全 文 ：第 50 卷 第 5 期
2 0 1 4 年 5 月
林 业 科 学
SCIENTIA SILVAE SINICAE
Vol. 50，No. 5
May，2 0 1 4
doi:10．11707 / j．1001-7488．20140511
Ｒeceived date: 2013 － 05 － 22; Ｒevised date: 2013 － 12 － 31．
Funded project: This work was supported by A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education
Institutions，Jiangsu Provincial Agricultural Science and Technology Supporting Project ( BE2012383 ) ＆ National Forestry Public Welfare Project
(200904051) ．
* Mention of proprietary product or company was included for the convenience of readers and does not imply any endorsement or preferential
treatment by Nanjing Forestry University or USDA-AＲS．
基于动态树木图像序列的实时拼接系统
及其深度信息检测*
郑加强1 贾志成1 周 博1 周宏平1 Zhu Heping2
(1．南京林业大学机械电子工程学院 南京 210037; 2．美国农业部 AＲS 应用技术研究中心 OH 44691，USA)
摘 要: 在为高大林木防治病虫害和减少农药使用量而开发对靶喷雾机时，需要拼接树木图像和测量目标树木
的深度信息，本文搭建双摄像头硬件平台和三维几何算法模型开发了树木图像采集和拼接系统来处理动态树木图
像序列和计算目标树木与摄像头之间的距离信息，建立起摄像机视野范围、光轴夹角、焦点距离和拼接图像重叠系
数等与目标树木距离信息之间的几何算法函数关系。算法试验验证显示: 本文树木图像采集和拼接系统能准确测
量远至 6. 5 m 的树木距离，而其最大测量误差仅为 0. 27 m 或 7. 5%。本文图像拼接系统可用来开发基于有无目标
树木和距离信息进行定量喷雾的精确喷雾机。
关键词: 农药精确喷雾; 几何算法; 动态树木图像序列; 图像处理与拼接; 距离检测
中图分类号: S491 文献标识码: A 文章编号: 1001 － 7488(2014)05 － 0082 － 08
Ｒeal-Time Mosaicing System and Distance Detection Based on
Dynamic Tree Image Sequence
Zheng Jiaqiang1 Jia Zhicheng1 Zhou Bo1 Zhou Hongping1 Zhu Heping2
(1 ． College of Mechanical and Electronic Engineering，Nanjing Forestry University Nanjing 210037;
2 ． USDA /AＲS Application Technology Ｒesearch Unit，Wooster，OH 44691，USA)
Abstract: Techniques to detect target tree distances are needed for development of target-oriented sprayers to protect
shade trees from pest and disease attacks and reduce pesticide use． A tree image acquisition and mosaicking system used
a two-camera hardware platform and a 3-D geometrical algorithm was developed to process dynamic tree image sequences
and to calculate the distance between the target tree and the two cameras． The geometric algorithm established the distance
as a function of the camera field-of-view，angle between optical axes，distance of two points of camera focus and the
overlapping coefficient of mosaicked images． Validation of the algorithm demonstrated that the image acquisition and
mosaicking system accurately measure the tree distance within a 6. 5 m range． The maximum error within this distance
range was 0. 27 m or 7. 5% ． The image mosaicking system would be a potential tool for future development of precision
sprayers to deliver the desired amount of sprays to target trees based on the presence and distance of target trees．
Key words: precision pesticide spraying; geometrical algorithm; dynamic tree image sequence; image processing and
mosaicing; distance detection
1 Introduction
Ornamental shade trees are used to beautify the
landscape and served as wind barriers． These trees are
usually planted singly at a site and consequently are
susceptible to be attacked by insects and diseases．
Applications of foliar pesticides are an economic and
effective control measure to protect these trees from the
pest damages． However， spray applications presents
special problems because the locations of these trees
are usually near residential areas， commercial
districts， industrial and recreational parks， water
第 5 期 郑加强等: 基于动态树木图像序列的实时拼接系统及其深度信息检测
resources or ecological sensitive regions． Conventional
spraying systems deliver constant rates of chemicals to
these trees regardless of tree size，shape and foliage
density as well as the spacing between trees． Thus，a
large portion of the pesticide is wasted on non-targeted
areas ( Zheng et al．，2006 ) ． Sensor technologies to
detect trees and their configurations and minimize off-
target losses of chemicals for target-oriented spraying
systems are needed when spraying these trees．
However， target-oriented sprayers have great
difficulties to maintain a consistent distance between
the sprayer nozzle and the target trees because these
trees may have random positions． Also，for tall trees
the sprayers should have adequate distance away from
the trees to allow sprays to cover the entire tree height．
Despite distance variability， to ensure sprays are
applied at the proper time after sensors detect target
trees，different delay times are required to discharge
sprays． That is， the sprayers must calculate the
