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<reference>
agriculture
Article

WG-3D: A Low-Cost Platform for High-Throughput
Acquisition of 3D Information on Wheat Grain
Wei Wu 1 , Yuanyuan Zhao 2,3 , Hui Wang 4 , Tianle Yang 2,3 , Yanan Hu 1 , Xiaochun Zhong 1, *, Tao Liu 2,3, *,
Chengming Sun 2,3 , Tan Sun 1 and Shengping Liu 1, *
1

2

3

4

*

Citation: Wu, W.; Zhao, Y.; Wang, H.;
Yang, T.; Hu, Y.; Zhong, X.; Liu, T.;
Sun, C.; Sun, T.; Liu, S. WG-3D: A
Low-Cost Platform for
High-Throughput Acquisition of 3D
Information on Wheat Grain.
Agriculture 2022, 12, 1861. https://
doi.org/10.3390/agriculture12111861
Academic Editor: Domenico Pignone

Key Laboratory of Agricultural Blockchain Application, Ministry of Agriculture and Rural Affairs,
Agricultural Information Institute, Chinese Academy of Agricultural Sciences, Beijing 100081, China
Jiangsu Key Laboratory of Crop Genetics and Physiology, Jiangsu Key Laboratory of Crop Cultivation and
Physiology, Agricultural College of Yangzhou University, Yangzhou 225009, China
Jiangsu Co-Innovation Center for Modern Production Technology of Grain Crops, Yangzhou University,
Yangzhou 225009, China
Lixiahe Institute of Agricultural Sciences of Jiangsu, Key Laboratory of Wheat Biology and Genetic
Improvement for Low & Middle Yangtze Valley, Ministry of Agriculture and Rural Affairs,
Yangzhou 225012, China
Correspondence: zhongxiaochun@caas.cn (X.Z.); tliu@yzu.edu.cn (T.L.); liushengping@caas.cn (S.L.)

Abstract: The three-dimensional (3D) morphological information of wheat grains is an important
parameter for discriminating seed health, wheat yield, and wheat quality. High-throughput acquisition of 3D indicators of wheat grains is of great importance for wheat cultivation management,
genetic breeding, and economic value. Currently, the 3D morphology of wheat grains still relies
on manual investigation, which is subjective, inefficient, and poorly reproducible. The existing 3D
acquisition equipment is complicated to operate and expensive, which cannot meet the requirements
of high-throughput phenotype acquisition. In this paper, an automatic, economical, and efficient
method for the 3D morphometry of wheat grain is proposed. A line laser binocular camera was used
to obtain high-quality point-cloud data. A wheat grain 3D model was constructed by point-cloud
segmentation, finding, clustering, projection, and reconstruction. Based on this, 3D morphological
indicators of wheat grains were calculated. The results show that the root mean square error (RMSE)
and mean absolute percentage error (MAPE) of the length were 0.2256 mm and 2.60%, the width,
0.2154 mm and 5.83%, the thickness, 0.2119 mm and 5.81%, and the volume, 1.7740 mm3 and 4.31%.
The scanning time was around 12 s and the data processing time was around 3.18 s under a scanning
speed of 25 mm/s. This method can achieve the high-throughput acquisition of the 3D information
of wheat grains, and it provides a reference for in-depth study of the 3D morphological indicators of
wheat and other grains.

Received: 7 August 2022
Accepted: 3 November 2022

Keywords: wheat grain; binocular camera; 3D point cloud; high throughput; phenotype

Published: 5 November 2022
Publisher’s Note: MDPI stays neutral
with regard to jurisdictional claims in
published maps and institutional affiliations.

Copyright: © 2022 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/

1. Introduction
Wheat is one of the most important foods for humans and the most popular ingredient
for bread. Wheat for bread alone accounts for 20% of the world’s calorie consumption [1].
As the “chip of agriculture”, the seed is the key to produce more and better food on limited
arable land. A complete and healthy wheat grain can yield more and better flour, which in
turn affects people’s consumption. The morphological characteristics of wheat grains are
not only important evaluation indicators of grains’ morphological quality and important
indicators of wheat processing quality but also important evaluation criteria for wheatgrain grading. Studies have shown that wheat-grain size and traits are closely related
to wheat flour production and yield [2,3]. Wheat-grain morphological characteristics are
important markers to distinguish different kinds of wheat, and they have become the

4.0/).

Agriculture 2022, 12, 1861. https://doi.org/10.3390/agriculture12111861

https://www.mdpi.com/journal/agriculture

Agriculture 2022, 12, 1861

2 of 18

preferred parameter to identify wheat quality. This is an important reference for wheat
cultivation management, genetic breeding, and economic value determination.
The morphological traits of wheat grains include the size and shape of the grain,
which are usually measured with vernier calipers. Farmers generally prefer to grow wheat
varieties with larger grains, as larger grains are beneficial for vigor in the seedling stage
of wheat and can promote yield growth [4]. At the same time, wheat grain morphology
also affects milling quality. Stronger kernels result in more and better flour, which in turn
affects people’s consumption. Hence, breeders have turned to very early wheat-grain
characterization [5]. Many previous studies have shown that quantitative trait loci (QTL)
for grain morphological traits are distributed on all 21 chromosomes in wheat [6]. The
chromosomal locations of QTL for grain length, grain width, and grain thickness have also
been identified [7–10]. Wheat grain weight is one of the yield components and a typical
quantitative trait controlled by microeffective polygenes. The weight consists of basic
elements such as grain length, grain width, and grain thickness [11]. Wheat-grain length,
width, and thickness show a highly significant positive correlation with grain weight [12].
Wheat-grain morphology is not only an important factor in determining grain weight
but also closely related to wheat quality [13], which determines the market grading and
commercial value of wheat [14]. Therefore, mining stable QTL controlling wheat grain
morphological traits in different genetic backgrounds is important for wheat yield and
quality breeding and an important goal for wheat genetic improvement. Therefore, the
rapid acquisition of high-throughput phenotypic morphological traits in wheat grains is
particularly important.
Conventional methods for manual assessment of grain quality are challenging even
for trained personnel because the effects of grain and environment cause changes in
visual characteristics [15]. Moreover, these methods are highly subjective, inefficient,
and poorly reproducible, with unreliable evaluation results and difficulty in obtaining
accurate quantitative data [16]. Along with the increasing level of information technology,
the advantages of rapid, nondestructive, and high-throughput measurement of grain
morphology based on computer vision technology are becoming increasingly significant
compared with the traditional manual measurement. Machine vision [17], near-infrared
spectroscopy [18], electronic sensors [19], infrared spectroscopy [20], X-ray techniques [21],
and hyperspectral imaging [22] are examples of such techniques. The associated studies
usually target two-dimensional (2D) morphological information and are mostly applied in
taxonomic classification (species classification) [23–26]. Compared with the 2D space, the
three-dimensional (3D) space has more valuable parameters, and scientists have started to
turn to the study of high-throughput phenotypic information acquisition methods for 3D
models in recent years. For example, Qian et al. [27] used high-resolution 3D point-cloud
data of rice obtained by laser scanning technology to reconstruct the 3D morphology of rice
and obtained several morphological characteristics parameters, such as volume and surface
area of rice. 3D technology was also applied to the classification of rice organs [28], panicle
segmentation [29,30], and leaf-size measurement [31]. However, there are few studies on
high-throughput acquisition methods for 3D morphological parameters of wheat grains.
Sun et al. [32] used stereo vision techniques to find out the thickness of wheat grains and to
detect the presence of wrinkles in wheat grain samples, but their measurement index is too
single to meet the standard of high-throughput acquisition.
In this paper, we present an automatic, cost-effective, and efficient method for a 3D
model of wheat grains (WG-3D). We made a high-quality point-cloud data acquisition
device by combining laser and binocular camera. The point-cloud data were also acquired
with the help of an automated operation platform. Point-cloud segmentation, finding,
clustering, projection, and reconstruction methods were used to realize the construction of
a 3D model of grains. The high-throughput morphological characteristics of wheat grains
were obtained based on the 3D grain model. Indicators such as length, width, thickness,
and volume were used to verify the accuracy of the 3D model.

