Design and Experiment of Laser Photogrammetric Instrument for Measuring

Forest

YANG Liyan, FENG Zhongke, FAN Guangpeng, Li Haiyue

(Beijing Forestry University, Beijing 100083, China)

Abstract: To solve the shortcomings that non-intelligent, non-integrated and low efficiency of traditional method

of measuring DBH, tree height and forest stand spatial structure parameters. This paper designed a laser

photogrammetric instrument for measuring forest based on the principle of photogrammetry, image processing

technology, sensor technology and forest measurement. The instrument composed of CCD sensor, laser, LED

flashlight, self-developed PDA and shell. There were three modular procedures which were compiled in the Java

language and developed in Android Studio 2.2 systems development environment. The three modules are DBH

measurements, tree height measurements and forest stand spatial structure parameters measurement. These three

functions are achieved by obtaining parameters such as dip angle, azimuth and image information. The

experiment of measuring DBH (diameter at breast height), tree height with 21 trees as samples and measuring

forest stand spatial structure parameters with 15 reference trees in a plot as samples. Compared with the traditional

measurement method, The mean value of the absolute value of the relative error of the DBH measurement was

2.55%, the tree height was 2.82%, the uniform angle index was 2.50%, the dominance was 2.86% and the

measurement of the mingling is consistent with the traditional measurement method. The measurement accuracy

of the instrument can meet the requirements of forestry survey. The method of using the laser photogrammetric

instrument for measuring forest to measure the forest stand spatial structure parameters can be done requires only

one person. Compared with the traditional measurement method, this method saves 1 times of labor and 31% of

the working time. The instrument has a good prospect in the field of forestry basic investigation and forest stand

spatial structure.

Key words：laser photogrammetric instrument for measuring forest; photogrammetry; tree height; DBH; forest

stand spatial structure; Android system

Introduction

The diameter at 1.3m above the root neck is

called the chest height diameter, which is abbreviated

as breast diameter [1]. The length of the tree neck or

ground to the top of the trunk is called the tree height.

The measurement of DBH and tree height is an

important basis for evaluating site quality and forest

growth. There are many kinds of tools for measuring

the diameter. Commonly used are calipers, diameter

tape measures and hook gauges [2]. The height of the

tree is generally measured by a height sensor. There

are many kinds of height measuring instruments, but

the principle of height measurement is relatively

simple, such as the Bleus height sensor and ultrasonic

height sensor [3-5]. The spatial structure of forest

stands is an important feature that reflects the spatial

location of forest trees within forest stands, and is a

visual reflection of the distribution pattern and

arrangement of forest trees in space[6-10]. At present,

the spatial structure parameters of forest stand mainly

include the angle scale, size ratio and mixed degree

[11-15]. In the calculation of the angular scale, the

relative positions of the central tree and the four

nearest trees need to be measured. The commonly

used methods mainly include the direct judgment of

the angle determiner and the total station instrument to

measure the coordinates of each tree. However, there

are manual interpretation errors for the two methods.

The Yamato Total Station is expensive and

cumbersome. Due to the uncertainty of the landform

of the forest, the surveyors could not reach certain

lands or they could not carry out manual

measurements on the ground. In order to overcome

the influence of these unfavorable factors, non-contact

measurement methods have received attention.

With the advent of the era of information

intelligence, the use of more integrated, intelligent,

and accurate forestry survey and observation

equipment has become the mainstream of forest

resources survey [16]. Feng Zhongke et al [17-22]

developed 3D electronic angle gauges, stylized

electronic theodolites, total tree surveying instruments,

remote photography superstations, and handheld tree

measurement smart stations to measure the DBH and

tree height. Huang Xiaodong et al. [23] developed a

multi-functional portable micro-super station to

measure breast diameter and tree height. Hou Xinxin

et al. [24] proposed a breast diameter measurement

method based on a single charge coupled device

image sensor CCD camera and a theodolite. Zhao

Fang et al. [25] used a total station to measure the tree

height and volume, and verified the accuracy. Qiu

Haoxuan et al [26] developed a forest intelligence

mapping recorder that can measure the DBH and tree

height. Xu Weiheng et al [27,28] developed a

multi-functional electronic tree testing gun to achieve

tree height measurement, diameter measurement at

any height, and spatial structure parameter

measurement of forest stands. In recent years,

domestically developed instruments have basically

solved problems such as single device function and

poor portability, but there are still problems such as

poor accuracy, low efficiency, and high equipment

cost.