delayed time required between the tree detected and
the tree sprayed． Thus， critical to the sprayers is
sensors that can detect the target tree and determine its
distance from the sprayers for target-oriented spray
applications．
Ultrasonic sensors are a type of sensors that have
been used to detect trees to control spray applications
(Giles et al．，1988; Tumbo et al．，2002; Zaman et al．，
2004) ． Jeon et al． (2011b; 2012) used these sensors to
detect the distance between the sprayer and the surface of
tree canopy to calculate tree size． However，the detection
range of a single ultrasonic sensor is limited． If multiple
sensors were used，interference between adjacent sensors
would compromise their accuracy (Tumbo et al．，2002;
Zaman et al．，2004; Jeon et al．，2011a) ． Another type of
sensor，LIDAＲ (Light Detection and Ｒanging) has been
used to measure target tree distances and canopy sizes
(Chen et al．，2012，Wei et al．，2005; Lee et al．，2008;
Ｒosell Polo et al．， 2009 )， but they are relatively
expensive．
Machine vision technology implanting image
acquisition systems has been widely used to detect
crops and weeds (Meyer et al．，1998; Hu et al．，2009;
Wang et al．，2011; Steward et al．，2002; Tian et al．，
1998; Jeon et al．， 2011a ) ． In other areas， this
technology incorporating stereoscopic mosaicking
technique with multi cameras has been used to
determine the depth of view for targets in satellite
mapping ( Song et al．，2003; Bignalet-Cazalet et al．，
2010 )， marine survey ( Nagahdaripour， 1998;
Ｒzhanov et al．， 2000 )， remote sensing practice
(Bielski et al．，2007; Joshi et al．，2010 )，medical
devices for clinical diagnosis ( Miranda-Luna et al．，
2008) and other areas (Guestrin et al．，1998) ．
To achieve target-oriented spraying systems，the
Charge-Coupled Device (CCD) technology with image
mosaicking technique，which uses one camera to detect
trees and measure tree characteristics，has the potential
to control spray applications． With this technique，
when real-time video images of trees are captured，a
set of relative color index is generated to obtain the
target tree structure characteristics from the
segmentation of target trees and background (Zheng et
al．，2005; Zhou et al．，2010 ) ． Employing the real-
time tree structure information into a control system，a
target-oriented sprayer could automatically control
spray output based on target needs． However，the use
of one camera without a reference target to measure the
distance between the camera and trees is a limiting
factor (Sawhney et al．，1999) ． Also，for a tall tree，
the images from one camera may not be able to cover
the entire tree height if the sprayer is close to the tree．
The use of mosaicking image technique to measure
tree distances and increase pesticide spray accuracy for
target-oriented sprayers has not been reported． To
address these problems，this research proposed a two-
camera system to simultaneously capture images of
entire trees and then use stereoscopic mosaicking
technology to combine these separate images into a new
image to obtain the tree structure and distance from the
cameras． Thus，the objective of this research was to
develop and validate a dynamic tree image mosaicking
system derived from a geometrical algorithm based on a
configuration of two digital cameras to determine the
distance between the target tree and the cameras along
with the tree structure．
2 Materials and methods
2. 1 Overlapping area of mosaicked tree images
Binocular stereoscopic vision function states that
an object position in three dimensional coordinates can
be determined from two perspective images obtained
from two angles when the two imaging surfaces form an
38
林 业 科 学 50 卷
intersection line． Specially，based on the triangulation
principle， the positions of three-dimensional objects
could be obtained through the corresponding
relationship of the pixels from the two images．
The three dimensional position of the object can
be determined by the transformation matrix from the
object points in the spatial coordinates to the image
coordinate system． In the image mosaicking process，
the corresponding points of two images can characterize
the relative position of the two images． However，to
obtain the object distance information from the images，
the first step was to know the relative spatial position of
two cameras and its own parameters such as the angle
