Study on the Accuracy of Tree’s Diameter Measurement by Laser Range
Finder System
M.R. Yaacob
Faculty of Electrical Engineering
Universiti Teknikal Malaysia Melaka,
Malaysia
rusdy@utem.edu.my
M.F. Miskon
Faculty of Electrical Engineering
Universiti Teknikal Malaysia Melaka
Malaysia
fahmimiskon@utem.edu.my
C.X. Zhi
Faculty of Electrical Engineering
Universiti Teknikal Malaysia Melaka,
Malaysia
chan_xin_zhi@hotmail.com
Keywords: Laser, Diameter, Tree
Abstract
This paper presents a study on the accuracy of laser range finder system for the measurement of tree’s
diameter. The study has been conducted by using Hokuyo URG-04LX-UG01 Laser Range Finder. The
measurement was done in different distances from the measured tree at a fix elevation in two different modes;
sensor held in hand and sensor mounted on a tripod. An algorithm was developed to derive the formula for
calculating the diameter by applying the principle of circle tangent theory. The results obtained are the values
of accuracy for the diameter measurement of a tree for different distances between the sensor and the tree
measured which are presented in graphs. Finally the accuracy levels between the two modes are compared to
find the most preferable mode for the measurement in real application.
1. Introduction
Contact and non-contact measurement devices have been developed for decades to measure the diameter of
a tree. These devices are still considered to be time consuming and low in accuracy while forestry and plantation
workers are still using one of these methods for diameter measurement. Fast responding and accurate noncontact measurement device is in need for this kind of measurement in order to reduce the time for measurement
of the whole plantation. Thus an accurate measurement device is required to determine the correct time for
fertilization and time to tap off the trees measured.
Available methods used to measure diameter of tree do not consist of Graphic User Interface (GUI), time
consuming and low in accuracy. This causes difficulty for forestry workers or researchers as well as affecting
the result of measurement values. Rubber Industry Smallholders Development Authority (RISDA) is one of the
estate developers in Malaysia who faces difficulty when dealing with problem in measuring circumference of
tree trunk. This is caused by massive amount of rubber trees to be measured using difficult and low accuracy
measurement methods such as tape measuring, calipers and Biltmore Sticks. In order to eliminate these
problems, alternative method is researched to measure tree diameter together with the study of its performance
in term of accuracy.
Previous researches have been done which involves measurement of tree’s diameter and circumference.
Researchers from the US Department of Agriculture have come out with Criterion Laser Instrument which
employs laser beam to measure tree diameter [1]. Despite considering its high cost, this device requires user to
manually entering the tick marks across the tree and distance from the tree into the keypad to calculate the
diameter of the tree which is then required for further analysis.
Another research was previously done by researchers from Universiti Teknikal Malaysia Melaka regarding
the linear and rotary infrared scan system for the circumference measurement of trees [2]. This measurement
system resulted in poor performance due to the step angle resolution of stepper motor used. Larger angular
resolution results in bigger approximation for analog linear scan method. There was also an issue related to the
limitation of IR sensors used as these sensors gave unstable results. Therefore another sensor that employs
different light source, which is laser, is much preferable to replace the infrared as the measurement medium.
In this paper, we will further discuss on the measuring principle in Section 2. Section 3 describes the
experimental setup used for the diameter measurement and finally in Section 4, we will thoroughly discuss the
results obtained from the experiments.2. Formatting your paper
2. Measuring principle
2.1. Hokuyo URG-04LX-UG01 Laser Range Finder
Hokuyo LRF is a laser sensor with infrared light source as shown in Fig. 1. Its scanning area is about 240°
at accuracy until 4000 mm as clearly illustrated in Fig. 2 [3]. Object’s color has minimum effect upon the
Laser Range Finder. The specifications of URG-04LX-UG01 are summarized in Table 1.
