m2)
andprecisions (5, 10 and15%)
This was calculated using the average values of the parameters a and b of the gamma distribution derived for each density over the 14 plots available
Sowing density (seedsm2) Parameters CV=5% CV=10% CV=15%
a b FSL (cm) FNP (Nb. Plt) FSL (cm) FNP (Nb. Plt) FSL (cm) FNP (Nb. Plt)
100 1.11 5.70 2478 363 620 90 250 39
150 1.15 3.01 1406 348 351 88 130 37
200 1.32 3.00 1398 308 350 78 130 33
300 1.10 2.41 1162 363 291 90 110 39
400 1.10 1.44 774 363 194 90 60 39
600 1.16 0.96 584 348 146 85 50 37
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Page 8 of 11
Liu et al. Plant Methods (2017) 13:38
here to the FSL one because there will be no additional
uncertainties introduced by the position of the first and
last plants of the segment with the corresponding start
and end of the segment. ese uncertainties may be sig-
nificant in case of small segments in the FLS approach.
e probability distribution of a gamma distribution
can be expressed as the sum of an arbitrary number of
independent individual gamma distributions [23]. is
property allows to compute the distribution of a segment
of length Ln corresponding to n plant spacing between
(n+ 1) consecutive plants with
as a
gamma distribution with n·a as shape parameter and
the same scale parameter b as the one describing the dis-
tribution of ∆X.
e parameters a and b will therefore be estimated by
adjusting the gamma model described in Eq. 12 for the
given value of n+1 consecutive plants.
e effect of the sampling size on the precision of a
and b parameters estimation was further investigated. A
numerical experiment based on a Monte-Carlo approach
was conducted considering a standard case correspond-
ing to the average of the 14 plots sampled in 2014 with
a=1.10 and b=2.27. e sampling size is defined by
the number of consecutive plants for the FNP approach
considered here and by the number of replicates. For
each sampling size 300 samples were generated by ran-
domly drawing in the gamma distribution (Eq.12) and
parameters a and b were estimated. e standard devi-
ation between the 300 estimates of a and b parameters
was finally used to compute the corresponding CV. is
process was applied to a number of replicates varying
between 20 to 300 by steps of 10 and a number of plants
per segment varying between 2 (i.e. spacing between two
consecutive plants) to 250 within 12 steps. is allows
describing the variation of the coefficient of estimated
values of parameters a and b as a function of the number
of replicates and the number of plants (Fig.8).
Results show that the sensitivity of the CV of estimates
of parameters a and b are very similar (Fig.8). e sensi-
tivity of parameters a and b is dominated by the number
of replicates: very little variation of CV is observed when
the number of plants per segment varies (Fig.8). Param-
eters a and b require about 200 replicates independently
from the number of plants per segment. It seems there-
fore more interesting to make very small segments to
decrease the total number of plants to count.
Additional investigations not shown here for the sake
of brevity, confirmed the independency of the number
of replicates to the number of plants per segment when
parameters a and b are varying. Further, the number of
replicates need to be increased as expected when the
shape parameter a decreases (i.e. when the plant spacing
is more variable) to keep the same precision on estimates
of a and b parameters.
Discussion andconclusions
A method was proposed to estimate plant density and
sowing pattern from high resolution RGB images taken
from the ground. e method appears to be much more
comfortable as compared with the standard outdoor
methods based on plant counting in the field. Images
should ideally be taken around Haun stage 1.5 for wheat
crops when most plants have already emerged and tiller-
ing has not yet started. Great attention should be paid to
the geometric correction in order to get accurate ortho-
images where distances can be measured accurately. e
processing of images here was automatic except the last
step corresponding to the interactive visual extraction
of the plants’ coordinates in the image. However, recent
work [24, 25] suggests that it will be possible to automa-
tize this last step to get a fully high-throughput method.
e method proposed is based on the modeling of
the plant distribution along the row. It was first dem-
onstrated that the plant spacing between consecutive
plants are independent which corresponds to a very
useful simplifying assumption. e distribution of plant
spacing was then proved to follow a gamma distribution.
Although the Weibull distribution showed similar good
performance, it was not selected because of the com-
paratively heavier tails of the distribution that may cre-
ate artefacts. Further the Weibull model does not allow
to simply derive the distribution law of the length of
Fig. 8 Contour plot of the CV associated to the estimates of param-
eters a (solid line) and b (dashed line) as a function of the number of
replicates of individual samples made of n plants (the y axis). The solid
(respectively dashed) isolines correspond to the CV of parameter a
(respectively parameter b). These simulations were conducted with [a,
b] = [1.10, 2.27]
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Page 9 of 11
Liu et al. Plant Methods (2017) 13:38
segments containing several consecutive plants [26]. e
gamma model needs a scale parameter that drives mostly
the intensity of the process, i.e. the plant density, and a
shape parameter that governs the heterogeneity of plant
spacing. is model was transformed into a count data
model to investigate the optimal sampling required to get
an estimate of plant density for a given precision level.
e adjustment of the gamma-count model on the
measured plant spacing using a maximum likelihood
method provides an estimate of the plant density (Eq.9).
e comparison to the actual plant density (Fig.9) sim-
ply computed as the number of plants per segment
divided by the area of the segments (segment length by
row spacing), shows a good agreement, with RMSE50
plantsm2 over the 14 plots available. e model per-
forms better for the low density with a RMSE of 21
plantsm2 for density lower than 400 plantsm2. ese
discrepancies may be mainly explained by the accuracy
in the measurement of the position of individual plants
(around 1–2 mm). Uncertainties on individual plant
spacing will be high in relative values as compared to
that associated with the measurement of the length of the
segment used in the simple method to get the ‘reference’
plant density. Hence it is obviously even more difficult to
get a good accuracy in plant spacing measurements for
high density, i.e. with a small distance among plants. In
addition, small deviations from the gamma-count model
are still possible, although the previous results were
showing very good performance.