of two camera optical axes，focus distance，and the
angle of field-of-view for each camera．
Fig． 1 The overlapping area of two images for a target at two
different distances ( a) 0. 3 m and ( b) 0. 5 m from the cameras
As shown in Fig． 1，when the position of two
cameras was assigned， the overlapping area of two
images of the same target tree varied with only the
distance between the tree and cameras． A shorter
distance could have fewer pixels in the overlapping
area． The distance information of the target tree could
be obtained by calculating the ratio between the height
of the overlapping area and the height of two combined
images． This ratio is defined as the overlapping
coefficient of mosaicked images． If the entire target
tree was treated as a plane in the process of image
mosaicking，the tree distance was actually the distance
between the plane of the target tree and the line across
the two focus points of two cameras．
2. 2 Tree distance model from image mosaicking process
Fig． 2 shows the geometry of relative positions of
two cameras to the target tree． Parameters in the
geometry are defined as: α for the angle of two camera
optical axes， b for the distance between the focus
points of two cameras，θ for the field-of-view angle of
each camera，D for the distance from the line of two
focus points to the target tree plane，H for the visual
height of target plane，and L for the height of the
overlapping area． When the target plane is projected to
the plane that is parallel to the imaging plane， the
projected visible height is H， and the projected
overlapping height is L， then the overlapping
coefficient K should be，
K = L
H
． (1)
Fig． 2 Geometry of spatial positions of two
cameras and target tree plane
Analyzing the geometry shown in figure 2 yields，
L =
cos θ
2
－( )α
cos θ － α
2
L， (2)
H =
cos θ +( )α
2
cosθ
2
H， (3)
and
H = 2sinθ
cosθ + cosα
D． (4)
D actually is the sum of distance d1 ( from the
plane of two focuses to the interception point of the two
camera views ) and the distance d2 ( from the
interception point to the target plane ) ( Fig． 2 ) ．
That is，
D = d1 + d2 ． (5)
The two distances d1 and d2 have the relationship
with parameters b，θ，α，and L as，
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第 5 期 郑加强等: 基于动态树木图像序列的实时拼接系统及其深度信息检测
d1 =
b
2tan θ － α
2
． (6)
d2 =
L
2tan θ － α
2
． (7)
Combining equations (1)，(2)，(3)，(4)，(6)
and (7) into equation (5) yields，
D = b
2tan θ － α
2 1 －
sinθcos θ + α2
cos θ
2
－( )α
2 cosθ + cos( )α cos
θ
2
sin θ － α
2


K
．
(8)
Equation (8) presents the relationship between D
and parameters K，θ，α，and b． K is not a constant，
but it can be determined through mosaicking two
images by matching corresponding points of the same
location on the pair of images taken by two cameras．
Parameters θ， α， and b are constants when two
cameras are mounted on a fixed stand． However，the
measurements of θ，α，and b are difficult and often
inaccurate． To simplify equation (8)，a new constant
w is introduced，
w =
sinθcos θ + α2
cos θ
2
－( )α
2 cosθ + cos( )α cos
θ
2
sin θ － α
2
． (9)
By substituting equations ( 6 ) and ( 9 ) into
equation (8)，the distance between cameras and the
target plane becomes，
D =
d1
1 － wK
． (10)
Hence，the involvement of four parameters K，θ，
α，and b for determination of D is now simplified into
three parameters K，d1 and w． Because d1 and w are
also constants，D only varies with K． Determination of
d1 and w values can be achieved by taking two pairs of
target images at two distances ( D1 and D2 ) between
the target plane and the two cameras， and then
determine two K values (K1 and K2 ) from mosaicking
the two pairs of images． From equation (10)，D1 and
D2 can be expressed as，
D1 =
d1
1 － wK1
， (11)
D2 =
d1
1 － wK2
． (12)
Then，d1 and w can be calculated from the known
values of K1，K2，D1 and D2，
d1 =
D1D2 K2 － K( )1
D2K2 － D1K1
， (13)
w =
D2 － D1
D2K2 － D1K1
． (14)
Therefore， with equation ( 10 ) the distance
between the camera and the target tree can be
determined with the calculation of K values through the
process of mosaicking pairs of tree images．
2. 3 Image mosaicking system
An image mosaicking system was developed (Fig．
3) to capture and mosaic sequential tree images from
two cameras for measuring target tree distances from
equation (10) ． The mosaicking system consisted of a
