# Influencing Factors in Estimation of Leaf Angle Distribution of an Individual Tree from Terrestrial Laser Scanning Data

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{−2}to 27 cm

^{−2}tested), the better the result is; (3) the performance is more sensitive to the scanner location than the number of scans. Increasing the scanner height improves LAD estimation, which has not been seriously considered in previous studies. It is worth noting that relatively tall trees suffer from a more severe occlusion effect, which deserves further attention in further study.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Simulated Point Clouds Data

^{3}) [7]), is calculated from the ratio of the total leaf area and the crown volume, and the crown volume is the volume of the envelope reconstructed from the simulated point clouds. There were large differences between the three tree models. The crown diameter (CD) (east–west) and tree height (TH) were very small for Tree1 (Aspen) (1.4 m × 1.3 m and 2.7 m, respectively), but the leaf area density (3.8 m

^{2}/m

^{3}) was the largest of all three trees (Figure 1(a1)). The CD of Tree2 (Pin Oak) (5.5 m × 5.5 m) was much larger than that of Tree1, and the TH (3.4 m) was slightly taller than that of Tree1 (Figure 1(a2)), with a leaf area density of 0.9 m

^{2}/m

^{3}. Tree3 (White Oak) was the tallest of all of three trees (6.5 m), and the CD was similar with that of Tree2, with a leaf area density of 1.7 m

^{2}/m

^{3}(Figure 1(a3)). The true LAD of each tree (illustrated in Figure 1(c1–c3), respectively) was calculated based on the coordinates of the triangles.

#### 2.2. LAD Estimation

#### 2.3. G-function Calculation

#### 2.4. Validation

#### 2.5. Sensitivity Analysis of the Influencing Factors

^{−2}, 4.6 cm

^{−2}, 1.4 cm

^{−2}, 0.4 cm

^{−2}, and 0.2 cm

^{−2}on average of the three trees, were compared. In the analysis of the effect of the number of scans and the scanner height, the difference between one scan and the merged point clouds of two, four, and eight scans of the simulated TLS data with the scanner height set to 1.5 m and 3 m were compared. Combining CPCs with a GPD of 5 mm and simulated point clouds data with an NPD of 5 mm, the influence of the occlusion effect was analyzed. Detailed information is listed in Table 1:

## 3. Results

#### 3.1. The Point Density Effect on the LAD and G-Function Calculations Based on CPCs

^{−2}(roughly equivalent to GPD = 1 cm) when using the point clouds to estimate the LAD in our studied cases.

#### 3.2. The Effect of the Number of Scans and Scanner Height on the LAD and G-Function Calculations and the Occlusion Effect

## 4. Discussion

#### 4.1. The Accuracy Assessment of LAD Estimation

^{3}, 3

^{3}, 4

^{3}, 5

^{3}, and 6

^{3}disks with a uniform distribution in the volume were used by Bailey and Mahaffee [18], and five trees in the 4th Radiation Transfer Model Intercomparison (RAMI-IV) were used by Vicari et al. [20]. Computer simulation used in this study can avoid the problem of the lack of the true LAD; however, there are some limitations due to the assumptions that are inconsistent with the real-world conditions: (i) simplifying the leaf as two triangles neglects the curvature and complex shape of leaves; (ii) the lack of noise and artifacts in the simulated point clouds is inconsistent with real TLS measurement; (iii) the Lambertian assumption of the leaf optical property; (iv) registration errors using multi-scan data, which were merged directly without suffering errors since they were simulated in the same coordinate system, is not considered; (v) the scanning stations are designed to be regular, with the same scanning distance around a tree; however, establishing the location of the TLS is usually difficult to define in fieldwork, which might be limited by the terrain and environmental conditions. Except for these assumptions which are difficult to avoid in the simulation, there is a problem in evaluating the method using simulated point clouds: it is difficult to distinguish whether the error is caused by incomplete scanning and the uneven points, or the method itself, since the occlusion effect also exists in simulated TLS.

#### 4.2. Possible Sources of Error in LAD Estimation

^{−2}(corresponding to GPD = 1 cm, see Table 1 for more details) in our studied cases with leaf length ranging from 8 cm to 13 cm and leaf width from 5 cm to 9 cm. In real measurement, this value should be considered according to the curvature and average size of the leaves. Closely related to the point density, the radius used for spherical search of adjacent points was four times the NPD of the simulated point clouds that was subsampled to an NPD of 5 mm. The setting of the searching radius is a tricky problem. Assuming a fixed NPD, larger radius leads to a higher probability of including points on adjacent leaf, especially for trees with crowded leaves (e.g., the AE (6.6%) computed from the CPC of Tree1 (with the largest leaf area density) is the largest of all the three trees); smaller radius (i.e., less adjacent points) causes the calculation of inclination angle to be more sensitive to the noise (see an experiment (Figure 8) of the influence of the noise on inclination angle calculation, when using different numbers of adjacent points) in real measurement.