e model proposed here concerns mainly relatively
nominal sowing, i.e. when the sowing was successful
on average on the row segments considered: portions
of rows with no plants due to sowing problems or local
damaging conditions (pests, temperature and moisture).
e sowing was considered as nominal on most of the
plots investigated in this study, with no obvious ‘acci-
dents’. However, it is possible to automatically identify
from the images the unusual row segments with missing
plants or excessive concentration of plants [25]. Rather
than describing blindly the bulk plant density, it would
be then preferred to get a nested sampling strategy: the
unusual segments could be mapped extensively, and the
plant density of nominal and unusual segments could
be described separately using the optimal sampling pro-
posed here.
is study investigated the sampling strategy to esti-
mate the plant density with emphasis on the variability of
plant spacing along the row, corresponding to the sam-
pling error. However additional sources of error should
be accounted for including measurement biases, uncer-
tainties in row spacing or non-randomness in the sample
selection [2729]. Unlike sampling error, it could not be
minimized by increasing sampling size. e non-sam-
pling error may be reduced by combining a random sam-
pling selection procedure with a measurement method
ensuring high accuracy including accounting for the
actual values of the row spacing measured over each seg-
ment [30].
Optimal sampling requires a tradeoff between mini-
mum sampling error obtained with maximum sampling
size and minimum cost obtained with minimum sam-
pling size [31]. e optimal sampling strategy should
first be designed according to the precision targeted
here quantified by the coefficient of variation (CV) char-
acterizing the relative variability of the estimated plant
density between several replicates of the sampling pro-
cedure. e term ‘optimal’ should therefore be under-
stood as the minimum sampling effort to be spent to
achieve the targeted precision. Two approaches were
proposed: the first one considers a fixed segment length
(FSL) over which the plants have to be counted; the sec-
ond one considers a fixed number of successive plants
(FNP) defining a row segment, the length of which needs
to be measured. e first method (FLS) is the one gener-
ally applied within most field experiments. However, we
demonstrated that it is generally sub-optimal: since the
segment length required to achieve a given CV depends
mainly on the actual plant density: the sampling will
be either too large for the targeted precision, or con-
versely too small, leading to possible degradation of the
precision of plant density estimates. Nevertheless, for
the plant density (>100 plantsm2) and shape param-
eter (a>0.9) usually experienced, a segment length of
6m will ensure a precision better than 10%. e second
approach (FNP) appears generally more optimal: it aims
at measuring the length of the segment corresponding to
a number of consecutive plants that will depend mainly
on the targeted precision. Results demonstrate that in
Fig. 9 Comparison between the actual density and that estimated
from the gamma-count model
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Page 10 of 11
Liu et al. Plant Methods (2017) 13:38
our conditions, the density should be evaluated over seg-
ments containing 90 plants to achieve a 10% precision.
e sampling size will always be close to optimal as com-
pared to the first approach where optimality requires the
knowledge of the plant density that is to be estimated.
Further, the FNP approach is probably more easy to
implement with higher reliability: as a matter of facts,
measuring the length of a segment defined by plants at
its two extremities is easier than counting the number of
plants in a fixed length segment, where the extremities
could be in the vicinity of a plant and its inclusion or not
in the counting could be prone to interpretation biases
by the operator. e total number of plants required
in a segment could be split into subsamples containing
smaller number of plants that will be replicated to get
the total number of plants targeted. is will improve
the spatial representativeness. Overall, the method pro-
posed meets the requirements defined by [32, 33] for
the next genearation of phenotyping tools: increase the
accuracy, the precision and the throughput while reduc-
ing the labor and budgetary costs.
e gamma-count model proved to be well suited to
describe the plant spacing distribution along the row
over our contrasted experimental situations. It can thus
be used to describe the heterogeneity of plant spacing
as suggested by [20]. is may be applied for detailed
canopy architecture studies or to quantify the impact of
the sowing pattern heterogeneity on inter-plant com-
petition [1, 2]. e heterogeneity of plant spacing may
be described by the scale and shape parameters of the
gamma model. Quantification of the heterogeneity of
plant spacing requires repeated measurements over seg-
ments defined by a fixed number of plants. Our results
clearly show that the precision on estimates of the
gamma count parameters depends only marginally on
the number of plants in each segment. Conversely, it
depends mainly on the number of segments (replicates)
to be measured. For the standard conditions experienced
in this study, the optimal sampling strategy to get a CV
lower than 10% on the two parameters of the gamma dis-
tribution would be to repeat 200 times the measurement
of plant spacing between 2 consecutive plants.
Authors’ contributions
SL and FB designed the experiment and XJ, BA, PB, MH and AC contributed
to the field measurement in different experimental sites. DA significantly
contributed to the method development. The manuscript was written by
SL and significantly improved by FB. All authors read and approved the final
Author details
1 INRA, UMR-EMMAH, UMT-CAPTE, UAPV, 228 Route de l’aérodrome CS 40509,
84914 Avignon, France. 2 UMR BioSP, INRA, UAPV, 84914 Avignon, France.
3 UMR ECOSYS, INRA, AgroParisTech, Université Paris-Saclay, 78850 Thiver-
val-Grignon, France. 4 UMR AGIR, INRA, INPT, 31326 Toulouse, France. 5 Hi-Phen,
84914 Avignon, France.
We thank the people from Grignon, Toulouse and Avignon who participated
to the experiments. Great thanks to Paul Bataillon and Jean-Michel Berceron
from UE802 Toulouse INRA for their help in field experiment. The work
was completed within the UMT-CAPTE funded by the French Ministry of
Competing interests
The authors declare that they have no competing interests.
Availability of data and materials
All data analyzed during this study are presented in this published article.
This study was supported by “Programme d’investissement d’Avenir” PHE-
NOME (ANR-11-INBS-012) and Breedwheat (ANR-10-BTR-03) with participation
of France Agrimer and “Fonds de Soutien à l’Obtention Végétale”. The grant of
the principal author was funded by the Chinese Scholarship Council.
