Leaf Orientation Retrieval From Terrestrial Laser Scanning (TLS) Data

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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 50, NO. 10, OCTOBER 2012

Leaf Orientation Retrieval From Terrestrial Laser Scanning (TLS) Data Guang Zheng and L. Monika Moskal

Abstract—Tree leaf orientation, including the distribution of the inclinational and azimuthal angles in the canopy, is an important attribute of forest canopy architecture and is critical in determining the within and below canopy solar radiation regimes. Characterizing leaf orientation is a key step to the retrieval of leaf area index (LAI) based on remotely sensed data, particularly discrete point data such as that provided by light detection and ranging. In this paper, we present a new method that indirectly and nondestructively retrieves foliage elements’ orientation and distribution from point cloud data (PCD) obtained using a terrestrial laser scanning (TLS) approach. An artificial tree was used to develop the method using total least square fitting techniques to reconstruct the normal vectors from the PCD. The method was further validated on live tree crowns. An equation with a single parameter for characterizing the leaf angular distribution of crowns was developed. The TLS-based algorithm captures 97.4% (RMSE = 1.094 degrees, p < 0.001) variation of the leaf inclination angle compared to manual measurements for an artificial tree. When applied to a live tree seedling and a mature tree crown, the TLS-based algorithm predicts 78.51% (RMSE = 1.225 degrees, p < 0.001) and 57.28% (RMSE = 4.412 degrees, p < 0.001) of the angular variability, respectively. Our results indicate that occlusion and noisy points affect the accuracy of normal vector estimation. Most importantly, this work provides a theoretical foundation for retrieving LAI from PCD obtained with a TLS. Index Terms—Aerial laser scanning (ALS), leaf area index (LAI), leaf orientation distribution, mobile laser scanning (MLS), normal vector, point cloud data (PCD), terrestrial laser scanning (TLS).

I. I NTRODUCTION

F

OREST canopy structure can be defined as the shape, size, orientation, and positional distributions of all the foliage elements aboveground [1]. It dictates the solar radiation regime within and below canopies through the interaction between Manuscript received August 8, 2011; revised November 12, 2011; accepted February 12, 2012. Date of publication April 5, 2012; date of current version September 21, 2012. This work was supported by National Science Foundationfunded University of Washington I/UCRC Center for Advanced Forest Systems (under Grant 0855690), the State Key Fundamental Science funds of China (2010CB950701), the High Technology Research and Development Program of China (863 program: #2012AA12A306), the Open Research Fund Program of State Key Laboratory of Hydroscience and Engineering in Tsinghua University (sklhse-2012-B-04), and the University of Washington Precision Forestry Cooperative. A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions. G. Zheng is with the International Institute for Earth System Science, Nanjing University, Nanjing 210093, China (e-mail: [email protected]). L. M. Moskal is with the Remote Sensing and Geospatial Analysis Laboratory, Precision Forestry Cooperative, School of Environment and Forest Science, University of Washington, Seattle, WA 98195-2100 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TGRS.2012.2188533

sunlight and leaves of the plants. The spatial location and orientation of leaves have considerable effects on the fraction of photosynthetically active radiation [2] and the amount of light intercepted by leaves in a canopy [3]. Among all of the factors affecting the radiation interception, leaf area index (LAI) is one of the most important biophysical parameters. Considerable progress has been achieved during the past several decades with respect to the retrieval of true LAI from field-based optical instrument measurements [4]–[8]. These efforts have previously been reviewed by Weiss et al. [9], Jonckheere et al. [10], and Zheng and Moskal [11]. However, most of these methods were developed from 2-D perspective without considering the foliage height distribution. Moreover, most of the LAI inversion methods only address the angular distribution of foliage elements for any given individual tree or forest stand while assuming the azimuthal or spatial distribution of foliage elements are random [12]–[14]. Leaf orientation estimation consists of two components: the theoretical development and the measurement instrument design. Ross and Nilson [15] developed a theoretical six-class model to explore the orientation of leaves and tested it on actual plants. It is a widely accepted method for describing the leaf orientation, which divides the angular and azimuthal angles into finite classes. As for field-based measurement, instruments have been developed to manually measure the orientation of a single leaf. However, the complexities of canopy structure prohibit precise determination of the azimuthal and inclination angles of all foliage elements in a crown without physically contacting and thus, disturbing or potentially destroying the foliage. One manual contact method uses a simple device, a protractor, and magnetic compass, for measuring leaf inclination [1]. In addition, a mechanical instrument was developed by Lang [16] which can measure the coordinates of any point on a leaf by recording the angular information of the instrument’s three arms. However, direct measurements are very labor intensive, particularly for standing trees due to height limitation. Some noncontact indirect methods of estimating the mean leaf inclination angle have been investigated by Shibayama and Watanabe [17] using reflected polarized light, but these methods have only been applied in agricultural plant canopies. A new indirect and nondestructive method is needed to determine the leaf orientation distribution of foliage elements for forest crown. Light detection and ranging (LiDAR) technologies have enabled mapping in 3-D space (3-D) making studies of 3-D canopy structure possible [18]. Discrete point aerial laser scanning (ALS), terrestrial laser scanning (TLS), and mobile laser scanning (MLS) are the most common platforms of LiDAR acquisition on the commercial market today. All three laser