In view of the above situation, this study is aimed

at the actual needs of forestry survey important basic

factors and the determination of spatial structure

parameters of forest stands, using CCD cameras, tilt

sensors, electronic compasses, laser pens, etc., based

on the principle of photogrammetry and the principles

of tree-measurement, from android system embeds the

procedures for automatically calculating the

parameters such as DBH, tree height, and spatial

structure parameters of forest stands, and designs a

one-stop photo tree measuring instrument—laser

photometer and tree measuring instrument to realize

the measurement of breast diameter and tree height,

angle scale measurement, size ratio measurement,

mixing degree measurement and other functions.

1 laser photogrammetric instrument for

measuring forest structure

1.1 Hardware composition

The laser photogrammetric instrument for

measuring forest hardware used the handheld PDAs

and heads independently developed by the Beijing

Key Laboratory of CCD sensor, laser, LED flashlight,

self-developed PDA and shell. as shown in Figure 1.

CCD sensor selection telescopic fixed-focus optical

lens, back-illuminated CMOS (Exmor R CMOS)

sensor, 6 groups of 7 (4 aspherical lens / AA lens

included) lens structure, F1.8-F4.9 maximum aperture ,

LED fill light, Micro SD/Micro SDHC memory card,

NP-BN/NP-BN1 lithium battery, 200 battery life. The

laser uses an optical lens composed of high-quality

acrylic lenses, a 5mW power die, and a high-quality

acrylic lens that projects a visible laser beam. The

handheld PDA is highly integrated and designed with

aluminum alloy housings such as CPU, GPU, RAM,

ROM, gyroscope, gravity sensor, WiFi chip,

electronic compass, GPS chip, color touch display,

and power supply. The overall hardware of the

instrument hardware is shown in Figure 2.

Fig.1 Photo of laser photogrammetric instrument

CPU

GPU

Power

supply

Gyro

Gravity sensor

WiFi chip

GPS chip

Electronic compass

Touch screen

ROM

RAM

PDA

PTZ

CCD

Light Source pen

Laser

Fig.2 Framework of hardware

The handheld PDA module uses Qualcomm

Snapdragon 617 processor (MSM8952), eight-core

A53, and 1.5GHz core frequency to interpret

instructions and process data. The GPU uses Adreno

530, which processes 64 bits and handles the

acquisition of image information. RAM uses

dual-channel LPDDR4X, capacity 2GB, maximum

frequency 1866MHz; HSPA+, CDMA, LTE baseband;

ROM uses C8051F410 on-chip flash memory design,

16GB, speed class Class 10, maximum sustained

speed 80m/s; 5.5-inch display, resolution 1920x1080,

pixel density 401PPI. The gyroscope and electronic

compass employ a three-axis gyro sensor L3G4200D

and a three-axis magnetic field sensor LSM303DLH

for measuring the magnetic azimuth of the instrument;

Gravity sensor uses triaxial acceleration sensor

LIS331DLH, used to measure equipment tilt angle,

WiFi chip uses dual-frequency MT6625, supports

802.11a/b/g/n wireless protocol sensor LIS331DLH,

used to connect CCD lens, control shooting and

transfer images; The GNSS chip supports GPS and

Beidou Double Star Positioning System Module L218

for calibrating the sample location. The light source

pen uses a zoom wide-angle miniature flashlight, LED

light, and 18650 lithium battery for light source

supply in dim conditions to increase the visibility of

the edges of the trees.

1.2 Software design

PDA embedded software is compiled in the

Android Studio 2.2 development environment using

the Java language, using a modular structure design,

respectively, breast diameter measurement module,

tree height measurement module and forest spatial

structure parameter measurement module. Figure 3a is

the software main program flow chart, the user

chooses to enter different functional modules

according to the actual measurement work

requirements. Figures 3b~3d are the flow chart of the

three main measurement modules. The measurement

result data are read and written through the SQLite

database and can be transmitted via the USB interface.