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in pub-
lished maps and institutional affiliations.
Received: 25 September 2016 Accepted: 2 May 2017
1. Olsen J, Kristensen L, Weiner J. Influence of sowing density and spatial
pattern of spring wheat (Triticum aestivum) on the suppression of differ-
ent weed species. Weed Biol Manag. 2006;6:165–73.
2. Olsen J, Weiner J. The influence of Triticum aestivum density, sowing pat-
tern and nitrogen fertilization on leaf area index and its spatial variation.
Basic Appl Ecol. 2007;8:252–7.
3. Reynolds MP, Ortiz-Monasterio JI, McNab A. CIMMYT: application of physi-
ology in wheat breeding. Mexico: CIMMYT; 2001.
4. Van der Heijden G, De Visser PHB, Heuvelink E. Measurements for
functional-structural plant models. Frontis. 2007;22:13–25.
5. Ma Y, Wen M, Guo Y, Li B, Cournede P-H, de Reffye P. Parameter optimiza-
tion and field validation of the functional-structural model GREENLAB for
maize at different population densities. Ann Bot. 2007;101:1185–94.
6. Tang L, Tian L. Plant identification in mosaicked crop row images for
automatic emerged corn plant spacing measurement. Trans ASABE.
7. Tang L, Tian LF. Real-time crop row image reconstruction for automatic
emerged corn plant spacing measurement. Trans ASABE. 1079;2008:51.
8. Jin J, Tang L. Corn plant sensing using real-time stereo vision. J Field
Robot. 2009;26:591–608.
9. Nakarmi AD, Tang L. Automatic inter-plant spacing sensing at early
growth stages using a 3D vision sensor. Comput Electron Agric.
10. Nakarmi AD, Tang L. Within-row spacing sensing of maize plants using 3D
computer vision. Biosys Eng. 2014;125:54–64.
11. Norman DW: The farming systems approach to development and appropri-
ate technology generation. Food & Agriculture Org.; 1995.
12. Marshall MN. Sampling for qualitative research. Fam Pract. 1996;13:522–6.
13. Gate P. Ecophysiologie du blé. Paris: Tec & Doc Lavoisier; 1995.
14. Whaley JM, Sparkes DL, Foulkes MJ, Spink JH, Semere T, Scott RK. The
physiological response of winter wheat to reductions in plant density.
Ann Appl Biol. 2000;137:165–77.
15. Haun J. Visual quantification of wheat development. Agron J.
16. Brown M, Lowe DG. Automatic panoramic image stitching using invariant
features. Int J Comput Vision. 2006;74:59–73.
17. Plackett RL. Karl pearson and the Chi squared test. Int Stat Rev/Revue
Internationale de Statistique. 1983;51:59–72.
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Page 11 of 11
Liu et al. Plant Methods (2017) 13:38
We accept pre-submission inquiries
Our selector tool helps you to find the most relevant journal
We provide round the clock customer support
Convenient online submission
Thorough peer review
Inclusion in PubMed and all major indexing services
Maximum visibility for your research
Submit your manuscript at
Submit your next manuscript to BioMed Central
and we will help you at every step:
18. Papalexiou SM, Koutsoyiannis D, Makropoulos C. How extreme is
extreme? An assessment of daily rainfall distribution tails. Hydrol Earth
Syst Sci. 2013;17:851–62.
19. Winkelmann R. A count data model for gamma waiting times. Stat Pap.
20. Liu S, Baret F, Andrieu B, Abichou M, Allard D, Solan Bd, Burger P. Modeling
the distribution of plants on the row for wheat crops: consequences
on the green fraction at the canopy level. Comput Electron Agric.
21. Winkelmann R. Duration dependence and dispersion in count-data
models. J Bus Econ Stat. 1995;13:467–74.
22. Zeviani WM, Ribeiro PJ Jr, Bonat WH, Shimakura SE, Muniz JA. The
Gamma-count distribution in the analysis of experimental underdis-
persed data. J Appl Stat. 2014;41:2616–26.
23. Steutel FW, Van Harn K. Infinite divisibility of probability distributions on
the real line. Boca Raton: CRC Press; 2003.
24. Jin X, Liu S, Baret F, Hemerlé M, Comar A: Estimates of plant density from
images acquired from UAV over wheat crops at emergence. Remote Sens
Environ. 2016 (accepted).
25. Liu S, Baret F, Andrieu B, Burger P, Hemerlé M: Estimation of plant density
from high resolution RGB imagery over wheat crops. Front Plant Sci. 2016
26. Rinne H. The Weibull distribution: a handbook. Boca Raton: CRC Press;
27. Lohr S. Sampling: design and analysis. Boston: Cengage Learning; 2009.
28. Israel GD: Determining sample size. University of Florida Cooperative
Extension Service, Institute of Food and Agriculture Sciences, EDIS; 1992.
29. Särndal C-E, Swensson B, Wretman J. Model assisted survey sampling.
New York: Springer Science & Business Media; 2003.
30. Scheuren F, Association AS: What is a survey? In. American Statistical
Association; 2004.
31. Biemer PP. Total survey error: design, implementation, and evaluation.
Public Opin Q. 2010;74:817–48.
32. Cobb JN, DeClerck G, Greenberg A, Clark R, McCouch S. Next-generation
phenotyping: requirements and strategies for enhancing our under-
standing of genotype–phenotype relationships and its relevance to crop
improvement. Theor Appl Genet. 2013;126:867–87.
33. Fiorani F, Schurr U. Future scenarios for plant phenotyping. Annu Rev
Plant Biol. 2013;64:267–91.
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Terms and Conditions
Springer Nature journal content, brought to you courtesy of Springer Nature Customer Service Center GmbH (“Springer Nature”).