0196-2892/$31.00 © 2012 IEEE

ZHENG AND MOSKAL: LEAF ORIENTATION RETRIEVAL

scanning techniques acquire point cloud data (PCD) which records two types of information: geometrical and spectral. Geometrical information is represented by the 3-D Cartesian coordinates (example: x, y, z) and spectral information or intensity is sensor-dependent and requires calibration due to the differences in sensor wavelength, spot sizes, and beam divergence [19]–[21]. Compared with ALS, MLS and TLS have a much higher density of laser pulses that can provide spatially explicit assessments of forest 3-D structural information at subcentimeter spacing, promising improvements in the accuracy of forest biophysical parameter estimates and for ALS calibration. Therefore, it is necessary to develop a new method to calculate the extinction coefficient specially designed for TLS and in the future to investigate this technique for MLS. Based on this methodology, one can improve on techniques using twodimension hemispherical photography [14], [22]. Furthermore, ALS-based LAI models can be directly validated with sampling using TLS or MLS. TLS and MLS enable us to scan an individual tree or forest stand and generate high spatial resolution 3-D PCD from single or multiview locations [23], [24], which allow us to explore the feasibility of extracting such biophysical parameters as gap fraction [25], stem profile map [26], [27] and LAI [28], [29]. However, the foliage area density estimated from TLS would be greatly affected by the angular distribution of foliage elements and different scanner setups, which has been proven by Hosoi and Omasa [30]. These issues would be further complicated by the constant movement of MLS platform. Currently, there are no systematic methods to estimate the leaf orientation distribution directly from PCD generated from TLS or MLS. Thus, the goal of this research was to develop these methods by meeting the following objectives. • Develop an approach for retrieving leaf orientation distribution from TLS measurements; • Develop an approach to compute the extinction coefficient for a tree crown and forest canopy from a PCD generated from TLS; • Validate the above methods using manually acquired data in a controlled experiment using artificial and live tree crowns. We focus on working with TLS data only in this project, but the methods could be adapted to PCD generated with MLS in future research.

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as reflection resulting from dust particles not recorded by TLS. The research was limited to broadleaved deciduous crowns only, because of the inability to capture individual foliage elements in a needle-leave with the TLS; and because the physical arrangement of needles in conifers involves considerably different geometry than that considered here. In this methods section, we first introduce a well-accepted leaf orientation distribution model in Section II-A, and focus on locating the foliage elements in 3-D space, reconstructing the normal vectors for PCD and estimating their orientation distribution using TLS from Sections II-B1–B3. In Section II-B4, we present a solution to determine the ratio of semilong to semishort axes of ellipsoidal model.

A. Leaf Orientation Distribution Model Leaf orientation distribution is a critical component for estimating LAI from optical measurements. The LAI estimation process is usually computed based on the following equation (1) [31]: P (θ) = exp[−G(θ)ΩL/ cos θ]

where P (θ) is the gap fraction, defined as the probability of a beam transmitted through the canopy with an incident angle θ, G(θ) is the extinction coefficient, defined as the mean projection of unit foliage area on the plane normal to the direction of the beam, L is LAI, and Ω is the clumping index. Part of the challenge in indirect LAI estimation is that the distributions of the foliage angles are unknown, which results in the uncertainties of the extinction coefficient. Scientists have tried to represent the distributions (from planophile to erectophile) using geometrical objects such as cylinders, spheres, or cones [32]. One of the most popular mathematical angular distribution models was developed by Campbell [33] using the geometrical ellipsoid model to approximate the angular distributions of a tree crown by adjusting the ratio of semilong (b) to semishort (a) axes of an ellipsoid (2); this is also known as the ellisoidal distribution of leaf angles and is represented as follows: ξ(α) =

II. M ETHODS Our methods rely on a number of theories based on the following assumptions. 1) The PCD generated from TLS has a consistent predefined sampling resolution; the resolution was kept the same through all scanning process at 1 mm with a beam width (6 mm) at 50 m; 2) Occlusion in the PCD is negligible. This was accomplished by multilocation scanning and coregistration of multiple PCDs; 3) PCD used for normal estimation was only sampled from the surface of target objects, atmospheric effects such

(1)

2χ3 sin α Λ(cos2 α + χ2 sin2 α)

(2)

2

where α is the leaf inclination angle, χ = b/a, and

Λ=

⎧ −1 ⎪ ⎨ χ + (sin ε)/ε,

χ < 1,

ε = (1 − χ2 ) 2

⎪ ⎩ χ+

χ > 1,

ε = (1 − χ−2 ) 2 χ=1

ln

(1+ε) (1−ε)

2εχ

2,

,

1

1

and 0 ≤ α ≤ π/2. In this equasion b and a are the semi-long and semi-short axis, respectively. In the case of a specific tree, parameters a and b are usually unknown in advance; our approach will determine them using TLS as a tool.

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B. Algorithm Development 1) Mathematical Model for Describing the Spatial Location of Leaves: A mathematical framework to spatially locate the foliage elements developed by Ross [34] was adopted in this paper and is summarized as follows. 1) A single, broad, flat leaf (all of other leaf shapes can be considered to be composed of a number of flat planes), was set up in the Cartesian coordinate system OXYZ as shown in Fig. 1. The bottom center point was the origin point O. The spatial location of a point within the leaf was determined by three different control coordinates. It was represented by pi (zi , αi , ai ), where zi is the distance above ground of point pi , αi is the angle turned clockwise from positive X axis, ai is the distance of the projected point of pi on XOY plane, which can be converted to the Cartesian coordinates (xi , yi , zi ) if necessary. 2) A normal vector ri (ϑi , φi ), where ϑi and φi are the incli nation and azimuthal angles of vector ri , was retrieved. 3) A longitudinal angle was derived by determining the angle ψi formed by the main axis being projected from origin to the location of projected pi . Thus, by following the above steps, the orientation of leaves in a volume V (pi ) around point pi was described as the distribution function (3) and (4) of leaf orientation (hereafter referred to as g-function) n

n 1 g(pi , ri )ΔΩi = 1, ΔΩi = 2π . (3) 2π i=1 i=1 The integral form of this function is 1 g(p, r)dΩ ≡ 1 2π

Thus, from (6) and (7), the leaf orientation distribution function (i.e., g-function) can be described by the two angular and azimuthal distribution functions. 2) Normal Vector Estimation for Each Point of 3-D Point Cloud Data: The 3-D PCD S = pi (xi , yi , zi ) ⊂ R3 generated from TLS explicitly contains information about distance and height. The normal vector for each point was estimated based on the local Total Least Squares (LStot) method [35], which has been improved and further developed by Lalonde et al. [36] for forestry application. It involves the following steps. 1) To estimate the tangent plane for a support region of a given point, let S = (p1 , p2 , . . . , pn ) which can be a point subsample of the whole PCD set S, including an individual tree or a forest stand. The tangent plane for point pi was then denoted as T (pi ) and reconstructed within a support region Sp which is defined as k nearest points around a given point pi (xi , yi , zi ), and represented by a centroid point Oi of Sp , where Oi was computed as Oi = (1/n) ni=1 pi , with a unit normal vector ni . In this paper, we assigned the support region size of 6. 2) The signed distance between any point p ⊂ S and the T (pi ) was calculated as dist(p) = (p − Oi ) · ni . Since the centroid point was already known for a given Sp , only the ni was needed, which was obtained using prin ciple component analysis. In order to obtain the ni , the covariance matrix of Sp was first calculated using the following: 1 (pi − Oi )(pi − Oi )T . n i=1 n