video capture module，a camera parameter adjustment
module，a tree image mosaicking program module，and
a tree distance acquisition module． The functions of
these modules included: setting up camera parameters
to obtain clear images， capturing sequential images
with two cameras，generating tree image sequences，
mosaicking and displaying sequential images，refining
mosaicked tree images by filtering background noise，
calculating overlapping coefficient K，and calculating
target tree distance D． The system also had flexibility
to mosaic images manually．
2. 4 Validation of the mosaicking system accuracy
A hardware platform was assembled to determine
the two parameters d1 and w with the algorithm derived
from equations (13) and (14) ． The platform consisted
of a computer，two factory-calibrated digital cameras
( Model # DH-SV1310FC， Da Heng Co．， Ltd，
Beijing)，a framework for mounting the cameras，a
1394 card and simulated trees． To obtain wider field-
of-view of videos and images for a tall tree，a camera
stand fixture with a fasten device was designed to
mount the two cameras and to adjust the angle of the
two camera optical axes (Fig． 4) ．
The cameras were coupled with a CCD to capture
and store images in a digital memory． The cameras
were able to capture tree images at a maximum speed
of 30 frames per second ( fps ) ． The process of
capturing sequential images included defining critical
variables，assigning the callback function，turning on
the digital cameras，defining camera parameters ( focal
length，white balance，exposure time and aperture)，
capturing and processing video images，and turning off
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林 业 科 学 50 卷
Fig． 3 An image mosaicking system with modules
and flow charts to capture and mosaic tree images
Fig． 4 Ｒeal-time mosaicking experimental system to manipulate
two cameras for capturing sequential tree images
the cameras． During the real-time image mosaicking
process，the matching area of each pair of images and
the final combined image were shown on the computer
screen．
The camera parameters were adjusted before the
image mosaicking process． This was because the focal
length， white balance and aperture affected image
clarity，color and image brightness，respectively，as a
result to affect the image segmentation． The white
balance was adjusted manually through the color
finding table with the G component as a benchmark and
the ratio of Ｒ and B components as input． During the
white balance adjustment，all the field-of-view of the
lens was made as white， and the automatic white
balance adjustment ratio was repeated with the camera
Get-White-Balance-Ｒatio function until clear and
precise images were captured．
For a moving object，the camera exposure time
affected the clearness of the captured images． The
minimum and maximum exposure times of the cameras
used in the test were 20 μs and 1 s，respectively． The
target image motion ( δ， μm ) in the camera
display was，
δ = 1 000 000vtλ． (15)
where，v was the camera travel speed when passing the
target tree (m·s － 1)，t was the exposure time (s)，and
λ was the optical magnification ( or the ratio of target
tree image size to the actual tree size) ． To obtain the
satisfied clearness of images，the target image motion
( δ ) should be shorter than the pixel size of image
resolution． For the cameras used in the test，the CCD
display height was 3. 096 mm and image pixel was
6. 45 μm． That is，δ should be shorter than 6. 45 μm．
To verify the accuracy of the distance algorithm
module，the values for geometry parameters d1 and w
were calibrated and determined． Steps included:
placing a 2. 0 m tall tree at 1. 0 and 7. 0 m away from
the camera stand fixture，taking two pairs of images
with the two cameras for the two tree positions，
mosaicking each pair of images and using equation (1)
to calculate overlapping coefficient K1 and K2， and
then using the equations (13) and (14) to calculate
the camera setting parameters d1 and w．
An experiment was conducted to verify the
accuracy of the algorithm developed for equation (10)
to calculate the tree distance D and the overlapping
coefficient K． Steps for the experiment were: placing
the target trees at 11 different distances from the
cameras with a 0. 50 m increase for the distances
ranging from 1. 50 to 6. 50 m，moving the tree at