Springer Nature supports a reasonable amount of sharing of research papers by authors, subscribers and authorised users (“Users”), for small-
scale personal, non-commercial use provided that all copyright, trade and service marks and other proprietary notices are maintained. By
accessing, sharing, receiving or otherwise using the Springer Nature journal content you agree to these terms of use (“Terms”). For these
purposes, Springer Nature considers academic use (by researchers and students) to be non-commercial.
These Terms are supplementary and will apply in addition to any applicable website terms and conditions, a relevant site licence or a personal
subscription. These Terms will prevail over any conflict or ambiguity with regards to the relevant terms, a site licence or a personal subscription
(to the extent of the conflict or ambiguity only). For Creative Commons-licensed articles, the terms of the Creative Commons license used will
We collect and use personal data to provide access to the Springer Nature journal content. We may also use these personal data internally within
ResearchGate and Springer Nature and as agreed share it, in an anonymised way, for purposes of tracking, analysis and reporting. We will not
otherwise disclose your personal data outside the ResearchGate or the Springer Nature group of companies unless we have your permission as
detailed in the Privacy Policy.
While Users may use the Springer Nature journal content for small scale, personal non-commercial use, it is important to note that Users may
use such content for the purpose of providing other users with access on a regular or large scale basis or as a means to circumvent access
use such content where to do so would be considered a criminal or statutory offence in any jurisdiction, or gives rise to civil liability, or is
otherwise unlawful;
falsely or misleadingly imply or suggest endorsement, approval , sponsorship, or association unless explicitly agreed to by Springer Nature in
use bots or other automated methods to access the content or redirect messages
override any security feature or exclusionary protocol; or
share the content in order to create substitute for Springer Nature products or services or a systematic database of Springer Nature journal
In line with the restriction against commercial use, Springer Nature does not permit the creation of a product or service that creates revenue,
royalties, rent or income from our content or its inclusion as part of a paid for service or for other commercial gain. Springer Nature journal
content cannot be used for inter-library loans and librarians may not upload Springer Nature journal content on a large scale into their, or any
other, institutional repository.
These terms of use are reviewed regularly and may be amended at any time. Springer Nature is not obligated to publish any information or
content on this website and may remove it or features or functionality at our sole discretion, at any time with or without notice. Springer Nature
may revoke this licence to you at any time and remove access to any copies of the Springer Nature journal content which have been saved.
To the fullest extent permitted by law, Springer Nature makes no warranties, representations or guarantees to Users, either express or implied
with respect to the Springer nature journal content and all parties disclaim and waive any implied warranties or warranties imposed by law,
including merchantability or fitness for any particular purpose.
Please note that these rights do not automatically extend to content, data or other material published by Springer Nature that may be licensed
from third parties.
If you would like to use or distribute our Springer Nature journal content to a wider audience or on a regular basis or in any other manner not
expressly permitted by these Terms, please contact Springer Nature at
... During the growth season, sowing and planting densities should be similar in optimal conditions. However, poor emergence, competition for resources, extreme weather events, technical issues within sowing machinery, and pests and diseases would influence planting density over the growing period [2][3][4][5]. Moreover, plant arrangements in the field are pivotal to precise crop management, which can determine plant establishment and growth [2,3] and guide site-specific irrigation and fertilization [6,7]. ...
... However, poor emergence, competition for resources, extreme weather events, technical issues within sowing machinery, and pests and diseases would influence planting density over the growing period [2][3][4][5]. Moreover, plant arrangements in the field are pivotal to precise crop management, which can determine plant establishment and growth [2,3] and guide site-specific irrigation and fertilization [6,7]. Therefore, developing accurate, detailed, and non-destructive approaches for plant density monitoring is crucial. ...
... Plant density monitoring was traditionally based on ground counts within quadrats or segments [2]. Manually counting plants in the field is time-consuming and destructive, using support-vector-machine-based number counting. ...
Full-text available
Plant density is a significant variable in crop growth. Plant density estimation by combining unmanned aerial vehicles (UAVs) and deep learning algorithms is a well-established procedure. However, flight companies for wheat density estimation are typically executed at early development stages. Further exploration is required to estimate the wheat plant density after the tillering stage, which is crucial to the following growth stages. This study proposed a plant density estimation model, DeNet, for highly accurate wheat plant density estimation after tillering. The validation results presented that (1) the DeNet with global-scale attention is superior in plant density estimation, outperforming the typical deep learning models of SegNet and U-Net; (2) the sigma value at 16 is optimal to generate heatmaps for the plant density estimation model; (3) the normalized inverse distance weighted technique is robust to assembling heatmaps. The model test on field-sampled datasets revealed that the model was feasible to estimate the plant density in the field, wherein a higher density level or lower zenith angle would degrade the model performance. This study demonstrates the potential of deep learning algorithms to capture plant density from high-resolution UAV imageries for wheat plants including tillers.
... However, previous studies that utilized machine learning only focused on the number of plants of a single type of crop. These supervised models may not work well if they were directly migrated to another crop because plant stand counting was affected by many factors (crop type, plant size, leaf overlap, variable spacing, etc.) (Csillik et al., 2018;Jin et al., 2017;Liu et al., 2017aLiu et al., , 2017bZhao et al., 2018). When these factors change, the model needs to be re-trained, which requires extensive training data, considerable time, and space (Machefer, 2020). ...
... Zhao et al. (2018) demonstrated the same conclusion that a strong correlation existed between plant shape and number. This problem caused by the shape of plants was particularly prominent on small crops such as wheat (Liu et al., 2017a(Liu et al., , 2017b. In such cases, the supervised learning methods provide excellent counting performance (Varela et al., 2018). ...
... This may be because the template method needs high-resolution images to train maize image features and can be affected by weed in the field. Similarly, a neural network was trained to extract wheat features and count the number of plants with a relative error of 12% (Liu et al., 2017a(Liu et al., , 2017b. These methods were suitable at early growth stage when the distance between crops was large and there was no weed. ...