Fig. 1 Hokuyo URG-04LX Laser Range Finder
Fig. 2 Detection Angle and Maximum Distance of Hokoyo LRF
Table 1: URG-04LX-UG01
Power Source
Detection Distance
Accuracy
Total Scan Angle
Weight
Life Span
Light Source
5V DC (from USB)
0.02 – 4.00m
Distance : 0.02mm – 1.00m (±0.03m)
Distance : 0.02m – 4.00m (±3% of measurement)
240°
Approximately 160g
Approximately 5 years
Laser Class 1
Hokuyo URG-04LX Laser Range Finder is appropriate to be used for detecting surface properties and
measure conditions although it is small in size [4]. Its accuracy depends on material properties and can be
calculated from the absolute error produced during measurement. Fig. 3 shows material properties used for
testing URG-04LX LRF. The actual distance of the object is at 1500 mm. Aluminum is most likely to be the
surface of detection because its data approaches 1500 mm. Wood material is considered very good to be the
surface used for LRF detection since its data is closer to 1500 mm compare to gray sheet, steel and electrical
steel.
Fig. 3 Material Properties
2.2. Tree Diameter Measurement Algorithm
The basic principle behind the tree diameter measurement algorithm is based on the circle tangent theory.
Cross section of tree is considered as circle and can be calculated using circle equations. From circle tangent
theory if a line is tangent to a circle, the straight line drawn from circle’s radius to the point of contact between
circle’s radius and the tangent line is perpendicular with both the tangent line and circle’s radius as illustrated in
Fig. 4.
Fig. 4 Line Tangent to Circle
Now consider in Fig. 5 that consist of two lines tangent to the circle located at different contact points but
both of them are extended to a same point. A straight line is drawn from the contact point up to the circle’s
radius for both the tangent lines. The intersection point of both lines drawn from the two tangent lines will
meet at centre point of the circle.
Fig. 5 Two Lines Tangent to Circle
Angle measured between the two tangent lines is represented by theta. Length a and b are both measured
from extended point of both tangent lines to the contact point of the tangent lines respectively.
Fig. 6 Finding the Length c
From Fig. 6, length c can be calculated using law of cosines formula provided that length a, length b and 𝜃
are known:
𝑐 2 = 𝑎2 + 𝑏 2 − 2𝑎𝑏𝑐𝑜𝑠(𝜃)
(1)
𝑐 = √𝑎2 + 𝑏 2 − 2𝑎𝑏𝑐𝑜𝑠(𝜃)
(2)
Meanwhile radius of the circle, R can be calculated if length c is found and thus yield to the determination
the circle’s diameter, D:
𝜃2 = 180° − 𝜃
(0)
𝑐 2 = 𝑅2 + 𝑅2 − 2 × 𝑅 × 𝑅 × cos⁡(𝜃2 )
(4)
𝑐 2 = 2𝑅2 − 2𝑅2 cos⁡(𝜃2 )
𝑐 2 = 2𝑅2 [1 − cos(𝜃2 )]
2𝑅2 [1 − cos(𝜃2 )] = 𝑐 2
𝑅2 =
𝑐2
2[1 − cos(𝜃2 )]
𝑐2
𝑅=√
2[1 − cos(𝜃2 )]
(3)
Diameter of the circle, D is:
D = 2𝑅
(4)
Therefore, the tree diameter can be measured using the algorithm derived where the distance to measure
the diameter of the tree can be varied for different set of measurements.
3. Experimental Setup
There were two experiments conducted to test the performance of the proposed method. The objective of
the experiments is to test the accuracy of the device when the device is held on hand and when the device is
fixed to the ground with tripod. The purpose of carrying out two experiments is because the reliability of data
collected with human’s hand holding the device difference from the reliability of data collected when the device
is fixed to the ground. Human’s hand tends to move around when holding measurement device while tripod can
help to fix the device to the ground.