Agriculture 2022, 12, x FOR PEER REVIEW

Agriculture 2022, 12, 1861

3 of 18

grains were obtained based on the 3D grain model. Indicators such as length, width, thickness, and volume were used to verify the accuracy of the 3D model.
3 of 18
2. Materials and Methods
Experimental
Materials
2.2.1.
Materials
and Methods
materials
used in the experiment were the Yangmai series varieties developed
2.1. The
Experimental
Materials
and The
supplied
by
the
Institute
Agriculturalwere
Science
Lixiahe,series
Jiangsu
Province,
China.
materials used
in theofexperiment
the in
Yangmai
varieties
developed
The
test
materials
were
divided
into
two
groups
according
to
different
experimental
purand supplied by the Institute of Agricultural Science in Lixiahe, Jiangsu Province, China.
poses.
The
first
group
was
a
validation
experiment,
which
included
three
varieties,
The test materials were divided into two groups according to different experimental purnamely
Zhenmai
No.was
9, Yangmai
No. experiment,
23, and Ningmai
13, each
with
100 randomly
poses.
The
first group
validation
whichNo.
included
three
varieties,
namely
selected
grains.
The
second
group
was
a
test
experiment
and
comprised
26
varieties
of
Zhenmai No. 9, Yangmai No. 23, and Ningmai No. 13, each with 100 randomly selected
Yangmai
series
(Table
1),
and
40
grains
from
each
variety
were
randomly
selected.
Figure
grains. The second group was a test experiment and comprised 26 varieties of Yangmai
1 shows
the images
wheat
grains
different
Yangmai
series
varieties.
series
(Table
1), and of
40 the
grains
from
eachofvariety
were
randomly
selected.
Figure 1 shows

the images of the wheat grains of different Yangmai series varieties.
Table 1. Yangmai series variety name and abbreviation.

Table
1. Yangmai series variety name
and abbreviation.
Variety
Abbreviation
Variety

Yangmai No.1
Variety
Yangmai No.2
Yangmai No.1
Yangmai No.3
Yangmai No.2
Yangmai
No.4
Yangmai No.3
Yangmai
No.5
Yangmai No.4
Yangmai No.5
Yangmai
No.6
Yangmai
No.6
Yangmai No.10
Yangmai No.10
Yangmai No.11
Yangmai No.11
Yangmai
No.12
Yangmai No.12
Yangmai
No.13
Yangmai No.13
Yangmai No.14
Yangmai
No.14
Yangmai No.15
Yangmai
No.15
Yangmai No.16
Yangmai No.16

Y 1#
Y 2#
Y 1#
Y 3#
Y 2#
Y 4#
Y 3#
YY
4# 5#
YY
5# 6#
Y 6#
Y 10#
Y 10#
Y 11#
Y 11#
Y 12#
Y 12#
YY
13#13#
Y 14#
Y 14#
Y 15#
Y 15#
Y 16#
Y 16#

Abbreviation

Yangmai No.17
Variety
Yangmai No.18
Yangmai No.17
Yangmai No.19
Yangmai No.18
Yangmai
YangmaiNo.20
No.19
Yangmai
YangmaiNo.21
No.20
YangmaiNo.22
No.21
Yangmai
Yangmai
No.22
Yangmai No.23
Yangmai No.23
Yangmai No.24
Yangmai No.24
Yangmai
YangmaiNo.25
No.25
Yangmai
YangmaiNo.26
No.26
YangmaiNo.27
No.27
Yangmai
Yangmai
No.28
Yangmai No.28
Yangmai 158
Yangmai 158

Abbreviation
Y 17#
Abbreviation
Y 18#
Y 17#
Y 19#
Y 18#
20#
YY19#
21#
YY20#
YY21#
22#
YY22#
23#
Y 23#
Y 24#
Y 24#
25#
YY25#
26#
YY26#
YY27#
27#
YY28#
28#
Y 158
Y 158

Figure1.1.Wheat
Wheat grains
grains of
of different
different Yangmai
Yangmai series
series varieties.
varieties.
Figure

2.2. Experimental Device
This study used a high-quality wide-field stereo camera (VZ-JGY-1300G-120M6, working distance: 20 cm; lens parameters: 6 mm–1/1.8”–120 mm) manufactured by Beijing
Weijing Intelligent Technology Co., (Beijing, China). It adopts line laser binocular stereo
vision technology system to acquire 3D spatial information through the binocular parallax
principle. The infrared laser is designed to be invisible. It is primarily designed to perform
auxiliary positioning to assist the intelligent binocular stereo camera in extracting only 3D

Agriculture 2022, 12, 1861

working distance: 20 cm; lens parameters: 6 mm–1/1.8″–120 mm) manufactured by Beijing
Weijing Intelligent Technology Co., (Beijing, China). It adopts line laser binocular stereo
vision technology system to acquire 3D spatial information through the binocular parallax
principle. The infrared laser is designed to be invisible. It is primarily designed to perform
4 of 18
auxiliary positioning to assist the intelligent binocular stereo camera in extracting only 3D
data from all points on the laser, thus excluding external light interference. The computer
configuration was as follows: 64-bit Windows 7 Professional operating system, Intel (R)
data from all points on the laser, thus excluding external light interference. The computer
Core
(TM) i5-7400
3.00
processor,
8 GB RAM,
120 GB (SSD)
hardsystem,
disk, and
Intel
configuration
was
as GHz
follows:
64-bit Windows
7 Professional
operating
Intel
(R) HD
Graphics
630
graphics
card.
Figure
2
shows
the
3D
point-cloud
acquisition
platform.
Core (TM) i5-7400 3.00 GHz processor, 8 GB RAM, 120 GB (SSD) hard disk, and Intel HD
Graphics 630 graphics card. Figure 2 shows the 3D point-cloud acquisition platform.

(a)

(b)

Figure
2. Wheat
graingrain
3D point-cloud
acquisition
platform.
(a) Overview
of theof
platform;
(b) binocFigure
2. Wheat
3D point-cloud
acquisition
platform.
(a) Overview
the platform;
ular(b)
camera.
binocular camera.

Grain
Point
Cloud
ProcessingPipeline
Pipeline
2.3. 2.3.
Grain
Point
Cloud
Processing
overall
processingpipeline
pipeline of
of the
is shown
in Figure
3. It 3. It
TheThe
overall
processing
the grain
grainpoint
pointcloud
cloud
is shown
in Figure
mainly includes 5 steps: point-cloud acquisition, point-cloud preprocessing, single-grain
mainly includes 5 steps: point-cloud acquisition, point-cloud preprocessing, single-grain
point-cloud extraction, 3D model construction, and 3D morphological feature calculation.

point-cloud extraction, 3D model construction, and 3D morphological feature calculation.
2.3.1. Point Cloud Acquisition