Main program

System initialization

Function selection

DBH

measureme

nt module

Tree height

measureme

nt module

Forest spatial

structure parameter

measurement module

（a）Main program

Star

initialization

Turn on CCD and

connect WiFi

normal photography to

obtain image at breast

diameter

Transfer to PAD

Image processing

Extract the left and right

points of the DBH

Turn on the laser

Calculate DBH

End

Star

initialization

Turn on CCD and

connect WiFi

normal photography to

obtain image at breast

diameter

Transfer to PAD

Image processing and

calculating instrument

to standing distance

Get laser point

Turn on the laser

Collecting the inclination

of the root of the tree

End

Collect the tip of the tree

Calculate tree height

（b）Breast diameter measurement program （c）Tree height measurement program

Star

initialization

Turn on CCD and connect WiFi

Input the sample location information

Call breast diameter

measurement module to

measure breast diameter

Select the center tree and the

adjacent 4-6 trees

Turn on the laser

Measurement results are

stored in the SQLite

database

Select the 4 nearest trees to the center

tree and calculate the size ratio, angle

scale and mingling angle

Manually determine the

similarities and differences

between the tree types of the

adjacent tree and the center tree,

the same record is 1 and the

different records is 0

Record the shooting

azimuth angle to the

stand distance

The number of measured trees

is greater than or equal to 4?

Storing data

Y

N

（d）Forest Stand Spatial Structure Parameter Measurement Procedure

Fig.3 Flowcharts of main system and 3 function modules

1.3 Main function parameters

The laser photometer includes three functions of

breast diameter measurement, tree height

measurement, and spatial structure measurement of

forest stand. The forest structure parameter

measurement integrates the functions of angular scale

measurement, size ratio measurement and mixed

degree measurement. Laser class II laser, laser

wavelength 532nm, power 100mW, spot diameter ≤

10mm, indoor and outdoor use, you can choose

between continuous laser and pulsed laser switching,

you can fine-tune the irradiation angle; The

inclination measurement range is -75° to 75°, the

measurement accuracy is 0.3°, the azimuth

measurement range is 0 to 360°, and the measurement

accuracy is 1°. The operating system is Android 5.0.2,

CPU is 1.8GHz eight-core processor, storage 16G

ROM, memory 2G RAM. The GNSS chip supports

GPS and BDS dual-star positioning, supports both

LBS (Base Station Location) and AGPS (Auxiliary

Positioning) functions, and embeds EPOTM

technology and second-order technology to enable fast

positioning. The single-point positioning accuracy is

2m, and SBAS accuracy is less than 1m. The PDA has

a size of 150.7mm x 75.3mm x 8.2mm, a power

supply capacity of 3140mAh and a continuous

operating time of 8h. CCD sensitivity of ISO

160-6400, WIFI wireless transmission support

802.11b/g/n, effective pixels 2020 million, exposure

compensation ± 3EV (1/3EV steps), the highest image

resolution 5472 pixels × 3648 pixels, support for live

view For obtaining image information, the battery's

continuous working time is 5h. The head size is

160mm x 78mm x 70mm. The variable light source

pen supports astigmatism and strong light, power is

3-10W, range is over 200m, continuous exposure time

is more than 2h.

2 Laser photometer measuring principle

2.1 Laser photographic tree test

There are two kinds of systematic errors in the

measurement of laser photometers, which are the

optical distortion of the CCD camera lens and the

error between the CCD main optical axis and the main

optical axis of the laser. In order to improve the

measurement accuracy, two types of systematic errors

need to be eliminated or decrease [16].

A direct linear transformation (DLT) model was

used to solve the internal orientation elements and

distortion parameters of the CCD camera. The specific

calibration method is described in [29]. In order to

reduce the offset error between the CCD main optical

axis and the laser main optical axis, a checkerboard

checker board of 60cm×100cm is manufactured. The

checkerboard size is 10cm×10cm. The CCD camera

and the laser are turned on and generated in the

real-time image screen. Main point centered cross

orthogonal line, first fine-tune the laser from left to

right so that the laser spot coincides with the vertical

line of the crosshair. A laser photometer was placed

and the calibration board was placed at positions N

and F about 3m and 10m away from the instrument,

and the image coordinates of the laser spot in the

image were read sequentially. The formula for

calculating the angle between the main optical axis of

the laser and the main optical axis of the CCD is:

2 2 2 2

2 2

tan

( ) ( )