Full-text available
Acquiring the crop plant count is critical for enhancing field decision-making at the seedling stage. Remote sensing using unmanned aerial vehicles (UAVs) provide an accurate and efficient way to estimate plant count. However, there is a lack of a fast and robust method for counting plants in crops with equal spacing and overlapping. Moreover, previous studies only focused on the plant count of a single crop type. Therefore, this study developed a method to fast and non-destructively count plant numbers using high-resolution UAV images. A computer vision-based peak detection algorithm was applied to locate the crop rows and plant seedlings. To test the method’s robustness, it was used to estimate the plant count of two different crop types (maize and sunflower), in three different regions, at two different growth stages, and on images with various resolutions. Maize and sunflower were chosen to represent equidistant crops with distinct leaf shapes and morphological characteristics. For the maize dataset (with different regions and growth stages), the proposed method attained R2 of 0.76 and relative root mean square error (RRMSE) of 4.44%. For the sunflower dataset, the method resulted in R2 and RRMSE of 0.89 and 4.29%, respectively. These results showed that the proposed method outperformed the watershed method (maize: R2 of 0.48, sunflower: R2 of 0.82) and better estimated the plant numbers of high-overlap plants at the seedling stage. Meanwhile, the method achieved higher accuracy than watershed method during the seedling stage (2–4 leaves) of maize in both study sites, with R2 up to 0.78 and 0.91, respectively, and RRMSE of 2.69% and 4.17%, respectively. The RMSE of plant count increased significantly when the image resolution was lower than 1.16 cm and 3.84 cm for maize and sunflower, respectively. Overall, the proposed method can accurately count the plant numbers for in-field crops based on UAV remote sensing images.
... Studies also quantified plant population density. Liu et al. [15] used a mobile structure to take images of a wheat crop. They manually determined for each image the coordinates of each existent plant. ...
... To facilitate image acquisition, we recorded a video using a mobile camera with resolutions of 13 MP, 1080 P, and 30 FPS (Figure 1b). To ensure an adequate pixel spatial resolution and minimal distortions [15], a height of one meter and a perpendicular angle (90 • ) were considered as the reference. We used a level indicator from the mobile device to maintain its stability and a standardized object beside the crop row. ...
... To facilitate image acquisition, we recorded a video using a mobile camera with resolutions of 13 MP, 1080 P, and 30 FPS (Figure 1b). To ensure an adequate pixel spatial resolution and minimal distortions [15], a height of one meter and a perpendicular angle (90°) were considered as the reference. We used a level indicator from the mobile device to maintain its stability and a standardized object beside the crop row. ...
Full-text available
Assessing planting to ensure well-distributed plants is important to achieve high yields. Digital farming has been helpful in these field assessments. However, these techniques are at most times not available for smallholder farmers or low-income regions. Thus, to contribute such producers, we developed two methods to assess intra-row spacing in commercial fields using mobile photos and simple image processing. We assessed a maize field after mechanized planting in 7 and 12 days after planting (DAP) and in two farming systems (conventional and no-till) to acquire images at height of one meter and perpendicular to the ground. In the first method, we used morphological operations based on the HSV scale and the center of mass to extract the region of interest (ROI) corresponding to the maize plant. In the second method, we used local maxima equations (Peaks) to find prominence values corresponding to the maize plant and extract their coordinates. No-till images were deleted due to excessive weeds. Thus, before acquiring the images, it is necessary to remove these elements (e.g., no-till adapted). The methods achieved an overall RMSE of 3.48 cm (<5.63 cm) and R² of 0.90 (>0.71) between the actual and estimated spacing. Precision and recall were higher than 0.88. There was no difference between actual and estimated CV values, except in conventional tillage in 7 DAP using ROI due to leaves overlapping. The method Peaks was more accurate to detect multiple spacing but miss spacing was correctly detected in both methods. However, the larger the plant leaves, the worse the detection. Thus, our proposed methods were satisfactory and are promising for assessing planting in a remote and accessible way.
... Estimation of seedling number before tillering is the basis for reflecting the size of the population. The researchers obtain visible color images through the UAVs or cameras and use image processing and deep learning technology to quickly obtain the number of wheat seedlings from images to provide primary data for farmland management Liu et al., 2017). These methods target the beginning of wheat population generation and are the first step in population size analysis, but they cannot calculate the tiller number after tiller formation. ...
Full-text available
Wheat (Triticum aestivum L.) is an essential crop that is widely consumed globally. The tiller density is an important factor affecting wheat yield. Therefore, it is necessary to measure the number of tillers during wheat cultivation and breeding, which requires considerable labor and material resources. At present, there is no effective high-throughput measurement method for tiller number estimation, and the conventional tiller survey method cannot accurately reflect the spatial variation of wheat tiller density within the whole field. Therefore, in order to meet the demand for the thematic map of wheat tiller density at the field scale for the variable operation of nitrogen fertilizer, the multispectral images of wheat in Feekes growth stages 2–3 were obtained by unmanned aerial vehicle (UAV), and the characteristic parameters of the number of tillers were used to construct a model that could accurately estimate the number of tillers. Based on the vegetation index (VIs), this work proposed a gradual change features (GCFs) approach, which can greatly improve the disadvantages of using VIs to estimate tiller number, better reflect the tiller status of the wheat population, and have good results on the estimation of tiller in common models. A Lasso + VIs + GCFs method was constructed for accurate estimation of tiller number in multiple growth periods and fertilizer-treated wheat, with an average RMSE of fewer than 9 tillers per square meter, average MAE less than 8 tillers per square meter, and R² above 0.7. The results of the study not only proposed a high-throughput measurement method for the number of tillers but also provided a reference for the estimation of tiller number and other agronomic parameters.
... It is determined by counting the number of individuals of a species in uniformly sized sample plots within a site (Carvalho & Batalha, 2013;Gadow & Klotze, 2014). Density data are used to monitor the effect of various land use treatments, such as plant survival following burning or herbicide application, particularly for woody species (Miller & Miller, 2004;Liu et al., 2017). Minden et al (2016) reported that local management is an important driver of species density across a particular landscape. ...