2.3.1. Point
Acquisition
TheCloud
process of
acquiring 3D point-cloud data with the binocular camera consists of
three
The parts.
process of acquiring 3D point-cloud data with the binocular camera consists of

three
1. parts.
Binocular calibration. This uses the known correspondence between the world coordinate system
(calibration
imagecorrespondence
coordinate system
(after processing
thecoorBinocular
calibration.
Thisplate)
usesand
the the
known
between
the world
image
of
the
calibration
plate)
to
calculate
the
parameter
information
of
the
binocular
dinate system (calibration plate) and the image coordinate system (after processing
camera in the current position relationship. Before binocular calibration, it is also necthe image of the calibration plate) to calculate the parameter information of the binessary to perform single camera calibration for each camera to determine its distortion
ocular
cameracamera
in the internal
currentreference
positionmatrix,
relationship.
Before
binocular calibration, it is
coefficient,
and other
parameters.
necessaryoftopoints
perform
single camera
eachprocess,
camerathe
to determine
2.alsoExtraction
of interest
(feature calibration
extraction). for
In this
binocular its
distortion
coefficient,
camera
internal
reference
matrix,
and
other
parameters.
camera extracts all data points on the laser line. Two pictures taken with the left and
2. Extraction
points
interestangles
(feature
extraction).
In the
thislaser
process,
binocular
right of
cameras
fromofdifferent
are used to
describe
line. the
Then, a
suitablecampre-processing
algorithm
added
to extract
laserwith
linesthe
from
theand
tworight
era extracts
all data
points is
on the
laser
line. and
Twosegment
picturesthe
taken
left
images.
cameras from different angles are used to describe the laser line. Then, a suitable preAccuratealgorithm
digital description
matching).
In this stage,
the “stereo
3.processing
is added(stereo
to extract
and segment
the laser
lines matching”
from the two
algorithm is used, which calculates the base matrix based on the coordinate points of
images.

1.

the feature points in the left and right images and corresponds the coordinate points
of the same name in the left and right images one by one. The calculation is performed
using the parallax principle (Figure 4).

3.

Accurate digital description (stereo matching). In this stage, the “stereo matching”
algorithm is used, which calculates the base matrix based on the coordinate points of
the feature points in the left and right images and corresponds the coordinate points
Agriculture 2022, 12, 1861
5 of 18
of the same name in the left and right images one by one. The calculation is performed
using the parallax principle (Figure 4).

Figure 3. Grain point-cloud
processing
pipeline.
Figure 3. Grain
point-cloud
processing pipeline.
The point P in Figure 4a is a point in 3D space; OL and OR are the left and right camera
optical centers; and PL and PR are the imaging points of the point P on the left and
right image planes. The parallax of the point P in the left and right cameras is defined
as
Disparity = |u L − u R |,
(1)
where u L and u R are the distances of the two imaging points on the left and right
image planes from the left edge of the image, respectively.

Agriculture 2022, 12, 1861
Agriculture 2022, 12, x FOR PEER REVIEW

6 of 18
6 of 18

(a)

(b)

Figure 4. Principle of the binocular stereo imaging parallax. (a) Schematic of depth information; (b)
Figure 4. Principle of the binocular stereo imaging parallax. (a) Schematic of depth information;
schematic of XY information.
(b) schematic of XY information.

The point 𝑃 in Figure 4a is a point in 3D space; 𝑂 and 𝑂 are the left and right
According to the similar triangle, it follows that
camera optical centers; and 𝑃 and 𝑃 are the imaging points of the point 𝑃 on the left
and right image planes. The parallax of the
d point
Z −𝑃f in the left and right cameras is defined
=
,
(2)
as
Tx
Z
|𝑢 − 𝑢 |,
𝐷𝑖𝑠𝑝𝑎𝑟𝑖𝑡𝑦
(1)
where Z denotes the depth information;
Tx is =
the
distance between the two camera optical
centers,
called
the the
baseline;
f is of
thethe
focal
and
d is calculated
where 𝑢also
and
𝑢 are
distances
twolength;
imaging
points
on the left as
and right image




planes from the left edge of the image, respectively.
L
L
− uR
= Tx
− uL −
(3)
According to d
the
similar
triangle, it−follows
that = Tx − (u L − u R ).
2
2
=
,
(2)
It can be deduced that
where 𝑍 denotes the depth information;
between the two camera optiTx ∗𝑇f is the Tdistance
x∗ f
Z
=
=
.
(4)
cal centers, also called the baseline; 𝑓u is−the
length; and 𝑑 is calculated as
u focalDisparity
L

R

𝑑 =𝑇 − 𝑢 − − −𝑢 =𝑇 − 𝑢 −𝑢 .
(3)
When the point P moves in the 3D space, the imaging position of the point P on the left
and right
will also
It cancameras
be deduced
that change, and thus, the parallax will also change accordingly. As
can be seen from the above equation, the parallax is inversely proportional to the distance
∗
∗
=
. projection. Therefore, as long
𝑍=
(4)as
from the point on the 3D space to the
center plane
of the
the parallax of a point is known, the depth information of that point can be known. From
When
𝑃 moves
in the 3D space, the imaging position of the point 𝑃 on the
Figure
4b, itthe
canpoint
be deduced
that
( and thus,
left and right cameras will also change,
f the parallax will also change accordx − x0
Xw = Zw
ingly. As can be seen from the above equation,
the
. parallax is inversely proportional to
(5)
y − y0
= Zfw
the distance from the point on the 3D spaceYwto the
center plane of the projection. Therefore,
as long
as the
of a point
information
of that point can be
Finally,
theparallax
3D coordinates
of is
theknown,
point Pthe
aredepth
determined
as
known. From Figure 4b, it can be deduced that

x − x0

 Xw = =f Zw
y − y0
(6)
Yw = f Z.w .
(5)


Z ==Z
w

Finally,
theare
3Dplaced
coordinates
the point
𝑃 in
areadetermined
as
All
grains
on theofcarrier
table
uniform position
with the back of the
belly facing down and the front facing up.𝑋 The
grains
can
be
quickly
adjusted
with tweezers
=
𝑍
and kept from overlapping and piling up. After the grains are prepared, the 3D point-cloud
.
(6)
𝑌 = table𝑍moves
scanning system is activated, and the carrier
between the limiters at an even
𝑍 = generating
𝑍
speed (25 mm/s). The binocular camera starts
valid point-cloud data in real
time as the carrier moves within the binocular camera capture distance. When the carrier

All grains are placed on the carrier table in a uniform position with the back of the
belly facing down and the front facing up. The grains can be quickly adjusted with tweezers and kept from overlapping and piling up. After the grains are prepared, the 3D pointcloud scanning system is activated, and the carrier table moves between the limiters 7atofan
18
even speed (25 mm/s). The binocular camera starts generating valid point-cloud data in
real time as the carrier moves within the binocular camera capture distance. When the
carrier
leaves
the capture
range
the binocular
camera,
all point-cloud
are generated
leaves the
capture
range of
the of
binocular
camera,
all point-cloud
data data
are generated
and
and
transferred
to
the
computer
for
point-cloud
data
processing.
transferred to the computer for point-cloud data processing.

Agriculture 2022, 12, 1861

2.3.2. Point Cloud Preprocessing
The raw point-cloud data contains both grain information and carrier information. It
was necessary to segment the two objects to obtain useful grain point-cloud
point-cloud information.
information.
We
set
the
segmentation
plane
threshold
φ1,
and
the
threshold
size
is
related
to
the height
We set the segmentation plane threshold ϕ1,
thecarrier
carriertable
tablefrom
from
binocular
camera,
shown
in 5b.
Figure
5b. The
horizontal
of the
thethe
binocular
camera,
as as
shown
in Figure
The
horizontal
height
height
the stage
carrierisstage
fixed. After
analyzing
amount
of itdata,
conof
the of
carrier
fixed.is After
analyzing a
largea large
amount of
data,
was it was
concluded
cluded
that
= can
−213.00
can
thefrom
grain
thestage.
carrierFigure
stage.5a
Figure
shows
the
that
ϕ1 =
− φ1
213.00
split
thesplit
grain
thefrom
carrier
shows5athe
original
point
cloud,
where
blue
represents
carrier
table,
andtable,
yellow-green
represents the
grain.
original
point
cloud,
where
blue the
represents
the
carrier
and yellow-green
represents
Figure
5c–e
shows5c–e
the shows
extracted
clouds
of the
grains
aftergrains
segmentation.
the
grain.
Figure
the point
extracted
point
clouds
of the
after segmentation.