(4)

M=

(8)

Ω

where dΩi is the ith solid angle of an imagery unit sphere with the center as pi divided into a finite number of equal parts with a solid angle ΔΩi = sin ϑi Δϑi Δφi , ri is the direction of the solid angle. The g-function (g(pi , ri )/2π) characterizes the fraction or probability of leaves whose normal vectors were falling within the unit solid angle around direction ri . By substituting dΩ with sin ϑdϑdφ, we can obtain π

1 2π

2

2π

0

g(p, r)dφ ≡ 1.

sin ϑdϑ

(5)

Eigenvalues of covariance matrix M are λ1 , λ2 , λ3 which correspond to three eigenvectors v1 , v2 , v3 , respectively, the normal vector was the eigenvector with the smallest eigenvalue. For example, if λ1 ≥ λ2 ≥ λ3 , then the normal vector will be v3 or −v3 . 3) These normal vectors were named unoriented normal vector and were oriented by constructing a Riemannian graph over the graph of the support region and by propagating a seed normal orientation within a minimum spanning tree computed over this graph [37].

0

Assuming the inclination angle (ϑ) and azimuthal angle (φ) are independent of each other, we integrate the azimuthal angle (φ) from 0 to 2π and inclination angle (ϑ) from 0 to π/2 separately, we can then get the inclination angle distribution function as follows: 1 g1 (p, ϑ) = 2π

2π g(p, ϑ, φ)dφ

(6)

sin ϑg(p, ϑ, φ)dϑ.

(7)

0 π

2 g2 (p, φ) = 0

Theoretically, the normal vector of each point of foliage element could be oriented to both upper and lower hemispheres. However, in practice, field measurements show that almost all of the normal vectors of foliage elements point to the upper hemisphere [2]. Thus, all of the vectors with negative direction (pointing to the lower hemisphere) were assigned opposite values in order to ensure that all vectors pointed to upper hemisphere. 3) Estimating Leaf Normal Orientation Distribution From PCD: By dividing the upper hemisphere into j (j = 1, 2, . . . , 9) horizontal layers and m (m = 1, 2, . . . , 18) sections with respect to inclination and azimuthal angles of foliage elements, respectively, the whole upper hemisphere was partitioned into


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Fig. 1. Schematic diagram of (a) the mathematical model to spatially locate individual foliage element in 3-D space where O is the origin of the Cartesian coordinate system OXY Z; ri is the normal for a single leaf; zi is the height of point pi above ground; αi is the azimuthal angle of point pi ; ai is the distance between the projected point of pi in X-Y plane and origin point O; ψi is the angle between the main axis of the single leaf with point pi with the projection direction of point pi ; and (b) a zoomed in volume V (pi )around point pi (zi , αi , ai ) about the leaf orientation distribution for a given volume where rk is the direction of a solid angle originated from point pi (zi , αi , ai ).

162 parts with different areas. Thus, (4) could be rewritten as follows: π

1 2π

2

2π sin ϑdϑ

0

=

g(p, r)dφ 0

1 2π

j=1

⎡

π

18 j

9

⎢ sin ϑdϑ ⎣

m=1 π

π 18 (j−1)

⎤

π

9 m

18

9

⎥ g(p, r)dφ⎦

∗ ×U Ajm ≈ Npt AV ≈ Npt × U

(m−1)

18 9 1 gjm ≡ 1. = 2π j=1 m=1

(9)

We obtained the expression for gjm as follows: π 18 j

gjm =

sin ϑdϑ

π 18 (j−1)

(12) (13)

∗ where Npt and Npt are the total number of points within solid angle Ωjm and the jth layer and mth section of upper hemisphere. By substituting (12) and (13) into (11), we obtain ∗ 1 Npt 1 gjm ≈ . 2π Ωjm Npt

π 9m

leaves within V (pi ). Thus, geometrical locations are converted into area information. Based on the assumption that each point obtained by the sensor encounters partial or whole surface area of foliage elements with a constant area U of a flat plane perpendicular to the normal vector of this point, the area information was obtained by multiplying the number of points by U, which gives

(14)

g(p, r)dφ π 9 (m−1)

= g(p, ϑ, φ)Ωjm .

(10)

gjm characterizes the percentage of areas with normal vector falling within the jth layer and m section solid angle Ωjm . For the purpose of obtaining leaf area, (10) could be rewritten in another format as follows: 1 1 Ajm gjm = 2π Ωjm AV

(11)

where Ajm represents the area of all leaves with normal vectors falling within solid angle Ωjm , and AV is the total area of

Based on the (14), we can directly apply the PCD obtained from TLS into the leaf orientation distribution model in (2). 4) Estimating the χ Value Directly From PCD for a Given Tree or Stand: In the leaf angular distribution approximation model described in (2), χ is a very important parameter but difficult to acquire due to unknown angular distributions for leaves for a given tree. The leaf normal orientation distribution information can be obtained through the computation of the normal vector of each point representing a leaf and recorded by TLS. Thus, the ellipsoidal model used to approximate the live angular distribution of a given tree can be determined through calculating the value of χ. By partitioning the upper hemisphere into 162 parts using the method in Section II-B3, in the jth

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TABLE I C HARACTERISTICS OF THE L EICA S CAN S TATION 2 TLS E QUIPMENT

layer, the angular distribution can be determined by integrating the azimuthal angle from 0 to 2π by as follows: π

gj∗

18 j =

2π sin ϑdϑ

π 18 (j−1)

g(p, r)dφ

(15)

0

where gj∗ denotes the average angular distribution of the jth layer of upper hemisphere. This characterizes the percentage of area of leaves with inclination angle falling in jth layer over the total area of leaves within the whole upper hemisphere. The angular distribution of a given tree can be obtained by summing up the gj∗ for all nine layers by calculating the following: g∗ =

9

gj∗ .