Full-text available
The tree species density and basal area form structural and functional variables of healthy forest ecosystems. Tree density and basal area are among useful parameters for management of natural forest resources. A study was carried out in Image Forest Reserve (IFR) in 2019 to determine tree species density and basal area. A total of 170 plots measuring 20 m x 40 m were set along the land cover types at an interval of 250 m from each other. Trees with a diameter at breast height (DBH - cm) ≥ 5 cm were measured for their DBH at a height of 1.3 m from ground level and used to calculate the basal area (BA) (m2). The tree individuals were used to calculate the density (D). The largest basal area was recorded from forest cover (13 279 m2 ha-1), followed by woodland (4394.09 m2 ha-1), and wooded grassland was the least). The minimum BA was recorded from woodland, while the largest was from forest (6.881 m2 ha-1). In all land cover types the DBH class (cm) >40 cm had the largest BA. Woodland had the highest density of all other land cover types, followed by forest and wooded grassland was the least. The maximum density was recorded from woodland followed by forest and wooded grassland
... It is then possible to access a few phenological events such as heading [110] or flowering [97], and to describe the dynamics of canopy structure as a proxy of functional traits. The use of simple models or more sophisticated ones [101,107,111,112] offers great potential for providing breeders with new insights into the functioning of the crop. This will be the focus of future investigations where crop functioning models are combined with high-throughput phenotyping observations to tune model parameters that describe the reaction of the crop to environmental factors. ...
Full-text available
There is currently a strong societal demand for sustainability, quality, and safety in bread wheat production. To address these challenges, new and innovative knowledge, resources, tools, and methods to facilitate breeding are needed. This starts with the development of high throughput genomic tools including single nucleotide polymorphism (SNP) arrays, high density molecular marker maps, and full genome sequences. Such powerful tools are essential to perform genome-wide association studies (GWAS), to implement genomic and phenomic selection, and to characterize the worldwide diversity. This is also useful to breeders to broaden the genetic basis of elite varieties through the introduction of novel sources of genetic diversity. Improvement in varieties particularly relies on the detection of genomic regions involved in agronomical traits including tolerance to biotic (diseases and pests) and abiotic (drought, nutrient deficiency, high temperature) stresses. When enough resolution is achieved, this can result in the identification of candidate genes that could further be characterized to identify relevant alleles. Breeding must also now be approached through in silico modeling to simulate plant development, investigate genotype × environment interactions, and introduce marker–trait linkage information in the models to better implement genomic selection. Breeders must be aware of new developments and the information must be made available to the world wheat community to develop new high-yielding varieties that can meet the challenge of higher wheat production in a sustainable and fluctuating agricultural context. In this review, we compiled all knowledge and tools produced during the BREEDWHEAT project to show how they may contribute to face this challenge in the coming years.
... The stalk count was 30 times faster and the stalk width measurement was 270 times faster compared to previous work. Consequently, Liu et al. [16] proposed a gamma count model to determine wheat crop planting density and quantify the plant spacing heterogeneity. Wu et al. [17] proposed an efficient method that used computer vision to count rice seedlings in digital images. ...
Full-text available
In recent years complex food security issues caused by climatic changes, limitations in human labour, and increasing production costs require a strategic approach in addressing problems. The emergence of artificial intelligence due to the capability of recent advances in computing architectures could become a new alternative to existing solutions. Deep learning algorithms in computer vision for image classification and object detection can facilitate the agriculture industry, especially in paddy cultivation, to alleviate human efforts in laborious, burdensome, and repetitive tasks. Optimal planting density is a crucial factor for paddy cultivation as it will influence the quality and quantity of production. There have been several studies involving planting density using computer vision and remote sensing approaches. While most of the studies have shown promising results, they have disadvantages and show room for improvement. One of the disadvantages is that the studies aim to detect and count all the paddy seedlings to determine planting density. The defective paddy seedlings’ locations are not pointed out to help farmers during the sowing process. In this work we aimed to explore several deep convolutional neural networks (DCNN) models to determine which one performs the best for defective paddy seedling detection using aerial imagery. Thus, we evaluated the accuracy, robustness, and inference latency of one- and two-stage pretrained object detectors combined with state-of-the-art feature extractors such as EfficientNet, ResNet50, and MobilenetV2 as a backbone. We also investigated the effect of transfer learning with fine-tuning on the performance of the aforementioned pretrained models. Experimental results showed that our proposed methods were capable of detecting the defective paddy rice seedlings with the highest precision and an F1-Score of 0.83 and 0.77, respectively, using a one-stage pretrained object detector called EfficientDet-D1 EficientNet.
