Research on Different Slicing Methods of Acquiring LAI from Terrestrial Laser Scanner Data

Zhen Zhu#*+1, Wuming Zhang#*+2, Ling Zhu#*+3, Jing Zhao#*+4 #State Key Laboratory of Remote Sensing Science Beijing Normal University , Beijing, 100875, China

*Beijing Key Laboratory for Remote Sensing of Environment and Digital Cities, Beijing Normal University Beijing, 100875, China

+School of Geography and Remote Sensing Science, Beijing Normal University, Beijing, 100875, China 1zhuzhen198610@mail.bnu.edu.cn, 2wumingz@bnu.edu.cn 3zhuling@bnu.edu.cn, 4200921170072@mail.bnu.edu.cn

Abstract— It has been possible to acquire precise point clouds of surface features using terrestrial laser technology. And it has been a research hot spot to figure up the LAI of a single tree combined point clouds of the tree with gap fraction model. While calculating the LAI using gap fraction model, it is a general procedure to slice the acquired point clouds. Zenith slicing and vertical height slicing are two ways often used for this purpose. We used the point clouds of a single tree with gap fraction model to determine which slicing method is better to compute the LAI, and found: (1) the results of LAI are closely related with the different slicing methods and slicing thickness; (2) the results of LAI apparently deviate from the ground truth when the slicing thickness is very big or very small; (3) the results of LAI are closer to the LAI of field measurements while the slicing thickness is smaller within the appropriate slicing range; (4) within the appropriate slicing range, the vertical height slicing is better than the zenith slicing. Keywords— Gap fraction model; LAI; slicing methods; point

clouds; terrestrial laser scanner

I. INTRODUCTION LAI (leaf area index) is one of the most elementary

parameters, which represents vegetation canopy structure. And it plays an important role in physiologic and physical processes of trees, such as photosynthesis, respiration, transpiration, carbon cycling and rain interception by forest canopy[1][2] . For the sake of different areas and purposes of application, various definitions of LAI have been proposed by different researchers[3][4] . In the domain of remote sensing, the general accepted definition of LAI is the cumulative one-sided surface area of the leaves in the canopy per unit ground area[5] .

Many methods are proposed to calculate LAI by many researchers, including litter traps, allometric[6] and inclined point quadrat, etc. Gap fraction model has been widely used to determine LAI of trees, because the time cycle is smaller and the method is less destructive to trees, for example, LAI-2000 can determine gap fraction of vegetation at five different zenith directions, and acquire LAI of trees [7].

Terrestrial laser scanner has been developing rapidly in the recent years. Depending on the technical features of high efficiency, high coverage and real 3-D measurements, it can be applied to not only the measurements and deformation monitoring of architectures, roads, bridges, dams, and so on[8], but also the extractions of structural parameters of trees. Many researchers have used terrestrial laser scanners to acquire trees’ structure parameters. Wenjian Ni extracted tree structure parameters from terrestrial laser scanner data. He first filtered the multiple scattering points effectively by checking the eight-neighbor’s distance to scanner, and then improved the multi-scale method for ground points’ recognition to rapidly extract the ground points in the research area. Based on the analysis of the point-cloud, the vertical continuity of trunks points were used to identify tree trunks. Finally, he extracted the information of tree position, diameter at breast height (DBH) and tree height. The results had good uniformity to the forestry data[9]. Dimitry Van der Zande used commercially available SICK Laser-Measurement-System-200(LMS200, Sick, A.G.) to obtain 3D structural datasets in different patterns (lateral sideway, lateral bottom-up, hemispherical bottom-up), and found that the pattern of bottom-up can cope with shadow effect well[10]. However, these two researchers only researched the calculations of tree height, DBH, etc, but not referred to LAI.

Tomomi Takeda measured distribution of plant area density (PAD) using a ground-based laser scanner, and compared the PAD with that obtained by the attenuation of solar radiation and litter traps. Firstly he divided the forest horizontally and vertically to define volume elements (voxels), and then calculated PAD using the gap fraction in every voxel. He finally found that: because the laser beam couldn’t reach the top of the forest, the method underestimated PAD in the upper layer of the forest; compared with result obtained by the attenuation of solar radiation, the method overestimated plant area index (PAI) by three units, but successfully captured the reduction of PAI between the time of bud break and leaf-fall; the horizontal distribution of PAI estimated by gap fraction

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was well correlated with that estimated by litter traps. And the horizontal non-uniformity of PAI was reproduced[11].

Fumiki Hosoi used precise voxel-based tree models combined with point quadrat method to figure up the LAI of a single tree. He demonstrated that LAI could be measured accurately without any prior knowledge about the actual leaf inclination angles. And he thought the G function as a fixed value when the zenith angle of laser beam was 57.5 [12]. However, he only tested this method through a small tree in the laboratory, and did not apply this method to the trees in a mature forest.

There are at least two slicing methods (zenith slicing and vertical height slicing[12] to calculate LAI of a single tree using gap fraction model. The result varies with different slicing methods. This paper sliced point clouds in these two manners, and then compared the results with the ground truth to find the better slicing manner.