N N N F F F

F N

ab

b a b a

m u v m u v

L L

DLm

f u u v v

（1）

N Fm m、 ——Photo scale factor for near and far

shooting

( , )N Nu v 、( , )F Fu v ——The image coordinates of

the laser point shot at the near and far points

N FL L、 ——The distance between the lens and

the calibration board when the laser point is shot at the

near point and far point

L——CCD Lens to calibration board distance

f——CCD Lens focal length

abD ——Arbitrary selection of a point and b point

in the checkerboard

( , )a au v 、 ( , )b bu v ——The image coordinates of

point a and point b in the image

m——Photo scale factor

If "+", the laser is fine-tuned upwards; otherwise,

the laser is fine-tuned downwards. After several

adjustments, it is close to 0, that is, the main optical

axis of the laser is parallel to the main optical axis of

the CCD, and the calibration is completed. The

distance K between the CCD main optical axis and the

laser main optical axis of the last calibration is used as

the instrument constant and is embedded in the

software side together with the CCD calibration

parameters. The formula for K is

2 2 2 21

2N N N F F FK m u v m u v （2）

2.2 Breast diameter measurement

From the image point distance from the laser

point to the main point of the image and the

corresponding object distance K, the image scale

factor m can be calculated. Extract the image

coordinates on the left and right side of the DBH in

the image and calculate the image distance of the

DBH. According to the principle of single

photogrammetry, the vertical diameter of the tree is

calculated.

2 2

2 2

( ) ( )R L R L

l l

D m u u v v

Km

u v

（3）

D——Breast diameter

( , )L Lu v 、 ( , )R Ru v ——The image coordinates

of the left and right breast diameter

( , )l lu v ——The image coordinates of the laser

spot

Fig.4 Interface of DBH measurement

2.3 Tree Height Measurement

The height of the tree is mainly measured by

using a single photogrammetry principle and

trigonometric function principle. The tree height

measurement method is shown in Figure 5. It is

similar to the breast diameter measurement method,

and obtains the image scale factor m. According to the

CCD focal length f and the angle of inclination of the

photographing photograph, the horizontal distance d

from the photographing center to the single wood is

calculated, and the inclination angle α of the

instrument aiming at the tree root and the inclination

angle of the aiming tree top are obtained. β, calculate

tall tree height H.

(tan tan )

cos

H d

d mf

（4）

Fig.5 Principle diagram of tree height measurement

Fig.6 Interface of tree height measurement

2.4 Forest Spatial Structure Parameters

Measurement

Forest spatial structure parameters reflect the

degree of competition, size differences, and horizontal

distribution patterns among trees. Among them, the

angular scale reflects the evenness of the distribution

of trees in the forest. The ratio of size to size reflects

the dominance of the tree growth distribution, and the

degree of mixture reflects the degree of spatial

isolation between different tree species [30]. The

significance of the corresponding value of the mixture

degree, size ratio, and angle scale is shown in Fig. 7.

零度混交 弱度混交 中度混交 强度混交 极强度混交

优势 亚优势 中庸 劣势 绝对劣势

绝对均匀 均匀 随机 不均匀 团状

混交度

代表两个树种

角尺度：

α：相邻木夹角

α0：标准角

大小比数

代表不同大小

：

：

0.00 0.25 0.50 0.75 1.00参数取值

α α0α<α0 α<α0

α<α0

α>α0 α<α0

Fig.7 The sketch map of mingling, dominance and uniform

angle index

The laser photometer can measure the spatial

structure parameters of the forest in a one-stop mode.

The instrument can automatically calculate and save

the values of angle scale, size ratio, and mixed degree.

In the specific measurement, the center tree to be

measured and the four nearest neighbor trees are

determined. The laser is aimed at the center tree T0 to

take pictures, and the diameter DB is automatically

calculated according to the breast diameter

measurement principle, and the inclination and

azimuth angle are obtained through the instrument. It

is similar to the method for measuring the center tree

T0. The adjacent tree Ti is measured in a clockwise

order, and at the same time, it is manually interpreted

whether the adjacent tree and the center tree are the

same tree species. The instrument can automatically

calculate the angle scale, size ratio, and blending

degree according to the above acquisition parameters

and display the result on the screen, and save it to the

SQLite database at any time for easy viewing and

export.

Fig.8 Uniform angle index measuring principle

P is the station; T0 is the center tree; T1~T4 are

the four trees closest to the center tree; δ is the

inclination angle; γ is the azimuth angle; and is the

angle between the center tree and the nearest four

trees.