The first experiment was done with data collecting by measuring a tree with LRF held on hand as depicted
in Fig. 7. Meanwhile the second experiment was done through data collecting by fixing LRF above the ground
with tripod as depicted in Fig. 8.The apparatus used for the experiments are:
i. Hokuyo URG-04LX-UG01 Laser Range Finder (LRF)
ii. Algorithm
iii. Lenovo G475 Notebook with Microsoft Windows 7 Professional
iv. Tree with actual diameter of 191mm and circumference of 600mm
v. Tree with actual diameter of 284mm and circumference of 892mm
vi. Tripod
The experiment was conducted on a field during daylight condition at temperature of approximately 30.
The temperature and lighting condition do not affect the performance of the laser. Therefore it is not critical to
control these variables. The experiment was conducted at different distance. 100 data of diameter and
circumference measurement were taken for each distance. The result was recorded. The experiment was
repeated by changing the distance between the Laser metric and the tree within range of 0.5m to 3m at an
interval of 0.1m.
Fig. 7 LRF held on hand
Fig. 8 LRF fixed to the ground with tripod
4. Results and Analysis
Fig. 9 shows the result for diameter measurement with LRF held in hand. Accuracy decreases when
distance increases where the highest accuracy achieved is 98.63% at diameter of 0.6m while the lowest one
obtained is 93.76% at diameter of 2.9m. The accuracy seems to be fluctuating and this is agreed with previous
research in which distance data obtained from Hokuyo LRF URG-04LX has been proven to be fluctuating along
its measurement [4]. Fluctuating measurement may be due to heat dissipation of the LRF during its activation
time. Heat dissipation of motor in the LRF may also be the cause of fluctuation data produced by LRF because
small vibration produced when motor rotates to spin the mirror used for LRF scan.
Fig. 9 Accuracy versus Distance (LRF held in hand)
Fig. 10 Accuracy versus Distance (LRF mounted to Tripod)
Fig. 10 shows the result for measurement with LRF mounted to tripod. Accuracy also fluctuates within
the range of 96% to 98% from distance of 1.3m to distance of 2.6m. The highest accuracy obtained 99% at
distance of 1.1m while the lowest accuracy obtained is 85.6782% at distance of 3m. Accuracy begins to drop
below 96% at 2.7m and drops significantly at distance 3m. However, when compared to the measurement with
hand held, results in Fig. 10 shows that the accuracy level is maintained at high level up to the distance of 2.6m.
5. Conclusions
Stability of holding the Laser Metric affects the accuracy as well. Holding the LRF with hand has
inconsistent data compared to fixing it to the ground. This may be due to human tiredness when holding the
device to measure tree diameter and circumference. Therefore it is more preferable to use the LRF with tripod in
taking the diameter measurement in the real application for more accurate results. Future work could be done by
investigating the effect of tilt angle when measuring tree and size of the tree on the accuracy of the
measurement. It would be interesting to find out how these variables affect the accuracy of the measurement
6. References
[1]
[2]
[3]
[4]
Instrument for Measuring Stem Diameters. S. Garrett, J.J. Kempf, R.L.
Copstead. Washington : United States Department of Agriculture, 1997.
Linear and Rotary Infrared Scan System for Measuring Circumference, M.F. Miskon, A. M. Deraman, A.Y.B. Ahmad, M. A. Ibrahim,
A. Ahmad, Z. Sani, M.H. Jamaluddin, Universiti Teknikal Malaysia Melaka, 2011.
Hokuyo Automatic Co, LTD. Scanning Laser Range Finder URG-04LX-UG01(Simple URG) Specifications. Hokuyo URG Series
Download Page. [Online] [Cited: Septermber 15, 2011.] http://www.hokuyo-aut.jp/02sensor/07scanner/download/products/urg04lx/data/URG-04LX_spec_en.pdf
Characteristics of the Compact Hokuyo URG-04LX 2D Laser Range Finder. L.Kneip, F.Tache, G.Caprari, R.Siegwart. Kobe,Japan :
IEEE, May 12-17, 2009.