(16)

j=1

For the continuous situation, the angular distribution of a live plant can be approximately described by (2); in terms of the discrete situation, the χ value could be found by computing the following equation (please refer to the Appendix A for the derivation of this equation): χ2 =

1 + 1. 3 sin2 α

(17)

In order to find the value of χ, based on the distribution of foliage elements’ inclination angles and analysis to (17), there will be a maximum value ξmax (α ) for α in the range from 0 to π/2. By statistically analyzing the frequency of inclination angle of the normal vectors of foliage elements in the 162 parts, we can find the angle α which corresponds to the highest frequency of foliage element’s normal vector. Finally, we can obtain the χ value for a given target tree through substituting the α in (17) with α . C. Algorithm Testing In this section, we discuss the methods used to test the algorithm using PCD for an artificial tree. The TLS used in this study was the Leica Scan Station 2; more detailed characteristics of the scanner are listed in Table I. The origin of the laser is located at the top of a tribrach mount at a height of 0.3072 m. The minimum vertical and horizontal angle resolution is 3e−6 radians (0.3 mm) with 100 m away from the scanner. The beam divergence at 50-m distance is 6 mm (0.15 m rad). The spot size is 4 mm at a distance of up to 50 m [38].

A PCD for an artificial tree was collected in a controlled environment where the influence of environmental factors such as wind, varying humidity, and changing illumination conditions were minimized. The experiment setup included a construction of an artificial tree with a 10-horizontal flat-branch structure. A cylinder PVC pipe was used to represent the stem. The first and second branches originated from the very top of the “stem.” Thus, the interval distance between branches were 0, 0, 0.03 m, 0.05 m, 0.08 m, 0.10 m, 0.21 m, 0.32 m, 0.47 m, 0.62 m, respectively. Two square-shape “leaves,” made from uniformly reflective paper material with a size of 7.6 cm × 7.6 cm, were placed on each branch. All branches had 0◦ inclination angle, but, the inclination for each leaf was randomized. The artificial tree was scanned from three locations on a circle with a 120◦ interval [Fig. 2(b)]. Fig. 2(b) shows the experiment setup, the solid circle dot representing the three TLS locations used to generate three individual PCDs for the artificial tree. Three, stationary, bilevel, target poles were used in all three scans to assist with PCD coregistration. The three solid stars in the locations of the target poles. Each target pole had two target objects, one at 1.5 m height, and the other at 50 cm height, thus six targets were used for the coregistration. The registration function in Cyclone 6.0 was used to merge the three directional PCD, the registration mean absolute error (MAE) was 0.007 m. The key step in registering the three PCD was to constrain them in all 6◦ of freedom or the movement in X, Y, and Z and rotation around the X, Y, and Z axis [39]. The total height of the artificial tree was 1.75 m. The inclination angle of each leaf or partial leaf was measured and recorded manually with a protractor. The angular information of each leaf was measured using the simple compass-protractor method [1]. The flat square was a two-degree of freedom object in 3-D space. Its position was determined by assign ing the normal vector n and another vector within the plane to representing its direction. The inclination angle of leaves was formed by vector l and Z axis, which is different from the inclination angle of its normal vector n. The relationship between these two angles allowed for their sum to equals π/2. Once the angular distribution of normal vector was known, we calculated the angular distribution of foliage elements for a given tree. D. Algorithm Validation We collected PCDs of two live crowns including a 2 m tall big leaf maple (Acer macrophyllum) (Fig. 2(d)) and a 10 m tall sugar maple (Acer saccharum) [Fig. 2(g)] to test and validate our methods. The data were collected during sunny and calm conditions. We scanned the two live trees with the same setup as the artificial tree experiment as shown in Fig. 2(e) and (h). The data sets were coregistered, and the registration MAE was below 0.009 m for both data sets. We computed the normal vector for each point of the two live crowns as shown in Fig. 2(e) and (i). In order to better illustrate our validation and test procedures, we selected three individual leaves from the big leaf maple tree as the up-close image shown in Fig. 2(d) and (e). One can clearly see the leaf shape and the linear feature of stem from the up-close image in Fig. 2(e). In Fig. 2(f), we


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Fig. 2. Three PCDs for algorithm development and validation. (a) Artificial tree; (b) artificial tree PCD with bounding box colored by height; (c) normal vector for artificial tree PCD; (d) sugar maple PCD with true color; (e) sugar maple PCD colored by height (black dots are the scanner placement and stars are target placements); (f) normal vectors for sugar maple PCD; (g) big leaf maple PCD with three leaves up close; (h) normal vector for big leaf maple and normal vector for three leaves up close (black dots are the scanner placement and stars are target placements); (i) schematic diagram for manually measure normal vectors for a single leaf, based on curvature, we divided the leaf surface into three parts denoted by number 1, 2, 3, and white dash lines represent the normal vectors that each part.

divided an individual maple leaf into three segments based on the leaf surface curvature variation and denoted them as parts 1, 2, and 3. The white dash line represented the boundary line for each region with different normal vectors. The dash arrows indicated the manually measured results of normal vectors. Thus, we demonstrate the procedures for manual measurement of the leaf orientation for each individual leaf using protractor according to the leaf’s curvature. Because of the 2 m height of the big maple, we were able to manually and nondestructively measure the inclination angle of every single leaf from the PCD. In addition, the normal vector for the PCD of big leaf maple was reconstructed using the method described in Section II-B2. The sugar maple tree shown in Fig. 2(i), was over 10 m in height, making direct manual measurement of the leaf elements

impractical. Instead, the measurements were obtained digitally by extracting individual leaves directly from the PCD and subsequently analyzing their dimensions. We chose leaves from random locations within the crown to compare the normal vectors results between TLS-based and direct PDC measurements. We measured 27 leaves in total from three different height planes: 3 m, 6 m, and 9 m, and three different radii from the center of the stem at: 0.5 m, 1 m, 1.5 m. For all of 27 leaves PCDs, we manually measured the normal vectors according to the procedures described in Fig. 2(f). Although additional leaves would have been preferred, the within crown occlusion of the dense canopy made identifying fully scanned leaves within our sampling parameters difficult and setting up the scanner within the crown itself to reduce the occlusion impact was viewed as a crown disturbance factor.