The calculation formula for the coordinates of the

central tree and the four adjacent trees is

( cos /2)cos

( cos /2)sin

x X m f Di P i i i i

y Y m f Di P i i i i

（5）

（i=0,1,2,3,4）

,i ix y ——Plane coordinates of the ith tree

,P PX Y ——Position the coordinates of instrument

point P

im ——Scale factor for measuring the ith tree

i ——The inclination of the i-th tree

i ——The azimuth of the i-th tree

iD ——The breast diameter of the i-th tree

According to the coordinates of the center tree and

the neighboring tree, the angle between the i-th tree

and the i+1 tree is obtained. The formula is

2 20, 0 0

2 20, 1 1 0 1 0

2 2, 1 1 1

2 2 20, 0, 1 , 1

0, 0, 1

( ) ( )

( ) ( )

( ) ( )

arccos( )2

i ii

i i i

i ii i i i

i i i i

i

i i

S x x y y

S x x y y

S x x y y

S S S

S S

（6）

i=1,2,3；When i=4, 3

4

1

360 i

i

S——The distance between each tree i ——The

angle between the i-th tree and the i+1 tree

4

1

1

4i

i

W z

（7）

1 the i-th is smaller than

the s tan dard angle )

0 others)

iz

o

，(

72

，(

（8）

（i=1,2,3,4）

The size ratio is calculated as Blending formula is

4

1

1

4i

i

U k

（9）

0 The DBH of the i-th adjacent tree is smaller

than the DBH of the central tree

others

ik

，(

)

1，( )

（10）

（i=1,2,3,4）

4

1

1

4i

i

M v

（11）

The i-th adjacent tree is the

same as the central tree

ohters

iv

0，(

)

1，( )

（12）

（i=1,2,3,4）

3 experimental results and analysis

3.1 DBH and tree height measurements test

To verify the breast diameter, height measurement

function, and measurement accuracy of the laser

photometer, an experiment was conducted at the

Jiufeng National Forest Park in Bei’anhe Township,

Haidian District, Beijing. The experiment selected

trees in different forest conditions to test the

measurement function of the forest. 21 trees were

selected as measurement samples, including 7 trees

such as poplar, Chinese pine and Robinia. It uses the

breast diameter measured by the DBH as the true

diameter of the DBH, and the tree height measured by

the total station as the true value of the tree height.

The DBH measured by the laser photometer and the

tree height are compared with the true values. After

calculation, the average absolute values of the relative

error of DBH and tree height were 2.55% and 2.82%,

respectively. The results of the measurement are

shown in Table 1.

Tab.1 Result of DBH and tree height measurement

Tree species

DBH

ruler

measue

DBH

/cm

laser

photogrammetric

instrument for

measuring forest

measure DBH /cm

absolute

relative error

/%

Total Station

measure tree

height /m

photogrammetric

instrument for

measuring forest

measure tree height

/m

absolute

relative error

/%

poplar 18.6 19.1 2.69 22.6 23.2 2.65

poplar 29.5 29.1 1.36 30.5 29.8 2.30

poplar 13.4 13.7 2.24 17.9 18.3 2.23

chinese pine 17.7 17.4 1.69 9.1 8.8 3.30

chinese pine 21.5 20.9 2.79 14.2 14.8 4.23

chinese pine 28.4 28.9 1.76 12.1 11.7 3.31

locust 16.3 15.7 3.68 8.2 8.5 3.66

locust 17.1 17.6 2.92 7.6 7.9 3.95

locust 16.8 16.4 2.38 8.3 8.0 3.61

oak 22.1 22.6 2.26 10.5 10.8 2.86

oak 19.7 19.3 2.03 9.8 9.9 1.02

oak 18.5 19.1 3.24 11.3 11.5 1.77

acer truncatum 15.2 15.6 2.63 8.5 8.3 2.35

acer truncatum 13.1 13.4 2.29 7.8 7.5 3.85

acer truncatum 15.3 14.9 2.61 9.4 9.6 2.13

orientalis 12.1 12.4 2.48 6.8 7.0 2.94

orientalis 10.3 10.8 4.85 7.5 7.2 4.00

orientalis 12.6 13.0 3.17 7.3 7.5 2.74

broussonetia

papyrifera 20.4 20.1 1.47 8.2 8.4 2.44

broussonetia

papyrifera 15.6 16.2 3.85 7.4 7.3 1.35

broussonetia

papyrifera 17.3 17.5 1.16 7.6 7.8 2.63

Mean 17.69 17.80 2.55 11.08 11.13 2.82

3.2 Forest stand spatial structure measurement

test

To verify the spatial structure parameter

measurement function and measurement accuracy of

the laser photometer and tree tester, a sample plot was

selected and tested in the Jiufeng National Forest Park

in Bei’anhe Township, Haidian District, Beijing.