2 m·s － 1 speed perpendicularly to the camera optical
views， taking sequential pairs of images at different
distances，automatically mosaicking pairs of images by
pixel overlay of overlapping regions ( Zhou et al．，
2011) to obtain the overlapping coefficient K at each
distance，using equation (10) to calculate the target
tree distance with the known values of d1 and w
obtained， and then comparing the actual and
calculated distances to verify the module accuracy．
3 Ｒesults and discussion
3. 1 Camera exposure time
As shown in equation ( 15 )， the target image
motion ( δ ) linearly increased as the camera travel
speed ( v )，camera exposure time ( t ) and optical
magnification (λ) increased． Choosing values of v，t，
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第 5 期 郑加强等: 基于动态树木图像序列的实时拼接系统及其深度信息检测
and λ must meet the requirement that δ should be
shorter than the CCD display pixel resolution 6. 45
μm． For example， when the distance between the
camera and target tree was 5 m，the maximum tree
height that the camera could display was 12 000 mm．
That is，λ = 3. 096 /12 000 = 0. 000 258． If the camera
travel speed ( v) was 5 m·s － 1(18 km·h － 1) and δ was
equal to 6. 45 μm ( the image resolution in CCD)，the
maximum exposure time ( t ) from equation ( 15 )
should be 0. 005 s ( 1 /200 s) ． Similarly， if t was
chosen with the SetExposureTime function in the
camera as 0. 002 s (1 /500 s)，the maximum travel
speed ( v) should be 12. 5 m·s － 1 which was much
higher than the travel speed normally used for pesticide
sprayers． Therefore，the cameras used in the system
were fast enough to capture quality sequential images of
trees at high camera travel speeds because their lowest
exposure time setting was 20 μs (0. 000 02 s) ．
3. 2 Dynamic tree image mosaicking
Because an extensive time was required for
mosaicking sequential pairs of images， not all the
frames captured at the 30 fps speed could be
processed． The processing frequency varied with the
image processing time which depended on the template
radius of the paired images． During each cycle，the
most recent frames in the storage from two cameras
were coupled as the start point， and then pairs of
partial tree images captured by the two cameras were
mosaicked with the tree image mosaicking module．
To maximize mosaicking accuracy，a continuous
sorting method was used to match the pairs of images
while each pair of images was processed independently
to form a new mosaicked image． Every mosaicked
image was then compared with the previous mosaicked
image to obtain an integrated value for the overlapping
coefficient ( K ) ． After numerous comparisons of
sequential images for the same tree， the average K
value was calculated． The experimental results
demonstrated that three to five pairs of images could
reach a stable K value．
Fig． 5 shows the two images ( top left and lower
left ) captured with two cameras and then were
mosaicked into a combined image ( middle ) in real
time． The“green extraction”frame shown at the lower
right corner in Fig． 5 was used to make decisions on
which segments to be selected for the image mosaicking
process． The selected segments were also displayed at
the lower right bottom of the interface．
Fig． 5 The interface of dynamic tree image
sequence mosaicking system
3. 3 Accuracy of the image mosaicking system
For calibrated result，the overlapping coefficient K
obtained from the image mosaicking module was
0. 191 7 at D1 = 1. 0 m and was 0. 458 3 at D2 =
7. 0 m． Ｒeplacing these values into equations ( 13 )
and (14) yields the geometry parameters d1 = 0. 618 8
and w = 1. 989． Then，equation (10) becomes，
D = 0 ． 618 8
1 － 1 ． 989K
． (16)
After the values of d1 and w were determined for
the image mosaicking hardware platform， the target
tree distance could be calculated with equation (16)
after automatically mosaicking pairs of images along
with the overlapping coefficient ( K ) value at that
distance． Fig． 6 shows the actual target tree distance
(D ) as the function of K，presented with equation
( 16 ) ． The overlapping coefficient increased non-
linearly as the distance increased． This was because
the overlapping area increased as the distance
increased for the constant camera optical angles． The
change in K value became obvious when the cameras