II. DATA AND METHOD Many point clouds of a single tree were acquired at

different locations by terrestrial laser scanner, and these point clouds had different point intervals. Three point clouds, whose point intervals were 1mm, 1.5mm, 5mm, were chosen to figure up the calculated LAI using gap fraction model. Meanwhile, LAI-3000 was taken advantage to measure every leaf area, and the projected area of the whole tree was calculated using Riscan-Pro, which is a point clouds processing software, so the measured LAI can be figured up.

A. Data Our research object was a longan tree, which was near New

Campus of Fuzhou University. And the height of the tree was about 4.5m, the leaf size of the tree was about 3cm 5cm.

The terrestrial laser scanner used was Riegl-VZ400. Its scanning error was 2mm when its scanning distance was 100m. Its largest scanning distance was 500m, and it can cope with the longan tree’s height well. Its scanning range in zenith direction was 100 , and that in azimuth direction was 360 .

Fig.1 is a point clouds with point interval of 1.5mm:

Fig.1 Point Clouds whose point interval was 1.5mm from VZ400

The point clouds acquired from VZ400 included various attribute types, the types we used were X value, Y value, Z value in local Cartesian coordinate system and Range value, Theta value, Phi value in polar coordinate system. The two coordinate systems were explained as the followings: in local Cartesian coordinates, the origin was scanning center, X axis pointed to scanning direction, Z axis pointed to plumb direction and the local Cartesian coordinate was right-handed coordinate system, so the Y axis direction could be determined; in polar coordinates, Range value represented the distance between scanning center and the object, Theta value represented the angle between scanning center and plumb direction, Phi value represented azimuth angle.

From the height of 1.6m off the ground (because there are no leaves under the height of 1.6m), the tree was divided into several space levels by 0.2m. The leaves in every space level were picked off, and the number and area of these leaves were measured using LAI-3000. The result was listed in table 1:

TABLE I

THE LEAF NUMBER AND LEAF AREA OF LONGAN TREE IN DIFFERENT SPACE

LEVEL

Tree height m Leaf number Leaf area cm21.6 – 1.8 68 403.9114

1.8 – 2.0 156 984.7635

2.0 – 2.2 602 4294.8

2.2 – 2.4 750 7256.1

2.4 – 2.6 450 4838.7

2.6 – 2.8 1324 15102

2.8 – 3.0 1738 14370

3.0 – 3.2 1590 23396

3.2 – 3.4 1340 18887

3.4 – 3.6 1315 17987

3.6 – 3.8 1146 18100

3.8 – 4.0 583 6660.5

4.0 – 4.2 680 5355.2

4.2 – 4.4 202 1220.2

Total 11944 138860

The total leaf area was 13.8860m2. The projected area of

the longan tree was 6.910 m2, so the LAI of the tree was 2.0096. This LAI is regarded as ground truth in the following procedures.

B. Gap Fraction Model If leaves are assumed to be randomly distributed, the

relationship between LAI and gap fraction could be expressed as following[13]:

* ( )/cos( )( ) LAI GgapP e � �� �� (1)

Where Pgap ( ) is gap fraction when the zenith angle is , G( ) is the G function ( mean projection of unit foliage

area ). To determine the gap fraction of every space level, the

number of laser pulses (Psend) passing through every space level and the number of pulses (Preceive) intercepted within every space level are counted. Then the relationship between Pgap, Psend and Preceive is expressed as following:

( ) /gap send receive sendP P P P� � (2)

Preceive can be determined by counting the number of points in every spatial level, and Psend can be determined by figuring up the azimuth angle range, height, azimuth angle resolution and height resolution of every spatial level. Every spatial level is assumed to be a cuboid to determine the Psend. However the spatial level actually isn’t a regular shape and this is an important source of error. According to limit theory, the thickness was smaller, the shape of spatial level was closer to cuboid and the error was smaller. G( ) is 0.5 in the calculating process, based on empirical coefficient. The total LAI of the longan tree is the sum of every space level:

1

( )i n

iC L A I L A I i

�

�

� � (3)

C. Slicing Methods The point clouds are sliced based on zenith (zenith slicing)

and vertical height (vertical height slicing) respectively, and the scale for the zenith slicing is slicing angle, while the scale for the vertical height slicing is slicing thickness.

Fig.2 Zenith Slicing and Vertical Height Slicing

For the purpose of comparing the results from these two slicing methods, the slicing thickness should be consistent. The total angle and the total height for the tree are known, and the total angle is equivalent with the total height. If the number of space levels of the zenith slicing is equal to the number of space levels, we think these two slicing methods are comparable.

III. RESULT The point clouds whose point interval is 1.5mm was used to

acquire the LAI in above gap fraction method, and table 2 is the result. The first column represents slicing thickness. The second column and the third column represent the LAI of longan tree in different slicing ways.