Fifteen central trees were selected in the plot, and one

operator measured the selected central tree using a

laser photometer, and two operators retested using the

traditional measurement method. When using the

traditional measurement method, the angular scale

measurement uses a horn to perform direct

interpretation, the size-ratio measurement uses a

breast diameter ruler to measure and read one by one,

the mixed degree measurement uses a direct

interpretation method, and the interpretation result

uses a paper record. Comparing the results of the two

methods, as shown in Table 2, the results show that

the absolute values of the absolute relative error of the

angular scale and size ratio measurement are 2.50%

and 2.86%, respectively, and the mixed degree

measurement results are the same. That is, the

absolute value of the relative error of the spatial

structure parameters of the three forest stands does not

exceed 3%, which can meet the measurement

accuracy requirements.

Tab.2 Result of forest stand spatial structure measurement

Observation point

No.

laser photogrammetric instrument for measuring

forest Observation method Traditional measurement

Angular scale Size ratio Mixed degree Angular

scale

Size

ratio

Mixed

degree

1 0.50 0.50 0.25 0.50 0.50 0.25

2 0.75 0.50 0.25 0.75 0.50 0.25

3 0.75 0.75 0.00 0.75 0.75 0.00

4 0.50 0.50 0.25 0.50 0.50 0.25

5 0.75 1.00 0.50 0.75 1.00 0.50

6 1.00 0.50 0.25 0.75 0.50 0.25

7 0.75 0.50 0.25 0.75 0.50 0.25

8 0.50 0.75 0.25 0.50 0.75 0.25

9 0.50 0.50 0.00 0.50 0.25 0.00

10 0.75 1.00 0.00 0.75 1.00 0.00

11 0.75 0.50 0.25 0.75 0.50 0.25

12 0.50 0.50 0.25 0.50 0.50 0.25

13 0.25 0.50 0.25 0.50 0.50 0.25

14 1.00 0.25 0.50 1.00 0.25 0.50

15 0.75 0.50 0.00 1.00 0.50 0.00

Mean 0.67 0.58 0.22 0.65 0.57 0.22

Relative error

absolute value /% 2.50 2.86 0.00

4 Conclusion

(1) A laser photometer measuring

instrument composed of CCD sensor, laser, LED

flashlight, self-developed PDA and shell. According

to the principle of photogrammetry and principle of

tree-measurement, using image processing technology

and Java development technology, three functions of

breast diameter measurement, tree height

measurement and spatial structure parameter

measurement of forest stand were achieved. The

spatial structure parameter measurement function of

forest stands achieves one-stop measurement of angle

scale, size ratio, and mixed degree. The function and

accuracy of laser photometer logging instrument

carried out in the Qifeng National Forest Park in

Bei’anhe Township, Haidian District, Beijing, The

results show: The average absolute value of the

relative diameter of breast diameter measurement is

2.55%, the average absolute value of the relative

height of the tree height measurement is 2.82%, the

average value of the absolute value of the angular

scale measurement relative error is 2.50%, and the

relative error of the absolute value of the size ratio

measurement is The average value is 2.86%,the mixed

measurement results are the same as traditional

measurement methods and can meet the accuracy

requirements of forestry surveys.

(2) The laser photometer was developed to achieve

paperless automatic measurement. The data can be

stored and exported, reducing the workload of the

internal processing and lowering the cost. In addition,

the instrument is a non-contact measurement during

operation and can be measured. Compared with the

laser distance measurement type instrument, problems

such as weak return signals due to the unevenness of

the bark during the measurement of the laser distance

meter or deviations of the return signal are avoided.

Therefore, the instrument has a good application

prospect in the field of basic investigation of forestry

and related fields of spatial structure parameter

measurement of forest stands.

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