(a)

(b)

(d)

(c)

(e)
Figure 5. Grain point-cloud data extraction. (a) Top view of the original 3D point cloud; (b) northeast
Figure 5. Grain point-cloud data extraction. (a) Top view of the original 3D point cloud; (b) northeast
view of the grain and carrier point−cloud data segmentation; (c) top view of the extracted grain
view
the grain
and view
carrier
−cloud data
(c) northeast
top view of
the of
extracted
grain
point of
cloud;
(d) right
of point
the extracted
grainsegmentation;
point cloud; (e)
view
the extracted
point
cloud;
(d)
right
view
of
the
extracted
grain
point
cloud;
(e)
northeast
view
of
the
extracted
grain
grain point cloud.
point cloud.

2.3.3. Single-Grain Point-Cloud Extraction
In the experimental environment, the grains were spaced apart and split from each
other more easily. However, there were also cases of grain adhesion. Therefore, we
partitioned between grains under more extreme conditions to obtain more reliable single
grain. First, setting a segmentation plane threshold ϕ2 to split grain point cloud into two

Agriculture 2022, 12, x FOR PEER REVIEW

8 of 18

2.3.3. Single-Grain Point-Cloud Extraction
Agriculture 2022, 12, 1861

In the experimental environment, the grains were spaced apart and split from 8
each
of 18
other more easily. However, there were also cases of grain adhesion. Therefore, we partitioned between grains under more extreme conditions to obtain more reliable single grain.
First, setting a segmentation plane threshold φ2 to split grain point cloud into two parts:
parts: the upper and lower parts. Second, the AlphaShape function method for constructing
the upper and lower parts. Second, the AlphaShape function method for constructing polpolyhedra from points was used for the upper part [33]. By setting the Alpha shape radius
yhedra from points was used for the upper part [33]. By setting the Alpha shape radius
value, the upper part of grains could be clustered into different polyhedra. Final, for the
value, the upper part of grains could be clustered into different polyhedra. Final, for the
lower part of the point cloud, each point was classified to its nearest polyhedron.
lower part of the point cloud, each point was classified to its nearest polyhedron.
Usually, the thickness of the grain was not less than 2 mm, and setting the segmentation
Usually, the thickness of the grain was not less than 2 mm, and setting the segmenplane
ϕ2plane
= −211.5,
for the for
easily
of the grain
two
tation
φ2 = which
−211.5, allowed
which allowed
thesplitting
easily splitting
of thepoint
graincloud
point into
cloud
parts:
the upper
andupper
lowerand
parts
(Figure
As6a,b).
can be
inseen
Figure
6c, the6c,
redthe
line
into two
parts: the
lower
parts6a,b).
(Figure
As seen
can be
in Figure
distance
is
larger
than
the
green
line
distance,
which
ensured
that
the
right
radius
was
red line distance is larger than the green line distance, which ensured that the right radius
used
categorize
the different
grain
point
clouds.
Setting
the
α=
wasto
used
to categorize
the different
grain
point
clouds.
Setting
theAlpha
Alphashape
shape radius
radius α
0.5,
which
could
accurately
cluster
the
grain
point
clouds
of
the
same
category
together
= 0.5, which could accurately cluster the grain point clouds of the same category together
(Figure
theupper
upperpart
partofof
grain
point
cloud
was grouped
into different
(Figure6d).
6d). Thus,
Thus, the
thethe
grain
point
cloud
was grouped
into different
polpolyhedra
(Figure
6e)
to
extract
the
upper
part
of
a
single
grain
point
cloud.
lower
yhedra (Figure 6e) to extract he upper part of a single grain point cloud. ForFor
thethe
lower
part
of
the
point
cloud,
classifying
the
point
to
its
nearest
polyhedron
and
repeating
this
part of the point cloud, classifying the point to its nearest polyhedron and repeating this
until
the
parts of
ofthe
thepoint
pointcloud
cloud(Figure
(Figure7).7).
until
thending
endingclassification
classificationof
ofall
all of
of the
the lower parts

(a)

(b)

(c)

(d)

(e)

Figure 6. Single-rain point-cloud extraction. (a) All grain point clouds with segmented plane;
(b) two grains’ point clouds and segmentation plane; (c) analysis of two grains’ point clouds and
segmentation planes. The red line and green line indicate the distance between grains at different
height levels.; (d) the upper part of the grain point cloud; (e) classification result of the upper part of
different grains.

Agriculture 2022, 12, x FOR PEER REVIEW

9 of 18

Agriculture 2022, 12, x FOR PEER REVIEW

9 of 18

Figure 6. Single-rain point-cloud extraction. (a) All grain point clouds with segmented plane; (b)

Agriculture 2022, 12, 1861

Figure
Single-rain
extraction.
(a) Allplane;
grain point
clouds of
with
segmented
plane;clouds
(b) and segtwo6.grains’
pointpoint-cloud
clouds and
segmentation
(c) analysis
two
grains’ point
two grains’
point
cloudsThe
andred line
segmentation
plane;
(c)indicate
analysis of
grains’ point
clouds
and
mentation
planes.
and green
line
thetwo
distance
between
grains
at segdifferent height
mentation planes. The red line and green line indicate the distance between grains at different height
levels.; (d) the upper part of the grain point cloud; (e) classification result of the upper part of diflevels.; (d) the upper part of the grain point cloud; (e) classification result of the upper part of different grains.
ferent grains.

9 of 18

Figure 7. Complete single−grain classification results. The blue dot represents the nearest polyhe-

Figure 7. Complete single−grain classification results. The blue dot represents the nearest polyhedron
dron on the left and the red dot represents on the right.
Figure
Complete
single−grain
classification
results. The blue dot represents the nearest polyheon the
left 7.
and the
red dot
represents
on the right.
dron on the left and the red dot represents on the right.
2.3.4. 3D Model Construction

2.3.4.All
3D
Construction
theModel
grain point-cloud
data were taken from the grain frontal scan. To construct a
2.3.4. 3D Model Construction

complete
body, the
grain bottom
obtained.
Usinggrain
overhead
projecAll 3D
thegrain
grain
point-cloud
dataneeded
wereto be
taken
from the
frontal
scan. To construct
All the
grain
point-cloud
data
were
taken
from
thecarrier
graintable,
frontal
scan.could
To construct a
tion
to
project
all
grain
point
clouds
to
the
height
level
of
the
which
a complete
3Dgrain
grain
body,
the grain
bottom needed
to beUsing
obtained.
Using overhead
complete
body,
the grain
bottom
obtained.
overhead projecsimulate
the 3D
bottom
of the
grains
(Figure
8b). needed
Combiningtoitbewith
the bottomless
point
projection
to
project
all
grain
point
clouds
to
the
height
level
of
the
carrier
table, which
tion
to
project
all
grain
point
clouds
to
the
height
level
of
the
carrier
table,
which
could
cloud (Figure 8a) o obtain a complete grain point cloud (Figure 8c). Again, setting the
could
simulate
the
bottom
the all
grains
(Figure
8b).a it
Combining
it
with
bottomless
simulate
the
bottom
the of
grains
(Figure
8b).
Combining
with
themodel
bottomless
point
Alpha
shape
radius α
= 0.5,of
which
clustered
point
clouds
into
complete
3D
of the
the
grains
(Figure
8d).
point
cloud
(Figure
8a)
to a
obtain
a complete
grain
point
cloud8c).
(Figure
Again,
cloud
(Figure
8a) to
obtain
complete
grain point
cloud
(Figure
Again,8c).
setting
the setting

α =α0.5,
which
clustered
all point
a into
complete
model of
the Alpha
Alphashape
shaperadius
radius
= 0.5,
which
clustered
allclouds
point into
clouds
a 3D
complete
3D model
thegrains
grains (Figure
of the
(Figure8d).
8d).