TABLE II

THE RESULT OF POINT CLOUDS WHOSE POINT INTERVAL WAS 1.5MM

Slicing thickness

Zenith slicing Vertical height slicing

10 0.508m 1.27637 1.58527 9 0.506m 1.31649 1.58527

8 0.422m 1.37722 1.75007 7 0.361m 1.54839 1.58232 6 0.316m 1.66674 1.8072

5 0.281m 1.66649 1.76082 4 0.230m 1.72499 1.7857 3 0.169m 2.12135 2.02701

2 0.115m 2.32242 1.13979 1 0.057m 3.37032 2.76729

Tabular data is displayed by line charts as following:

Fig.3 the result of point clouds whose point interval was 1.5mm

Firstly, generally speaking, the result is smaller than the

ground truth when slicing thickness is too large; the result is larger than the ground truth when the thickness is too small. The result is close to the ground truth when the slicing angle ranged from 2 to 6 . By the way, the slicing thicknesses range from 2 to 6 is thought as the appropriate slicing range in this paper. When the slicing thickness is less than 2 , the number of laser pulses intercepted from some space level is so small that appropriate result cannot be figured up, because gap fraction model is a statistical model, and sufficient quantities of point clouds must be ensured. However the slicing thickness should not be too large too, because great

slicing thickness results in large variation in , and large error will come with large variation in .

Secondly, the result of LAI is closer to the ground truth while the thickness is smaller within the appropriate slicing range. As mentioned before, every space level is assumed to be a cuboid, but the true size of the space level is smaller than it, so the gap fraction acquired from formula (2) is larger than the true gap fraction in the space level. According to the limit theory, the thickness is smaller, the shape of spatial level is closer to cuboid and the error is smaller. Fig.3 can demonstrate this conclusion.

At last, within the appropriate slicing range, the vertical height slicing is more suitable than the zenith slicing for estimating LAI. Maybe that’s because the shape of spatial level divided by zenith slicing is more irregular than that divided by vertical height slicing.

The point clouds of 1mm interval and 5mm interval were also used to figure up the LAI to further verify the above conclusion. The result from 5mm interval point clouds expresses as following:

TABLE III

THE RESULT OF POINT CLOUDS WHOSE POINT INTERVAL WAS 5MM

Slicing thickness

Zenith slicing Vertical height slicing

10 0.528m 2.26878 1.54327

9 0.502m 2.4539 1.52469

8 0.440m 2.46608 1.34662

7 0.377m 2.74026 1.23272

6 0.330m 2.85043 2.50474

5 0.294m 3.12033 1.95484

4 0.240m 3.67449 2.63822

3 0.176m 3.95773 2.6396

2 0.120m 4.96833 3.22354

1 0.0614m 6.24843 4.48999

Tabular data is displayed by line charts as following:

Fig.4 the result of point clouds whose point interval was 5mm

It is well known that the result from gap fraction model is appropriate only when the number of pulses in every spatial level is large enough. Compared with point clouds whose point interval was 1.5mm, the slicing thickness of point clouds whose point interval was 5mm should be larger, and then the number of pulses in every spatial level is large enough to compute reasonable LAI. The results from zenith slicing are all larger than field measurements when slicing thickness ranged from 1 to 10 . When slicing angle is 5 , the result from vertical height slicing is close to field measurements.

Reasonable result can’t be figured up from point clouds whose point interval was 1mm, because it isn’t consistent with the fact that Psend should be larger than Preceive. In data obtaining process, there are always “flying points” because of very small point interval and the wind, so we can’t compute reasonable LAI.

Fig.5 the “flying spot” in point clouds whose point interval was 1mm

IV. DISCUSS

A. Error Analysis The main factor leading to error in this paper is Psend. The

spatial level is assumed to be cuboid to calculate the Psend, while the true shape of spatial level is irregular. Compared with the shape of spatial level of vertical height slicing, the shape of zenith slicing was more irregular, so the result from zenith slicing deviated larger.

B. Reasonable Number of Point Clouds Gap fraction model is a statistical model. To make sure a

correct result, the number of point clouds must be large enough. Because of this, the slicing thickness should not be too small, and the slicing thickness should also not be too large, because great slicing thickness results in large variation in , and large error will come with large variation in .

C. Reasonable Point Interval of Point Clouds Appropriate point interval is also important in the

calculating process. The number of point clouds in every space level may be not enough to figure up reasonable LAI when the point interval was too large. Furthermore, point clouds with

too large interval can’t depict small gap fraction in vegetation canopy. On the contrary, it is also difficult to acquire LAI with too small point interval, because of the phenomenon of “flying points”.

V. CONCLUSION This paper extracts LAI of a single tree from point clouds,

and tries to debate which slicing method is better. It is found that the result is relative to point interval, slicing thickness and slicing method. It is necessary to ensure slicing thickness large enough in the event that point interval of point clouds is very small, or unreasonable result was acquired because gap fraction model is a statistical model. For the point clouds whose point interval is 1.5mm, the vertical height slicing is better than zenith slicing when the slicing angle ranges from 2 to 6 .

ACKNOWLEDGMENT This work is supported by National Natural Science

Foundation of China Grant No. 40801131 and the National High-Tech Research and Development Plan of China Grant No. 2010AA122202. This work is also supported by the Special Foundation for Free Exploration of State Laboratory of Remote Sensing Science of China.

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