Bezelye, birçok ülkede kaba yem, kuru ot, silaj, haylaj veya saman şeklinde geviş getiren hayvanlar için üretilen bir yemdir. Sıra aralıklarını farklılaştırmak, tarla bitkileri üretiminde özellikle ışık ve biyokütle için olan rekabeti ve kaynak kullanımını etkileyen farklı mekansal düzenlemeler sağlar. Bu çalışmanın amacı, bezelyede (Pisum sativum L., c.v. Özkaynak) sıra aralığının kuru ot verimi ve kalitesi ile ilişkisini değerlendirmektir. Çalışma, 2018-2019 ve 2019-2020 yetiştirme sezonlarında Türkiye'nin Güney Anadolu Bölgesi'nde Mardin ili Kızıltepe ilçesine bağlı Köprübaşı köyünde gerçekleştirilmiştir. Farklı sıra arası mesafelerinin (SAM) (20, 30 ve 40 cm) bezelye verim ve kalitesine etkisi araştırılmıştır. Bitki boyu 20 cm SAM için yüksek (127,8 cm) ve 30 ve 40 cm SAM için düşük (sırasıyla 121,8 cm ve 121,2 cm) olmuştur . Yeşil ot verimi, 40 cm SAM için düşük (26,7 t/ha) ve 20 cm SAM için yüksek (28,8 t/ha) bulunmuştur. Kuru ot verimi, 40 cm SAM için düşük (5,21 t/ha) ve 20 cm SAM için yüksek (5,79 t/ha) olmuştur. Ham protein oranı 40 cm SAM'ler için düşük (%20,2) ve 20 cm SAM'ler için yüksek (%22,5 ve %21,6) tespit edilmiştir. Sindirilebilir kuru madde oranı, 20 cm SAM için düşük (2,67) ve 30 cm SAM için yüksek (2,83 ve 2,82) olmuştur. Nispi yem değeri, sırasıyla 20 cm SAM için düşük (129,9) ve 30 cm SAM için yüksek (139,1 ve 139,7) idi. Çalışmanın sonucunda, Türkiye Mardin koşullarında ticari satış hedefleyen yem üreticileri için 20 cm sıra arası mesafesi önerilebilir ki daha yüksek yeşil ot, kuru ot verimi ve ham protein oranları nedeniyle daha fazla gelir elde etmek bu sıra arası mesafe ile mümkündür. Ancak kendi çiftlik hayvanları için yem üreten çiftçiler için, yüksek kuru madde tüketim oranı ve nispi yem değerleri nedeniyle, 30 ve 40 cm sıra arası mesafe, en uygun ekim sıklığıdır.
Cotton (Gossypium hirsutum L.) is an important cash crop and primary materials for clothing, fine paper, animal feed, and oil industries. Cotton production is affected by a combination effect of crop varieties, environment, and management. Precision agriculture technology has shown great potential to improve cotton production with sufficient high-resolution spatiotemporal data of soil, environment, and cotton development from seedling to harvest. The advances in unmanned aerial vehicles (UAVs), computer vision, and remote and proximal sensing technologies make it possible to scan large-scale field efficiently and quantify crop development. The big data analytics enabled by artificial intelligence (AI) have significantly increased the capacity in processing and analyzing complex data to quantify the interactions of environment and management on crop growth and yield. This chapter aims to summarize UAV applications in cotton production, focusing on field scouting and decision making, such as stand count, growth monitoring, and yield prediction, under different soil, weather conditions, and irrigation management. Meanwhile, the potentials and challenges of using UAV technologies in cotton production are also discussed.KeywordsUAV imagingRemote sensingField managementCrop emergenceGrowth monitoringYield prediction
Full-text available
Quantification of interactions of soil conditions, plant available water and weather conditions on crop development and production is the key for optimizing field management to achieve optimal production. The goal of this study was to quantify the effects of soil and weather conditions on cotton development and production using temporal aerial imagery data, weather and soil apparent electrical conductivity (ECa) of the field. Soil texture, i.e., percent of sand and clay content, was calculated from ECa to estimate three soil quality indicators, including field capacity, wilting point and total available water. A water stress coefficient Ks was calculated using soil texture and weather data. Image features of canopy size and vegetation indices (VIs) were extracted from unmanned aerial vehicle (UAV)-based multispectral images at three growth stages of cotton in 2018 and 2019. Pearson correlation (r), analysis of variance (ANOVA) and eXtreme Gradient Boosting (XGBoost) were used to quantify the relationships between crop response derived from UAV images and environments (soil texture and weather). Results showed that soil clay content in shallower layers (0–0.4 m) affected crop development in earlier growth stages (June and July) while those in deeper layers (0.4–0.7 m) affected the later-season growth stages (August and September). Soil clay content at 0.4–0.7 m had a higher impact on crop development when water inputs were not sufficient, while Ks features had a higher contribution to the prediction of crop growth when irrigation was applied and water stress was less.
Full-text available
The upper part of a probability distribution, usually known as the tail, governs both the magnitude and the frequency of extreme events. The tail behaviour of all probability distributions may be, loosely speaking, categorized into two families: heavy-tailed and light-tailed distributions, with the latter generating "milder" and less frequent extremes compared to the former. This emphasizes how important for hydrological design it is to assess the tail behaviour correctly. Traditionally, the wet-day daily rainfall has been described by light-tailed distributions like the Gamma distribution, although heavier-tailed distributions have also been proposed and used, e.g., the Lognormal, the Pareto, the Kappa, and other distributions. Here we investigate the distribution tails for daily rainfall by comparing the upper part of empirical distributions of thousands of records with four common theoretical tails: those of the Pareto, Lognormal, Weibull and Gamma distributions. Specifically, we use 15 029 daily rainfall records from around the world with record lengths from 50 to 172 yr. The analysis shows that heavier-tailed distributions are in better agreement with the observed rainfall extremes than the more often used lighter tailed distributions. This result has clear implications on extreme event modelling and engineering design.
Full-text available
Event counts are response variables with non-negative integer values representing the number of times that an event occurs within a fixed domain such as a time interval, a geographical area or a cell of a contingency table. Analysis of counts by Gaussian regression models ignores the discreteness, asymmetry and heterocedasticity and is inefficient, providing unrealistic standard errors or possibily negative predictions of the expected number of events. The Poisson regression is the standard model for count data with underlying assumptions on the generating process which may be implausible in many applications. Statisticians have long recognized the limitation of imposing equidispersion under the Poisson regression model. A typical situation is when the conditional variance exceeds the conditional mean, in which case models allowing for overdispersion are routinely used. Less reported is the case of underdispersion with fewer modelling alternatives and assessments available in the literature. One of such alternatives, the Gamma-count model, is adopted here in the analysis of an agronomic experiment designed to investigate the effect of levels of defoliation on different phenological states upon the number of cotton bolls. Results show improvements over the Poisson model and the semiparametric quasi-Poisson model in capturing the observed variability in the data. Estimating rather than assuming the underlying variance process lead to important insights into the process.