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Fig. 3. Scatterplot (a) is comparing the TLS and manually measured based inclination angles for artificial tree, R square = 0.975 and n = 20. Scatterplot (b) is comparing the TLS and manually measured based inclination angles for big leaf maple tree, R square = 0.73 and n = 43. Scatterplot (c) is comparing the TLS and manually measured-based inclination angles for sugar maple, R square = 0.573 and n = 27. Black solid lines are the linear models, black dash lines are the 1 : 1 line, and gray dash lines are the 95% confidence interval for linear regression models.

III. R ESULTS

IV. D ISCUSSIONS

A. χ Value Calculation

A. Normal Vector Estimation for Points

In the geometrical ellipsoidal angular distribution models, once the parameter of χ is determined, the angular distribution density function can be obtained. Based on this procedure, there should only be one inclination angle with the maximum frequency over the range of [0, π/2]. In this wok, this single inclination angle was 35.13◦ with 13 490 times frequency. Thus, the χ value based on (17) was calculated as: χ = 1.2567. The leaves’ angular distribution for the artificial tree was approximated by an ellipsoidal model with a ratio value (1.2567) of semilong over semishort axis. For the big leaf maple and the sugar maple, the χ values were computed as 1.1660 and 1.1579 with the inclination angles 68 and 78◦ for maximum frequency of normal vectors, respectively.

Obtaining normal vector estimation from PCD was a key step in this work. However, changing the size of the support region is expected to affect the accuracy of normal vector estimation for a given point. Mitra et al. [40] proposed a procedure to determine the optimal size of support region automatically by calculating the local density and curvature iteratively. In this approach, the local density plays an important role in that algorithm and is determined by both sampling resolution and the spatial distribution of foliage elements. Similarly, in our work, we suspected that the sampling resolution is an important factor in estimating the normal vector for a given PCD, thus, we scanned all artificial and live trees at the highest possible resolution for our system (1 mm) from three directions with a visible green light (510 nm). The higher resolution, the more detailed structure can be captured from TLS; the spectral region of the sensor might also have an impact. Therefore, future research focused on characterization of foliage element sizes, particularly the leaves, for different species with varying size of foliage elements is needed to determine what resolution is appropriate.

B. Comparison Between LiDAR Modeled and Manually Measured Inclination Angle In the case of the artificial tree, since the sample resolution in this work was very fine (1 mm), there were on average close to 10 000 points for each flat square “leaf,” and the normal vectors of each leaf were averaged to get one representative normal vector for each leaf. The results were then compared to the manually measured leaf inclination angle. We found strong agreement between the manually measured and TLSbased leaf inclination angle. The TLS-modeled leaf inclination angle distribution captured 97.5% (RMSE = 1.0957 degrees, p < 0.001) [Fig. 3(a)] variation of the actual leaf angular distribution. In terms of the big leaf maple tree, the TLS-based inclination angle explained 73% (RMSE = 1.555 degrees, p < 0.001) [Fig. 3(b)] variation of the actual leaf angular distribution. However, the normal vector distribution obtained through TLS using the LStot method only explained 57.28% (RMSE = 4.412 degrees, p < 0.001). By observing the linear regression models and residuals between the predicted and actual measured values in Fig. 3, we conclude that the residuals increase progressively from the artificial tree model, to the big leaf maple model, and finally are greatest for the sugar maple model. This pattern is influenced by the complexity of the crowns from a simple artificial tree to a seedling to a mature tree crown.

B. Noise Points Effects Noise points acquired with TLS, MLS, and ALS are a wellknown factor which cannot be ignored. In our experiment, for the artificial tree, the leaves were not associated with natural biological structural and optical properties. The intensity information of live trees varies and will further affect the energy returned to the sensor. Some noise points are to be expected, even for a perfect flat plane, due to the physical interaction between the laser beam and target object properties such as: texture, color, roughness, and reflectance. In practice, this can increase the thickness or height of the TLS-based modeled objects. In addition, particularly when the tree or forest stands are in an open area with windy condition, a point trailing effect can be observed on dense scans collected at slower speeds, due to the movement of foliage elements. Therefore, calm wind conditions are recommended for PCD collection using TLS in order to minimize one source of noisy points. The amount of noisy points in the PCD will affect the accuracy of the normal vector estimation for PCD, preliminary study by Dey et al. [41]


has explored this issue, but more experiments controlling for various sources of noise are needed. C. Beam Divergence Effect As the distance increase from the laser scanner, the spot size also increases due to the process of beam divergence. The Leica Scan Station 2 system used in this research has a beam divergence of 0.15 m/rad, thus, the beam widens to 6 mm at 50-m distance from the scanner. This increasing spot size may impact the ability to capture the level-of-detail of an individual leaf or small branch structure at far distances. In addition, the sampling resolution determines the azimuthal angle between two adjacent laser beams and the distance between the target and sensor increases as the sensors moves away from the object of interest. The point density sampled from one location will increase with distance, which may impact the accuracy of normal vector estimation and further change the ellipsoidal model parameter approximation results. D. Recommendations Our approach compliments previous work on deriving extinction coefficients of vegetation canopies [42], [43], where TLS data were not available. We show that only one parameter is needed to determine the angular distribution density function for a specific forest tree or stand. This could serve as a calibration tool to determine the extinction coefficient for ALS-based or even satellite-based LAI estimation method. This method could improve the techniques using 1-D hemispherical photography [44], [45]. Moreover, theoretically, the methods described here could be applied to the PCD derived from full waveform LiDAR for LAI estimation purposes. However, this research only focused on the geometrical information of the PCD rather than the intensity information also available from full waveform LiDAR. Due to the occlusion effect of foliage elements within tree crown, multilocation scanning is usually needed to fully capture 3-D structural information of trees or forest stands [46]. Furthermore, if the method is to be used to calibrate ALS models of LAI, the details of the sampling protocol including placement and number of scanning directions deserve further exploration. Our methods were developed with deciduous tree crowns. If one wishes to apply this method to coniferous crowns or canopies, the following suggestions may be considered: 1) using the finest sampling possible to collect PCD (example: 1–2 mm); 2) scanning individual trees from multiple locations (example: three locations); 3) using the “leaf” at shoot level proposed by Chen [5], [47] to treating the shoot PCD as a “big leaf”; this direction in particular deserves further research. In addition, for a given value of χ, one maximum value of ξmax exists over the range [0, π/2]. This maximum value indicates that the maximum probability of the foliage elements pointing to the direction where it receives the maximum illumination area from a direct solar beam within an individual tree or forest stand in associated with a specific geographical region. This is a result of a long-lasting evolutionary process that is