were close to the target tree while the K value tended to
become a constant as the distance between the cameras
and the target tree increased． Therefore，it was critical
to calculate the K values accurately for obtaining the
accurate distance (D) when the cameras were close to
the target tree．
The K values obtained through the real-time
mosaicked pairs of target tree images at 11 different
distances were illustrated in table 1． The mosaicked K
values agreed well with the calculated K values that
employed the actual distances into equation ( 16 )
(Fig． 7) ． The linear coefficient for the calculated and
78
林 业 科 学 50 卷
Fig． 6 The actual distance between two cameras and the
target tree (D) as the function of overlapping coefficient (K)
obtained from mosaicked pairs of images
mosaicked K values was 0. 966 with r2 of 0. 995．
Therefore，the image mosaicking module was able to
map the pairs of images with a high accuracy．
Fig． 7 Comparison of K values mosaicked through the
real-time tree images and calculated with equation
(16) at 11 different distances
Tab. 1 also compares the actual target tree
distances and calculated tree distances with equation
(16 ) through the real-time mosaicking pairs of tree
images at 11 different distances． Within the range from
1. 50 to 6. 50 m，the maximum difference between the
actual and calculated distances was 0. 27 m． The error
occurred mainly due to the limitation of image
resolution to match the same points on the pairs of
images during the mosaicking process． There was no
trend showing the error had a relationship with the
actual distance ( Fig． 8 ) ． Within the distance range
tested，the maximum error was 7. 5% ． For shade trees
planted on roads，streets，or parks，their height are
normally taller than 2. 0 m，Compared to these tree
heights for target-oriented spray applications，this error
should be acceptable．
Hence，for the pesticide application on high range
trees，the sequential pairs of images with the whole
tree can be acquired and mosaicked which the
integrated tree image can be segmented from the
background． Then the high-range target-oriented
precision pesticide sprayer will be controlled to spray
the pesticide on the target trees according to the
mosaicked and segmented tree images．
Tab． 1 Calculated tree distances and mosaicked
overlapping coefficient obtained from the image
mosaicking system at different target tree positions
Target tree
position
Tree distance
to cameras，D /m
Actual Calculated
Difference
between
actual and
calculated
distances /m
Mosaicked
overlapping
coefficient K
1 1. 50 1. 50 0. 00 0. 295 8
2 2. 00 2. 15 0. 15 0. 358 3
3 2. 50 2. 60 0. 10 0. 383 3
4 3. 00 3. 15 0. 15 0. 404 2
5 3. 50 3. 61 0. 11 0. 416 7
6 4. 00 3. 99 － 0. 01 0. 425 0
7 4. 50 4. 77 0. 27 0. 437 5
8 5. 00 5. 09 0. 09 0. 441 7
9 5. 50 5. 46 － 0. 04 0. 445 8
10 6. 00 5. 89 － 0. 11 0. 450 0
11 6. 50 6. 39 － 0. 11 0. 454 1
Fig． 8 Measurement errors of tree distances from
the automatic image mosaicking process
4 Conclusions
A geometric algorithm， established with 3-D
binocular stereo vision concept was developed to calculate
the distance between targeted trees and cameras． The
targeted tree distance was the function of the mosaicked
image overlapping coefficient，camera mounting position，
the angle of two cameras optical axes，and optical view
angles． The algorithm simplified the function comprising
the overlapping coefficient and two measured geometry
parameters at two known distances．
Based on the geometric algorithm， an image
acquisition and mosaicking system that included an
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第 5 期 郑加强等: 基于动态树木图像序列的实时拼接系统及其深度信息检测
image mosaicking program and hardware platform was
developed to capture，process and mosaic sequential
images of trees in real time． Validation of the system
demonstrated that it was able to accurately measure the
tree distance within a 6. 5 m range． The difference
between the measured and actual distances was less
than 0. 27 m or 7. 5% ． Compared to the spacing
between trees，this difference was negligible for high-
range target-oriented pesticide spray application
systems． More precise delivery of pesticides to target
trees would be realized by integration of the image
mosaicking system with precision spraying systems．
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