This work investigates the spatial distribution of wheat plants and its consequences on the canopy structure. A set of RGB images were taken from nadir on a total 14 plots showing a range of sowing densities, cultivars and environmental conditions. The coordinates of the plants were extracted from RGB images. Results show that the distance between-plants along the row follows a gamma distribution law, with no dependency between the distances. Conversely, the positions of the plants across rows follow a Gaussian distribution, with strongly interdependent. A statistical model was thus proposed to simulate the possible plant distribution pattern. Through coupling the statistical model with 3D Adel-Wheat model, the impact of the plant distribution pattern on canopy structure was evaluated using emerging properties such as the green fraction (GF) that drives the light interception efficiency. Simulations showed that the effects varied over different development stages but were generally small. For the intermediate development stages, large zenithal angles and directions parallel to the row, the deviations across the row of plant position increased the GF by more than 0.1. These results were obtained with a wheat functional-structural model that does not account for the capacity of plants to adapt to their local environment. Nevertheless, our work will extend the potential of functional-structural plant models to estimate the optimal distribution pattern for given conditions and subsequently guide the field management practices.
Image processing algorithms for individual corn plant and plant stem center identification were developed. These algorithms were applied to mosaicked crop row image for automatically measuring corn plant spacing at early growth stages. These algorithms utilized multiple sources of information for corn plant detection and plant center location estimation including plant color, plant morphological features, and the crop row centerline. The algorithm was tested over two 41 m (134.5 ft) long corn rows using video acquired two times in both directions. The system had a mean plant misidentification ratio of 3.7%. When compared with manual plant spacing measurements, the system achieved an overall spacing error (RMSE) of 1.7 cm and an overall R 2 of 0.96 between manual plant spacing measurement and the system estimates. The developed image processing algorithms were effective in automated corn plant spacing measurement at early growth stages. Interplant spacing errors were mainly due to crop damage and sampling platform vibration that caused mosaicking errors. © 2008 American Society of Agricultural and Biological Engineers.
In-field variations in corn plant spacing and population can lead to significant yield differences. To minimize these variations, seeds should be placed at a uniform spacing during planting. Since the ability to achieve this uniformity is directly related to planter performance, intensive field evaluations are vitally important prior to design of new planters and currently the designers have to rely on manually collected data that is very time consuming and subject to human errors. A machine vision-based emerged crop sensing system (ECSS) was developed to automate corn plant spacing measurement at early growth stages for planter design and testing engineers. This article documents the first part of the ECSS development, which was the real-time video frame mosaicking for crop row image reconstruction. Specifically, the mosaicking algorithm was based on a normalized correlation measure and was optimized to reduce the computational time and enhance the frame connection accuracy. This mosaicking algorithm was capable of reconstructing crop row images in real-time while the sampling platform was traveling at a velocity up to 1.21 m s -1 (2.73 mph). The mosaicking accuracy of the ECSS was evaluated over three 40 to 50 m long crop rows. The ECSS achieved a mean distance measurement error ratio of -0.11% with a standard deviation of 0.74%. © 2008 American Society of Agricultural and Biological Engineers.
Pearson's paper of 1900 introduced what subsequently became known as the chi-squared test of goodness of fit. The terminology and allusions of 80 years ago create a barrier for the modern reader, who finds that the interpretation of Pearson's test procedure and the assessment of what he achieved are less than straightforward, notwithstanding the technical advances made since then. An attempt is made here to surmount these difficulties by exploring Pearson's relevant activities during the first decade of his statistical career, and by describing the work by his contemporaries and predecessors which seem to have influenced his approach to the problem. Not all the questions are answered, and others remain for further study. /// La communication de Pearson en 1900 présentait ce que ultérieurement est devenu l'épreuve de Chi-carré d'excellence d'ajustement. La terminologie et les allusions d'il y a quatre-vingt ans créent une barrière pour le lecteur moderne, qui trouve que l'interpretation du procédure de l'épreuve de Pearson et la détermination de ce qu'il a achevé ne sont pas très nettes en dépit des avances techniques qui ont été faites depuis lors. Ici j'ai fait un effort de surmonter ces difficultés par les moyens de l'exploration des activités pertinantes de Pearson pendant la premiere décade de sa carrière en statistiques, et de la description du travail de ses contemporains et prédécesseurs qui semble avoir eu une influence sur son approche au problème. Je n'ai pas eu une réponse à toutes les questions, et il y en a d'autres qui resteront pour une étude ultérieure.
Within-row plant spacing plays an important role in uniform distribution of water and nutrients among plants which affects the final crop yield. While manual in-field measurements of within-row plant spacing is time and labour intensive, little work has been done on an alternative automated process. We have attempted to develop an automatic system making use of a state-of-the-art 3D vision sensor that accurately measures within-row maize plant spacing. Misidentification of plants caused by low hanging canopies and doubles were reduced by processing multiple consecutive images at a time and selecting the best inter-plant distance calculated. Based on several small scale experiments in real fields, our system has been proven to measure the within-row maize plant spacing with a mean and standard deviation error of 1.60 cm and 2.19 cm, and a root mean squared error of 2.54 cm, respectively.
The total survey error (TSE) paradigm provides a theoretical framework for optimizing surveys by maximizing data quality within budgetary constraints. In this article, the TSE paradigm is viewed as part of a much larger design strategy that seeks to optimize surveys by maximizing total survey quality; i.e., quality more broadly defined to include user-specified dimensions of quality. Survey methodology, viewed within this larger framework, alters our perspectives on the survey design, implementation, and evaluation. As an example, although a major objective of survey design is to maximize accuracy subject to costs and timeliness constraints, the survey budget must also accommodate additional objectives related to relevance, accessibility, interpretability, comparability, coherence, and completeness that are critical to a survey's “fitness for use.” The article considers how the total survey quality approach can be extended beyond survey design to include survey implementation and evaluation. In doing so, the “fitness for use” perspective is shown to influence decisions regarding how to reduce survey error during design implementation and what sources of error should be evaluated in order to assess the survey quality today and to prepare for the surveys of the future.