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specific to a region and relates to the abiotic factors which affect tree growth such as latitude, temperature, and precipitation. Work focusing of exploring these maximum potential values has potential in evolutionary theory of plant physiology and should be further documented and investigated with TLS. V. C ONCLUSION This research illustrates the importance of leaf orientation on the retrieval of LAI based on the gap fraction theory and demonstrated the procedures of using TLS to acquire the leaf orientation distribution directly from PCD. The TLS-based leaf orientation distribution showed strong agreement with the manually measured orientation distribution for an artificial tree in a controlled indoor experiment and only slightly weaker relationships for live crowns captured outdoors. We have provided a novel noncontact way to determine the foliage orientation distribution, and obtained the following conclusions. 1) The PCD generated using TLS from multiple locations can explicitly provide the 3-D structural information of forest canopies. 2) The reconstructed normal vectors for tree canopy PCD capture the variation of leaf orientation distribution well by using the LStot fitting technique. 3) The coupling of the TLS-based leaf orientation retrieval method and ellipsoidal model provides the estimate and calibration data of the extinction coefficient for ALSbased LAIe estimation. The method demonstrated here enhances our ability to characterize the leaf orientation distribution of an individual tree or forest stand from 3-D perspective. The method leads to the development of an extinction coefficient eliminating one of the errors associated with LAI estimates where a general coefficient would be assigned for the whole canopy [48]. With this new method, a per crown coefficient is feasible when TLS data are available and could be related to per crown coefficient for ALS providing robust referencing exists between the two data sets. This ability allows us to acquire LAI at forest stand level, which could further serve as a calibration tool for ALS through the use of TLS-based extinction coefficient introduced in this research. The need for this type of research has been identified by Richardson et al. [48] and the first step to solving this challenge laid by Danson et al. [25] in research on the gap fraction estimate with TLS. Furthermore, the extinction coefficient introduced by us could be used with LAI estimated derived from satellite optical and active sensors; however, additional research investigations into the TLS sampling protocols, instrument setup, and feasibility of applying this method to MLS data are needed. Furthermore, an approach for implementing this method on conifer needles is still required. The work presented here will benefit long-term ecosystem monitoring research such as National Ecological Observation Network in experimental forests, the Long-Term Ecological Research network, and more local investigations such as the Evergreen Ecological Observation Network. Specifically, our ability to determine LAI from TLS and apply it to ALS will enhance research focusing on modeling biogeochemical cycling through processbased models. This will aid in the success of monitoring

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and therefore in the understanding of ecological processes under global climate change pressures at various scales. A PPENDIX A For the continuous situation, the angular distribution of a live plant can be approximately described by (2); in terms of the discrete situation, the (9) can be used to obtain the angular distribution of foliage elements. When j → ∞, the (9) will be identical to (2). Theoretically, (2) will only have one maximum value over the range [0, π/2], similarly, a maximum value can be found from (9) for a PCD. In order to find the χ value, the first-order derivation of (2) with respect to α was first calculated, thus, we can rewrite the (2) as follows: ξ(α) =

1 2χ3 · 2 . 3 1 Λ (χ2 − 1) sin 2 α + sin− 2 α

(A1)

In order to find the maximum value of ξ(α) over the range [0, π], let t = sin α, and find the minimum value of f (t) = (χ2 − 1)t 2 + t− 2 3

1

(A2)

by differentiating f (t) =

1 3 2 1 3 (χ − 1)t 2 − t− 2 2 2

(A3)

and solving (A3) for f (t) = 0, t2 =

1 3(χ2 − 1)

or

sin2 α =

1 . 3(χ2 − 1)

(A4)

ACKNOWLEDGMENT This research was conducted at the University of Washington Remote Sensing and Geospatial Analysis Laboratory and International Institute of Earth System Science at Nanjing University in China. The authors thank M. Ziyu, P. Johnsey, J. Richardson, and A. Kato for assistance with the field data collection. The authors also like to acknowledge W. Xingting and the anonymous reviewers for comments and suggestions that improved this manuscript. R EFERENCES [1] J. M. Norman and G. S. Campbell, “Canopy structure,” in Plant Physiological Ecology. Field Methods and Instrumentation, J. E. R. W. Pearcy, H. A. Mooney, and P. W. Rundel, Eds. New York: Chapman & Hall, 1989, pp. 301–325. [2] J. Ross, “1.3 Phytometric methods,” in The Radiation Regime and Architecture of Plant Stands. Boston, MA: Kluwer, 1981, pp. 42–44. [3] H. J. Barclay, “Distribution of leaf orientations in six conifer species,” Can. J. Botany-Revue Canadienne DeBotanique, vol. 79, no. 4, pp. 389– 397, Apr. 2001. [4] J. M. Chen, T. A. Black, and R. S. Adams, “Evaluation of hemispherical photography for determining plant area index and geometry of a forest stand,” Agric. Forest Meteorol., vol. 56, no. 1/2, pp. 129–143, Jul. 1991. [5] J. M. Chen and T. A. Black, “Measuring leaf area index of plant canopies with branch architecture,” Agric. Forest Meteorol., vol. 57, no. 1–3, pp. 1– 12, Dec. 1991. [6] J. M. Chen and J. Cihlar, “Plant canopy gap-size analysis theory for improving optical measurement of leaf-area index,” Appl. Opt., vol. 34, no. 27, pp. 6211–6222, Sep. 1995.