(a)

(b)

Agriculture 2022, 12, x FOR PEER REVIEW

(a)

10 of 18

(b)

(c)

(d)

Figure 8. Complete grain 3D model construction. (a) Northeast view of the single−grain point cloud;

Figure(b)
8. mapped
Complete
grain
3D model
construction.
(a)bottom
Northeast
of(d)
thenortheast
single−grain
point
grain
bottom;
(c) complete
grain with
pointview
cloud;
view of
the cloud;
(b) mapped
grain
bottom; (c) complete grain with bottom point cloud; (d) northeast view of the grain
grain 3D
model.
3D model.
2.3.5. 3D Morphological Feature Calculation
The grain length and width were calculated based on the minimum bounding rectangle (MBR) method on the bottom of the grain obtained after mapping. The grain thickness (T) is the difference between the maximum value of the grain on the Z-axis and the
Z-axis value of the carrier table. The formula used to calculate it is as follows:

Agriculture 2022, 12, 1861

10 of 18

2.3.5. 3D Morphological Feature Calculation
The grain length and width were calculated based on the minimum bounding rectangle
(MBR) method on the bottom of the grain obtained after mapping. The grain thickness
(T) is the difference between the maximum value of the grain on the Z-axis and the Z-axis
value of the carrier table. The formula used to calculate it is as follows:
T = Zmax − Zre f ,

(7)

where Zmax is the maximum coordinate point of the grain in the Z-axis direction, and Zre f
is the coordinate of the carrier table in the Z-axis.
Volumes of more complicated polyhedra may not have simple formulas. Volumes
of such polyhedra may be computed by subdividing the polyhedron into smaller pieces
(for example, by triangulation). For example, the volume of a regular polyhedron can be
computed by dividing it into congruent pyramids, with each pyramid having a face of the
polyhedron as its base and the center of the polyhedron as its apex. In general, it can be
derived from the divergence theorem, which states that the volume of a polyhedral solid is
given by
1
(8)
V = ∑ F ( Q F · NF )S( F ) ,
3
S( F ) = ∑i ( xi−1 + xi )·(yi−1 − yi )/2,

(9)

where the sum (S) is over the faces F of the polyhedron; Q F is an arbitrary point on face F;
NF is the unit vector perpendicular to F pointing outside the solid; and the multiplication
dot is the dot product; xi and yi are the horizontal and vertical coordinates of each point on
the surface.
2.4. Manual Measurement Indicators
High-precision electronic vernier calipers were used to measure the size of the longest,
widest, and thickest parts of the grains. We marked and positioned 100 grains acquired
from the 3D images to achieve matching of the manual measurement data with the data
measured by the WG-3D platform.
General methods of solid volume measurement include the sand discharge method
and drainage method. These conventional methods are less effective because the volume of
individual grains is too small, the accuracy of the measuring cylinder is not high, and water
bubbles will be attached to the surface of the grains. This experiment used a high-precision
burette as a volumetric measuring device (Figure 9), in which water
replaced with
Agriculture 2022, 12, x FOR PEER REVIEW
11 of was
18
alcohol to reduce the air bubbles adhering to the surface of the grains. We divided 100
grains into 10 groups and took readings for each of the sunken 10 grains to obtain the total
divided 100
grains
10 groups and took readings for each of the sunken 10 grains to
volume
of the
10into
grains.
obtain the total volume of the 10 grains.

Figure 9. Manual measurement of grain volume.

Figure 9. Manual measurement of grain volume.
2.5. Evaluation Indicators
The root mean square error (RMSE) and mean absolute percentage error (MAPE)
were used to evaluate the WG-3D measurement accuracy. The formulae are as follows:
∑ 𝑥 −𝑦

(10)

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2.5. Evaluation Indicators
The root mean square error (RMSE) and mean absolute percentage error (MAPE) were
used to evaluate the WG-3D measurement accuracy. The formulae are as follows:
s
RMSE =

MAPE =

∑i ( xi − yi )
n

2

(10)

1
| xi − yi |
× 100%
n∑
yi
i

(11)

where xi is the WG-3D measurement, yi the manual measurement, and n is the number
of grains.
2.6. Data Processing and Analysis Software
The point-cloud data processing software was MATLAB R2019a, and IBM SPSS
Statistics 26 and Microsoft Excel 2019 Professional Edition were used for data analysis
and plotting.
3. Results
3.1. Measurement Accuracy
This research verified the usefulness of the grain 3D model construction by assessing
the accuracy of four indicators: length, width, thickness, and volume. The WG-3D measurements of 100 grains of three varieties were compared with manual measurements at a
carrier table moving speed of 25 mm/s. The results are shown in Table 2. The measurement
error of length, width, and thickness of three varieties was at the same level, and the RMSE
was about 0.20 mm. Length was lower than width and thickness in the MAPE evaluation
index due to its large base number. The volume data are the total value of the measured
10 grains. The measurement error of volume fluctuated among varieties, and the RMSE
was within 20.00 mm3 . From the distribution of all samples (Figure 10), the manual measurement data and WG-3D measurement data were evenly distributed around the 1:1 line.
The RMSE and MAPE of the length were 0.2256 mm and 2.60%. The RMSE and MAPE of
the width were 0.2154 mm and 5.83%. The RMSE and MAPE of the thickness were 0.2119
mm and 5.81%. The RMSE and MAPE of the volume were 1.7740 mm3 and 4.31%. Overall,
the measurement accuracy of the four indicators was relatively reliable. This indicates
that our method can be used as an effective means for high-throughput acquisition of 3D
information of wheat grains.
Table 2. Three varieties measurement accuracy.
Zhenmai No.9

Yangmai No.23

Ningmai No.13

Indicators

RMSE
(mm)

MAPE
(%)

RMSE
(mm)

MAPE
(%)

RMSE
(mm3 )

MAPE
(%)

Length (n = 100)
Width (n = 100)
Thickness (n = 100)
Volume (n = 10)

0.2000
0.2235
0.2054
18.1267

2.24
6.10
5.32
3.56

0.2369
0.2095
0.2164
21.8453

2.61
5.53
6.10
5.66

0.2400
0.2133
0.2137
13.2494

2.96
5.86
5.99
3.72

In order to further evaluate the accuracy of the method proposed in this paper,
26 varieties of Yangmai series were tested. The results are shown in Table 3. There was no
abnormal value, and the measurement accuracy of all varieties is good. The average RMSE
and MAPE of the length were 0.2181 mm and 2.93%. The average RMSE and MAPE of the
width were 0.1974 mm and 5.43%. The average RMSE and MAPE of the thickness were
0.2027 mm and 5.15%. The average RMSE and MAPE of the volume were 1.8997 mm3 and

Zhenmai No.9
Yangmai No.23
Ningmai No.13
RMSE
MAPE
RMSE
MAPE
RMSE
MAPE
(mm)
(%)
(mm)
(%)
(mm3)
(%)
Length (n = 100) 0.2000
2.24
0.2369
2.61
0.2400
2.96
Width (n = 100) 0.2235
6.10
0.2095
5.53
0.2133
5.86 12 of 18
Thickness (n =
0.2054
5.32
0.2164
6.10
0.2137
5.99
100)
Volume
(n = 10)
18.1267
3.56with the 21.8453
5.66
13.2494which
3.72
4.61%. These
results
are consistent
previous verification
results,
shows that
the method has strong robustness.
Indicators

Agriculture 2022, 12, 1861

4.50
RMSE = 0.2256 mm
MAPE = 2.60%
n = 300

8.00

3D-WG Measurements (mm)

3D-WG Measurements (mm)

9.00

7.00
6.00
5.00
4.00

RMSE = 0.2154 mm
MAPE = 5.83%
n = 300

4.00
3.50
3.00
2.50
2.00
1.50

4.00

5.00

6.00
7.00
8.00
Manual Measurements (mm)

9.00

1.50

2.00

(a)

3.00

3.50

4.00

4.50

330
390
450
510
Manual Measurements (mm3)

570

(b)
570
3D-WG Measurements (mm3)

4.50
3D-WG Measurements (mm)

2.50

Manual Measurements (mm)

RMSE = 0.2119 mm
MAPE = 5.81%
n = 300

4.00
3.50
3.00
2.50
2.00
1.50

RMSE = 17.7405 mm3
MAPE = 4.31%
n = 30

510
450
390
330
270
210

1.50

2.00

2.50
3.00
3.50
4.00
Manual Measurements (mm)

(c)

4.50

210

270

(d)

Figure
Figure 10.
10. The
The sample
sample accuracy
accuracy analysis.
analysis. (a)
(a) Length,
Length, (b)
(b) width,
width, (c)
(c) thickness,
thickness, (d)volume.
(d)volume.