[7] T. Nilson, “A theoretical analysis of the frequency of gaps in plant stands,” Agric. Meteorol., vol. 8, pp. 25–38, 1971. [8] J. M. Chen and J. Cihlar, “Retrieving leaf area index of boreal conifer forests using landsat TM images,” Remote Sens. Environ., vol. 55, no. 2, pp. 153–162, Feb. 1996. [9] M. Weiss, F. Baret, G. J. Smith, I. Jonckheere, and P. Coppin, “Review of methods for in situ leaf area index (LAI) determination Part II. Estimation of LAI, errors and sampling,” Agric. Forest Meteorol., vol. 121, no. 1/2, pp. 37–53, Jan. 2004. [10] I. Jonckheere, S. Fleck, K. Nackaerts, B. Muys, P. Coppin, M. Weiss, and F. Baret, “Review of methods for in situ leaf area index determination—Part I. Theories, sensors and hemispherical photography,” Agric. Forest Meteorol., vol. 121, no. 1/2, pp. 19–35, Jan. 2004. [11] G. Zheng and L. M. Moskal, “Retrieving Leaf Area Index (LAI) using remote sensing: Theories, methods and sensors,” Sensors, vol. 9, no. 4, pp. 2719–2745, Apr. 2009. [12] N. J. J. Breda, “Ground-based measurements of leaf area index: A review of methods, instruments and current controversies,” J. Exp. Botany, vol. 54, no. 392, pp. 2403–2417, Nov. 2003. [13] S. G. Leblanc, J. M. Chen, R. Fernandes, D. W. Deering, and A. Conley, “Methodology comparison for canopy structure parameters extraction from digital hemispherical photography in boreal forests,” Agric. Forest Meteorol., vol. 129, no. 3/4, pp. 187–207, Apr. 2005. [14] P. R. van Gardingen, G. E. Jackson, S. Hernandez-Daumas, G. Russell, and L. Sharp, “Leaf area index estimates obtained for clumped canopies using hemispherical photography,” Agric. Forest Meteorol., vol. 94, no. 3/4, pp. 243–257, May 1999. [15] Y. K. Ross and T. Nilson, “The spatial orientation of leaves in crop stands and its determination,” Photosynthesis of Productive System, pp. 86–991967. [16] A. R. G. Lang, “Leaf orientation of a cotton plant,” Agric. Meteorol., vol. 11, no. 1, pp. 37–51, 1973. [17] M. Shibayama and Y. Watanabe, “Remote assessment of wheat canopies under various cultivation conditions using polarized reflectance,” Plant Prod. Sci., vol. 9, no. 3, pp. 312–322, Jul. 2006. [18] M. van Leeuwen and M. Nieuwenhuis, “Retrieval of forest structural parameters using LiDAR remote sensing,” Eur. J. Forest Res., vol. 129, no. 4, pp. 749–770, Jul. 2010. [19] W. Wagner, “Radiometric calibration of small-footprint full-waveform airborne laser scanner measurements: Basic physical concepts,” ISPRS J. Photogramm. Remote Sens., vol. 65, no. 6, pp. 505–513, Nov. 2010. [20] I. Korpela, H. O. Ørka, J. Hyyppä, V. Heikkinen, and T. Tokola, “Range and AGC normalization in airborne discrete-return LiDAR intensity data for forest canopies,” ISPRS J. Photogramm. Remote Sens., vol. 65, no. 4, pp. 369–379, Jul. 2010. [21] S. Kaasalainen, A. Krooks, A. Kukko, and H. Kaartinen, “Radiometric calibration of terrestrial laser scanners with external reference targets,” Remote Sens., vol. 1, no. 3, pp. 144–158, 2009. [22] F. Montes, P. Pita, A. Rubio, and I. Cañellas, “Leaf area index estimation in mountain even-aged Pinus silvestris L. stands from hemispherical photographs,” Agric. Forest Meteorol., vol. 145, no. 3/4, pp. 215–228, Aug. 2007. [23] J. G. Henning and P. J. Radtke, “Ground-based laser imaging for assessing three-dimensional forest canopy structure,” Photogramm. Eng. Remote Sens., vol. 72, no. 12, pp. 1349–1358, Dec. 2006. [24] A. H. Strahler, D. L. B. Jupp, C. E. Woodcock, C.B. Schaaf, T. Yao, F. Zhao, X. Yang, J. Lovell, D. Culvenor, G. Newnham, W. Ni-Miester, and W. Boykin-Morris, “Retrieval of forest structural parameters using a ground-based LiDAR instrument (Echidna ®),” Can. J. Remote Sens., vol. 34, no. S2, pp. S426–S440, Nov. 2008. [25] F. M. Danson, D. Hetherington, F. Morsdorf, B. Koetz, and B. Allgower, “Forest canopy gap fraction from terrestrial laser scanning,” IEEE Geosci. Remote Sens. Lett., vol. 4, no. 1, pp. 157–160, Jan. 2007. [26] X. Liang, P. Litkey, J. Hyyppa, H. Kaartinen, M. Vastaranta, and M. Holopainen, “Automatic stem mapping using single-scan terrestrial laser scanning,” IEEE Trans. Geosci. Remote Sens., vol. 50, no. 2, pp. 661–670, Feb. 2012. [27] X. Liang, P. Litkey, J. Hyyppa, A. Kukko, H. Kaartinen, and M. Holopainen, “Plot-level trunk detection and reconstruction using one-scan-mode terrestrial laser scanning data,” in Proc. EORSA, 2008, pp. 1–5. [28] A. S. Antonarakis, K. S. Richards, J. Brasington, and E. Muller, “Determining leaf area index and leafy tree roughness using terrestrial laser scanning,” Water Resour. Res., vol. 46, p. W06 510, Jun. 2010.