3.2. In
Measurement
Efficiency
order to further
evaluate the accuracy of the method proposed in this paper, 26
varieties
Yangmai
series were
tested. The
results
shown in
Table 3.
There
was no
The of
WG-3D
information
acquisition
platform
can are
perform
point-cloud
data
acquisition,
abnormal
value, and
measurement
accuracy of
all varieties is
good. The
average
3D
point-cloud
datathe
processing,
and several
indicator
measurement
tasks in
realRMSE
time.
and
MAPE of the
length
0.2181 mm
and 2.93%.
The is
average
RMSEThe
and
MAPE
the
Therefore,
evaluating
the were
real-time
measurement
efficiency
necessary.
two
mainoftimewidth
were
0.1974
mm
and
5.43%.
The
average
RMSE
and
MAPE
of
the
thickness
were
consuming blocks involved are the scan acquisition of the point-cloud data and the amount
of calculation of the 3D point-cloud data processing and measurement indicators. The
results are shown in Figure 11a at a carrier table scanning speed of 25 mm/s. The scanning
time consumption was not affected, as the number of grains increased and remained stable
at approximately 12 s. This is because we set the whole scanning process to scan the pointcloud data above the carrier (if there are no grains, only the carrier point-cloud data are
available). Therefore, the total amount of point-cloud data remained the same at a constant
scanning speed, and the time consumed was also stable. However, the time consumed for
the processing of the grain 3D point-cloud data and the indicator measurement increased
positively with the number of grains. At a scanning speed of 25 mm/s, the effective interval
time (calculation time) for each batch was approximately 9 s. This enables automated wheat
grain 3D data measurement in batches of up to 500 grains.

Agriculture 2022, 12, 1861

13 of 18

Table 3. Measurement accuracy of Yangmai series varieties.

Varieties

Length (n = 40)

Width (n = 40)

RMSE
(mm)

RMSE
(mm)

MAPE
(%)

MAPE
(%)

Thickness (n = 40)

Volume (n = 40)

RMSE
(mm)

RMSE
(mm3 )

MAPE
(%)

MAPE
(%)

Y 1#
0.2157
3.04
0.2070
6.08
0.2195
5.99
1.9167
5.77
Y 2#
0.2195
3.07
0.1748
4.95
0.1928
4.69
1.7286
4.56
Y 3#
0.2021
2.85
0.2024
5.86
0.1846
4.86
1.7815
4.64
Y 4#
0.2540
3.25
0.1864
5.05
0.1981
4.88
1.9893
4.42
Y 5#
0.2109
2.67
0.1920
5.24
0.2103
5.05
2.2179
5.60
Y 6#
0.2223
2.99
0.1759
4.65
0.2070
5.36
1.8763
4.56
Y 10#
0.2251
2.89
0.2076
6.02
0.2196
5.90
2.1199
5.18
Agriculture
x FOR PEER REVIEW
Y 11# 2022, 12,
0.2099
2.65
0.2047
5.73
0.1794
4.60
2.0713
4.89 14 of 18
Y 12#
0.2064
2.77
0.1919
5.65
0.1898
4.99
1.9241
5.05
Y 13#
0.2264
3.36
0.2223
6.40
0.2103
5.31
1.8587
4.53
Y 14#
0.2205
2.90
0.2114
5.49
0.1958
4.75
1.8364
4.05
the effective0.1975
interval time
(calculation0.1992
time) for each
approximately
Y 15#
0.1990
2.70
4.96
4.80batch was1.8151
4.009 s. This
enables
automated
wheat
grain
3D
data
measurement
in
batches
of
up
to
500
grains.
Y 16#
0.2248
2.93
0.2212
6.54
0.2019
5.24
1.7937
4.40
Usually,
the slower 4.81
that the carrier
table is set to
move, the slower
Y 17#
0.2267
2.96
0.1910
0.2077
5.17
1.8920 the scanning
4.53 speed
Y 18#
0.2212
2.87
5.30 of point-cloud
0.2088 data can
5.23be acquired
1.9557
will be, and0.1927
the more amount
with higher4.60
quality. To
Y 19#
0.2005
2.87
0.2116
5.89
0.2128
5.51
1.8025
4.06
better balance the relationship between speed and quality, we tested 100 grains
and comY 20#
0.2451
3.32
0.1748
4.80
0.2045
5.36
1.7236
3.98
pared the effect of different scanning speeds on the total measurement time consumed
Y 21#
0.2101
2.56
0.1709
4.60
0.2023
5.05
1.8269
4.04
and RMSE. 0.2086
The results are
shown in Figure
within
Y 22#
0.2392
3.59
5.66
0.1955 11b. If the
5.06speed is controlled
2.1455
5.5330 mm/s,
a
high
measurement
accuracy
can
be
effectively
guaranteed.
However,
too-slow
Y 23#
0.1944
2.47
0.1992
5.74
0.1998
5.30
1.6590
4.16 speed
Y 24#
0.2204
3.08
0.1949
1.9749
4.69scanning
will seriously
affect the 5.22
efficiency. 0.2092
Therefore, 25 5.04
mm/s was set as
the normal
Y 25#
0.1878
2.34
0.1974
5.06 for one0.1951
4.68 14 s. Of1.8148
4.08 is also
speed, and the
time consumed
batch was around
course, this value
Y 26#
0.2379
3.15
0.1897
4.82
0.2289
6.01
1.9700
4.43 and the
related to the computer configuration, the number of measurement indicators,
Y 27#
0.1950
2.67
0.2005
5.39
0.2011
4.93
1.9104
4.56
efficiency of the algorithm. The higher the computer configuration and the smaller the
Y 28#
0.2246
3.01
0.1989
5.40
0.2009
4.92
1.6983
4.10
number of measurement
indicators, the
more efficient
will be, the
Y 158
0.2315
3.11
0.2059
5.85
0.1957
5.10the algorithm
2.0877
5.40faster the
data processing
consumption will1.8997
be.
Average
0.2181
2.93
0.1974will be, and
5.43 the lower the
0.2027time
5.15
4.61

12

RMSE of volume

50

10

Scanning time

8

Data processing time

6
4
2

40

12.00

30

9.00

20

6.00

10

3.00

0

0
50

100 150 200 250 300 350 400 450 500
Grain Number

(a)

18.00
15.00

Measurement time (s)

Time (s)

Measurement time

60

RMSE of volume (mm3)

14

0.00
5

10

15

20

25

30

35

40

45

50

Scanning speed (mm/s)

(b)
Figure
11. Measurement
Figure 11.
Measurement efficiency:
efficiency: (a)
(a) measurement
measurement time
time consumption
consumption for
for different
different numbers
numbers of
of
grains; (b) relationship between scanning speed and measurement time and RMSE of volume. The
grains; (b) relationship between scanning speed and measurement time and RMSE of volume. The
red line is selected reference line.
red line is selected reference line.

4. Discussion
Usually, the slower that the carrier table is set to move, the slower the scanning speed
4.1.
Related
Studiesof point-cloud data can be acquired with higher quality.
willComparison
be, and theofmore
amount
To better
the of 3D
relationship
between traits
speedofand
quality,
testedthe
100 grains
The balance
significance
morphological
grains
has we
attracted
attentionand
of
compared
the
effect
of
different
scanning
speeds
on
the
total
measurement
time
consumed
many researchers, and Table 4 shows the comparison result with related studies. The reand RMSE.
arethe
shown
in Figure
If the speed
is controlled
within 30
mm/s,
sults
showsThe
thatresults
most of
methods
used 11b.
binocular
cameras
for its cheapness
and
high
a
high
measurement
accuracy
can
be
effectively
guaranteed.
However,
too-slow
accuracy. Among them, the accuracy of reference [27] is the best, but this methodspeed
only
measures one grain at a time. Therefore, it is not suitable for mass screening scenarios
because of its low efficiency. The methods in reference [34,35] and WG-3D-5 in this paper
have the same accuracy level, while the former two do not measure volume parameters.
In addition, they have unstable threshold segmentation results of two-dimensional im-

Agriculture 2022, 12, 1861

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will seriously affect the efficiency. Therefore, 25 mm/s was set as the normal scanning
speed, and the time consumed for one batch was around 14 s. Of course, this value is also
related to the computer configuration, the number of measurement indicators, and the
efficiency of the algorithm. The higher the computer configuration and the smaller the
number of measurement indicators, the more efficient the algorithm will be, the faster the
data processing will be, and the lower the time consumption will be.
4. Discussion
4.1. Comparison of Related Studies
The significance of 3D morphological traits of grains has attracted the attention of
many researchers, and Table 4 shows the comparison result with related studies. The
results shows that most of the methods used binocular cameras for its cheapness and high
accuracy. Among them, the accuracy of reference [27] is the best, but this method only
measures one grain at a time. Therefore, it is not suitable for mass screening scenarios
because of its low efficiency. The methods in reference [34,35] and WG-3D-5 in this paper
have the same accuracy level, while the former two do not measure volume parameters. In
addition, they have unstable threshold segmentation results of two-dimensional images
and low efficiency in obtaining point clouds from multiple angles. The accuracy and
efficiency of reference [32] are good, but the measurement indicator is single. Compared
with WG-3D-25, WG-3D-5 improves accuracy, but with reduced efficiency. Therefore, the
proposed method can meet the challenges of different grain morphology measurement.
Table 4. Comparative results of relevant studies.
Methods

Device

Length
(mm)

Width
(mm)

Thickness Volume
(mm)
(mm3 )

Efficiency

Additional

Reference [32]
Reference [34]
Reference [27]
Reference [35]
WG-3D-25
WG-3D-5

Binocular camera
Single camera
Binocular camera
Binocular camera
Binocular camera
Binocular camera

-0.0988
0.0300
0.1840
0.2256
0.1018

-0.0841
0.0428
0.0700
0.2154
0.0938

0.1635
0.0917
0.0362
0.0420
0.2119
0.0916

high
high
low
low
high
middle

Single indicator
Unstable accuracy
One grain one time
Multi-angle acquisition
Scanning speed at 25 mm/s
Scanning speed at 5 mm/s

--0.3789
-1.7740
0.6457

The ‘–’ means no measurement in the reference.

4.2. 3D Morphological Cluster Analysis
Based on the rapid batch measurement of grain 3D morphology, the 3D morphological
traits such as length, width, thickness, and volume were used as cluster analysis variables
for the stratified clustering of Yangmai series varieties. As shown in Table 5 and Figure 12,
the differences in grain 3D morphology were small, and the Yangmai series varieties
could be classified into two classes at the genetic distance of 5-level. The first category
is dominated by small-grain wheat, with the volume generally not exceeding 35 mm3 ,
including Y 1#, Y 2#, Y 3#, Y 6#, Y 12#, Y 16#, Y 22#, Y 23#, and Y 158. The second category
was dominated by large-grain wheat with a volume of more than 35 mm3 and included Y
4#, Y 5#, Y 10#, Y 11#, Y 13#, Y 14#, Y 15#, Y 17#, Y 18#, Y 19#, Y 20#, Y 21#, Y 24#, Y 25#,
Y 26#, Y 27#, and Y 28#. Zhang et al. [36] clustered the Yangmai series varieties into two
categories using different quality traits as variables, which was supported by the results of
genealogical analysis. The results of the present study are similar to their findings, such as Y
158 being the genetic basis of the strong-gluten and small-grain varieties of Yangmai, Y 23#
being inherited from Y 16#, and Y 16# being inherited from Y 158 superior line Yang91F138.
Yang80Jian3 and Ningmai No.9 are the genetic basis of the weak-gluten and large-grain
varieties of Yangmai, Y 15# is inherited from Yang 89-40, and Yang 89-40 is inherited from
Yang80Jian3; Y 20# and Y 13# are also inherited from Yang80Jian3; Y 18# and Y 21# are
inherited from Ningmai No.9.

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Table 5. Mean value of 3D morphological indicators of Yangmai series varieties.
Length
(mm)

Varieties
Y 1#
Y 2#
Y 3#
Y 4#
Y 5#
Y 6#
Y 10#
Y 11#
Y 12#
Y 13#
Y 14#
Y 15#
Y 16#
Y 17#
Y 18#
Y 19#
Y 20#
Y 21#
Y 22#
Y 23#
Agriculture 2022, 12, x FOR PEER REVIEW
Y 24#
Y 25#
Y 26#
YY26#
27#
YY27#
28#
YY28#
158
Y 158

5.96
6.04
6.15
6.84
6.34
6.27
6.71
6.74
6.39
5.90
6.46
6.31
6.83
6.48
6.72
6.04
6.28
6.97
5.97
6.49
6.27
6.44
6.63
6.63 6.27
6.27 6.32
6.32 6.30
6.30

3.32
3.18
3.17
3.12

Width
(mm)

Thickness
(mm)

2.98
3.13
3.11
3.22
3.08
3.20
3.12
3.16
2.96
3.15
3.44
3.44
3.08
3.37
3.09
3.17
3.11
3.15
3.20
3.15
3.27
3.37
3.32
3.18
3.17
3.12

3.21
3.41
3.34
3.56
3.57
3.46
3.38
3.36
3.33
3.44
3.55
3.75
3.31
3.49
3.51
3.47
3.46
3.55
3.36
3.20
3.62
3.64
3.46
3.5837.69
3.6037.43
3.2936.44

3.46
3.58
3.60
3.29

34.05

Volume
(mm3 )
29.92
34.12
34.06
39.93
37.00
34.81
36.92
38.49
33.23
37.00
38.99
39.88
34.51
37.84
37.20
38.39
36.21
40.53
34.50
33.63
16 of 18
36.93
38.45
37.69
37.43
36.44
34.05

Figure 12. Cluster analysis of 3D morphological of Yangmai series varieties.