[29] P. Huang and H. Pretzsch, “Using terrestrial laser scanner for estimating leaf areas of individual trees in a conifer forest,” Trees-Struct. Function, vol. 24, no. 4, pp. 609–619, Aug. 2010. [30] F. Hosoi and K. Omasa, “Factors contributing to accuracy in the estimation of the woody canopy leaf area density profile using 3D portable LiDAR imaging,” J. Exp. Botany, vol. 58, no. 12, pp. 3463–3473, Oct. 2007. [31] J. M. Chen, P. M. Rich, S. T. Gower, J. M. Norman, and S. Plummer, “Leaf area index of boreal forests: Theory, techniques, and measurements,” J. Geophys. Res.—Atmos., vol. 102, no. D24, pp. 29 429–29 443, Dec. 1997. [32] G. S. Campbell, “Extinction coefficients for radiation in plant canopies calculated using an ellipsoidal inclination distribution,” Agric. Forest Meteorol., vol. 36, no. 4, pp. 317–321, Apr. 1986. [33] G. S. Campbell, “Derivation of an angle density-fucntion for canopies with ellipsoidal leaf angle distributions,” Agric. Forest Meteorol., vol. 49, no. 3, pp. 173–176, Feb. 1990. [34] J. Ross, The Radiation Regime and Architecture of Plant Stands. Boston, MA: Kluwer, 1981. [35] H. Hoppe, T. DeRose, T. Duchamp, J. McDonald, and W. Stuetzle, “Surface reconstruction from unorganized points,” Comput. Graph.-New York Assoc. Comput. Mach., vol. 26, no. 2, pp. 71–78, Jul. 1992. [36] J. F. Lalonde, R. Unnikrishnan, N. Vandapel, and M. Hebert, “Scale selection for classification of point-sampled 3-D surfaces,” in Proc. 5th Int. Conf. 3-D Digit. Imag. Model., 2005, pp. 285–292. [37] L. S. Pierre Alliez and G. Guennebaud, “Surface reconstruction from point sets,” CGAL User and Reference Manual 3. 7 ed., CGAL Editorial Board, 2010. [38] G. Jacobs, “3D Scanning: Understanding spot size for laser scanning,” Prof. Surveyor Mag., vol. 26, no. 10, pp. 1–3, Oct. 2006. [39] HDS Scanning & Cyclone Traning Manual, Leica Geosystems HDS, St. Gallen, Switzerland, 2008. [40] N. J. Mitra, A. Nguyen, and D. L. Guibas, “Estimating surface normals in noisy point cloud data,” Int. J. Comput. Geom. Appl., vol. 14, no. 4/5, pp. 261–276, Oct. 2004. [41] T. K. Dey, G. Li, and J. Sun, “Normal Estimation for Point Clouds: A Comparison Study for a Voronoi Based Method,” in Proc. Point-Based Graph., Eurograph./IEEE VGTC Symp., 2005, pp. 39–46. [42] W. M. Wang, Z. L. Li, and H. B. Su, “Comparison of leaf angle distribution functions: Effects on extinction coefficient and fraction of sunlit foliage,” Agric. Forest Meteorol., vol. 143, no. 1/2, pp. 106–122, Mar. 2007. [43] C. Macfarlane, S. K. Arndt, S. J. Livesley, A. C. Edgar, D. A. White, M. A. Adams, and D. Eamus, “Estimation of leaf area index in eucalypt forest with vertical foliage, using cover and fullframe fisheye photography,” Forest Ecol. Manage., vol. 242, no. 2/3, pp. 756–763, Apr. 2007. [44] J. M. N. Walter and E. F. Torquebiau, “The computation of forest leaf area index on slope using fish-eye sensors,” Comptes Rendus Acad. Sci. Serie III-Sci. Vie-Life Sci., vol. 323, no. 9, pp. 801–813, Sep. 2000.

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[45] C. Macfarlane, M. Coote, D. A. White, and M. A. Adams, “Photographic exposure affects indirect estimation of leaf area in plantations of Eucalyptus globulus Labill,” Agric. Forest Meteorol., vol. 100, no. 2/3, pp. 155– 168, Feb. 2000. [46] J. L. Lowell, D. L. P. Jupp, G. J. Newnham, and D. S. Culveror, “Measuring tree stem diameters using intensity profiles from ground-based scanning LiDAR from a fixed viewpoint,” ISPRS J. Photogramm. Remote Sens., vol. 66, no. 1, pp. 46–55, Jan. 2011. [47] J. M. Chen and S. G. Leblanc, “A four-scale bidirectional reflectance model based on canopy architecture,” IEEE Trans. Geosci. Remote Sens., vol. 35, no. 5, pp. 1316–1337, Sep. 1997. [48] J. J. Richardson, L. M. Moskal, and S. H. Kim, “Modeling approaches to estimate effective leaf area index from aerial discrete-return LIDAR,” Agric. Forest Meteorol., vol. 149, no. 6/7, pp. 1152–1160, Jun. 2009.

Guang Zheng received the B.Eng. degree in urban planning from Nanjing Forestry University, Nanjing, China, in 2004, the M.Sc. degree in cartography and geographic information systems from Nanjing University, Nanjing, China, in 2007, and the Ph.D. degree in forest resources and management from the University of Washington, Seattle, in 2011 where he also worked as a Research Assistant in the Remote Sensing and Geospatial Analysis Laboratory (RSGAL). Currently he is a Research Scientist at the International Institute for Earth System Science, Nanjing University, China. His research interests are the application of light detection and raging (lidar) in retrieving forest canopy structural parameters and the application of remote sensing and geographic information systems in the field of forest ecosystem.

L. Monika Moskal is an Assistant Professor of remote sensing at the University of Washington (UW), College of the Environment, School of Environmental and Forest Sciences, where she directs the Remote Sensing and Geospatial Analysis Laboratory (RSGAL) founded by her in 2003. She is one of the core faculty in the UW Precision Forestry Cooperative. Her goal is to understand multiscale and multidimensional dynamics of landscape change through the application of remote sensing. Her research has been applied to the following themes: ecosystem services and function, bioenergy/biomass, forest inventories, forest health, change analysis, biodiversity, habitat mapping, spatiotemporal wetland assessment, geostatistical analysis of prairie vegetation communities, urban growth and forest fragmentation.