Figure 12. Cluster analysis of 3D morphological of Yangmai series varieties.
4.3. Advantages and Disadvantages
The WG-3D phenotyping platform has obvious advantages. First, it enables automated high-throughput acquisition of grain 3D indicators at a higher level of accuracy.
Second, it uses a line laser binocular camera (which costs only a few hundred dollars) to
greatly reduce the cost compared to other expensive 3D acquisition equipment (which can
cost up to tens of thousands of dollars for tomography). In addition, it can acquire RGB

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4.3. Advantages and Disadvantages
The WG-3D phenotyping platform has obvious advantages. First, it enables automated high-throughput acquisition of grain 3D indicators at a higher level of accuracy.
Second, it uses a line laser binocular camera (which costs only a few hundred dollars) to
greatly reduce the cost compared to other expensive 3D acquisition equipment (which can
cost up to tens of thousands of dollars for tomography). In addition, it can acquire RGB
color information and fuse it into RGBD point-cloud data. The grain color characteristics
can be analyzed effectively. It is not limited to morphological indicators and will be developed for more indicators, such as surface area, curvature, and roughness. However,
there are also some shortcomings of the platform. When the back side of the grain belly
is placed facing upward, it causes the grain to be tilted at an angle. This is not suitable
for horizontal scanning. Therefore, it is currently recommended to scan only the frontal
point-cloud data of the grain. The 3D point-cloud data and indicator parameters about the
grain belly back are not available. In the future, we will consider how to achieve a standard
for grain belly balance, such as by designing notches in the carrier table.
5. Conclusions
Grain 3D morphological indicators have good application value and research prospects.
This study developed a low-cost WG-3D platform for high-throughput acquisition of wheat
grain 3D indicators to lay the foundation for the in-depth study of grain 3D characteristics.
The platform uses a line laser binocular camera to capture high-quality point-cloud data.
It realizes the construction of grain 3D models using point-cloud segmentation, finding,
clustering, projection, and reconstruction. The grain length and width information are
calculated using the MBR method. The grain thickness is calculated using height difference. The grain volume is calculated using the division method to derive the irregular
polyhedral volume. Validation of the manual measurement data proved that the WG-3D
platform can achieve an effective and reliable accuracy level. The platform also has high
efficiency in point-cloud scanning and parameter calculation. It is a reliable platform for
high-throughput acquisition of wheat grain 3D indicators and lays the foundation for
in-depth study of other grain 3D morphologies.
Author Contributions: Conceptualization, W.W., X.Z., T.S. and S.L.; methodology, W.W.; software,
W.W.; validation, Y.Z. and H.W.; formal analysis, W.W.; investigation, Y.Z. and T.Y.; resources, X.Z.,
H.W., C.S. and T.S.; data curation, Y.Z., H.W. and T.Y.; writing—original draft preparation, W.W.
and Y.Z.; writing—review and editing, X.Z. and S.L.; visualization, W.W.; supervision, X.Z. and S.L.;
project administration, X.Z., S.L. and T.L.; funding acquisition, Y.H., T.L., C.S. and S.L. All authors
have read and agreed to the published version of the manuscript.
Funding: This research was funded by Central Public-interest Scientific Institution Basal Research
Fund (JBYW-AII-2022-09, JBYW-AII-2022-16, JBYW-AII-2022-17), Science and Technology Innovation
Project of Chinese Academy of Agricultural Sciences (CAAS-ASTIP-2016-AII), Special Fund for
Independent Innovation of Agricultural Science and Technology in Jiangsu, China (CX(21)3065,
CX(21)3063), National Natural Science Foundation of China (32172110, 32001465, 31872852), the
Key Research and Development Program (Modern Agriculture) of Jiangsu Province (BE2020319),
Supported by Bingtuan Science and Technology Program (2021DB001).
Institutional Review Board Statement: Not applicable.
Data Availability Statement: Not applicable.
Acknowledgments: We thank LetPub (www.letpub.com (16 June 2022)) for its linguistic assistance
during the preparation of this manuscript.
Conflicts of Interest: The authors declare no conflict of interest.

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</reference>

<statements>
1. The published grain, field and reconstruction pipelines justify treating the scanner, motion stage or robot, illumination, focus, reconstruction software and trait-analysis layer as one controllable dynamic system.
2. The evidence supports three load-bearing conclusions, each developed below from quantified pipeline results and control results.
3. while a low-cost line-laser binocular wheat-grain platform reports length, width, thickness and volume RMSEs of 0.10–0.23 mm and 0.65–1.77 mm³ depending on scan speed
4. The design contribution is therefore not to invent a new sensor, but to couple these methods into a supervisory digital twin that optimizes scan speed, viewpoint, focus, illumination and scheduling against a trait-uncertainty cost, while explicitly budgeting registration, mixed-pixel, laser-penetration, occlusion and benchmark-transfer errors that the literature quantifies only separately
5. conventional 3D acquisition equipment can be complicated and expensive for high-throughput phenotyping
6. The measured dependencies in the cited pipelines—stage speed, acquisition geometry, focus, illumination and camera height, and plant motion—support abstracting the controllable system as
7. \(u\) is the manipulated acquisition vector
8. scan speed is a measured accuracy–throughput variable
9. WG-3D uses a carrier table at 25 mm/s and shows improved accuracy at 5 mm/s with reduced efficiency
10. In WG-3D, grains are placed on a carrier table and scanned at an even speed, with the line-laser binocular camera acquiring 3D spatial information through binocular parallax and stereo matching
11. WG-3D instead uses a line-laser binocular camera costing only a few hundred dollars and computes disparity from left and right image coordinates
12. In WG-3D, the pipeline includes point-cloud acquisition, preprocessing, single-grain extraction, 3D model construction and morphological feature calculation; alpha-shape clustering, overhead projection, minimum bounding rectangles and a thickness formula \(T = Z_{\max}-Z_{\text{ref}}\) are used
13. WG-3D is low-cost and high-throughput but single-sided, so the back of the grain belly is unavailable
14. For individual grains, WG-3D explicitly cannot recover the back side of the grain belly from single-sided scanning
15. The available evidence does not provide one consolidated per-trait variance decomposition, but it supplies separate quantified terms—placement and scanner error, speed-dependent point-cloud error, registration and mixed-pixel error, representation error and environmental thresholds—that can be assembled into a design budget.
16. WG-3D reports length RMSE 0.2256 mm at 25 mm/s and 0.1018 mm at 5 mm/s
17. Sub-millimetre grain traits require active benchtop sensing and controlled stage speed
18. Fixtures, orientation control and multi-view or projection strategies must be part of the plant model
19. WG-3D measured length, width, thickness and volume for 26 Yangmai-series varieties
20. The acquisition layer should use model predictive control over scan speed
21. The evidence supplies separate constraints but not a single published joint controller; the separate constraints are scan speed
22. WG-3D quantifies the speed–accuracy trade: 25 mm/s gives length RMSE 0.2256 mm and volume RMSE 1.7740 mm³, while 5 mm/s improves length RMSE to 0.1018 mm and volume RMSE to 0.6457 mm³ but reduces efficiency.
23. The separate cost terms can be drawn from the cited measurements: scan time from stage speed and image count
24. \(T_{\text{scan}}\) is acquisition time
25. \(T_{\text{scan}}\) is measured by scan speed and image count
26. Are grain dimensions accurate? MAPE, RMSE and R² against micrometer or caliper measurements
27. WG-3D validated length, width, thickness and volume against electronic vernier calipers
28. The case studies show how the architecture should specialize across benchtop, consumer organ-level and field scales
29. Scan speed is a constrained optimization variable, not a fixed setting
30. 25 mm/s gave length RMSE 0.2256 mm and volume RMSE 1.7740 mm³; 5 mm/s improved accuracy but reduced efficiency; back-side data are unavailable
31. The literature supplies separate quantified terms—scanner accuracy [1][6], speed-dependent point-cloud error [2]
32. The evidence supports each component separately: scan speed [2]
33. For kernel-level and sub-millimetre grain traits, the evidence favours active benchtop sensing with controlled stage motion, calibrated illumination, adaptive focus and recursive pose or calibration observers, because structured light and line-laser binocular systems provide the quantified accuracy needed for length, width, thickness and volume [1][6][2]
</statements>

Begin the assessment now. Output only the JSON list, without any conversational text or explanations.