^{2}/m

^{3}, Tree2 is between Tree 1 and Tree3, and its calculation accuracy is the highest among them. The LAD error of Tree3 with a height of 6.5 m is the largest (64.2% for two scans), indicating that the influence of the occlusion effect is more serious when the trees are taller. The above results are all obtained with a scanner height of 1.5 m, which is the general height of a TLS tripod and was adopted in other studies [18,20]. It should be noted that the result may be greatly improved (from 64% to 38%) when the scanner height is doubled (3 m). Raising the height of the instrument can reduce the influence of the occlusion effect for tall trees. Larger scanner heights are not considered in this study considering the limitation of the tripod used in current measurements. Furthermore, only factors relevant to the measurement are considered; future study should focus on the wind effect, and the impact of tree structure on LAD estimation.

#### 4.3. Difference between the Effect of Number of Scans and Scanner Location on TLS-Based LAD and G-Function Estimation

#### 4.4. Future Research Perspectives

## 5. Conclusions

^{−2}(corresponding to a grid point distance of 1 cm) in our studied cases (leaf length $\times $ leaf width: 8 cm $\times $ 5 cm, 12 cm $\times $ 8 cm, 13 cm $\times $ 9 cm). Even though the number of points per unit leaf area of 1 cm

^{−2}is just obtained from CPCs, it is helpful in designing scanning distance (s) of TLS to acquire an average point spacing (d, d $=2\xb7\mathrm{s}\xb7\mathrm{tan}\partial /2$) with a certain scan angle resolution ($\partial $); (iii) increasing the number of scans at different locations at the same height does not result in apparent improvement (there is an average improvement of 6.4% in AE of the three trees using two-scans data than just single-scan data). Future research should focus on improving LAD using high-resolution single-scan data to avoid the influence of registration error when using multi-scan data; (iv) the height of the instrument should be seriously considered for LAD estimation. The occlusion effect is greatly mitigated when the scanner height is two times the traditional height (1.5 m) in our experiments; with a distance of 5 m from the tree locations to the scanner, and the height from the scanner to the bottom of the tree crown of 2.77 m, 2.64 m, and 2.80 m for Tree1, Tree2, and Tree3, respectively. For tall trees with large leaf area density, we should pay special attention to LAD and G-function calculation using TLS point clouds due to the serious occlusion effect.

## Author Contributions

## Funding

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Overview of the simulated data. The three-dimensional (3D) tree models generated in OnyxTREE with different structures, and the details of the number of leaves, leaf size, crown diameter (CD), tree height (TH), and leaf area density are shown in (

**a1**–

**a3**). Examples of the leaves and leaf structure of the three tree models are illustrated in (

**b**). Each leaf is made up of two triangles with a common edge. (

**c1**–

**c3**) are the true leaf angle distribution (LAD) curves, and (

**d1**–

**d3**) illustrate the TLS scanning strategy in the Discrete Anisotropic Radiative Transfer (DART) model for the three tree models.

**Figure 2.**Schematic diagram of the materials and methods. See Section 2.1 for details of the “3D tree models” and “terrestrial laser scanning (TLS) point clouds”, Section 2.2 and Section 2.3 for the leaf angle distribution (LAD) and G-function calculation, Section 2.4 for the “Complete Point Clouds (CPC)”, and Section 2.5 for the “Influencing factors”.

**Figure 3.**(

**a**) The schematic diagram of the complete point clouds (CPC) calculation and (

**b**) an example of part of a CPC in a tree. Red points are the vertexes of the triangles that make up a leaf, white lines show how the triangles are gridded, and the white points are the calculated grid points and are called a CPC.

**Figure 4.**The estimated leaf angle distributions (LADs) (

**a1**–

**a3**) for Tree1, Tree2, and Tree3, respectively) and G-functions (

**b1**–

**b3**) for Tree1, Tree2, and Tree3, respectively) for the three tree models computed from the complete point clouds (CPCs) with different grid point distances (GPDs) (2 mm, 5 mm, 1 cm, 2 cm, and 4 cm): the “Exact” curves in black are the true LADs and G-functions; AE denotes percentage of the overall deviation between the estimated value and the true value, and the corresponding calculations are given in Equations (4) and (5).

**Figure 5.**The effect of the number of scans and the scanner height on the leaf angle distribution (LAD) (

**a**) and the G-function (

**b1**,

**b2**) for Tree1; (

**b1**,

**b2**) are the results for scanner heights (SHs) of 1.5 m and 3 m, respectively: the “Exact” curves in black are the true LADs and G-functions computed from the three-dimensional (3D) tree model; the green curves are the LAD and the G-function computed from the complete point clouds (CPC) with a grid point distance (GPD) of 5 mm, which can represent the accuracy without the occlusion effect; TLS_SIM denotes simulated TLS point clouds. The scanning strategy is illustrated in Figure 1(d1).

**Figure 6.**The effect of the number of scans and the scanner height on the leaf angle distribution (LAD) (

**a**) and the G-function (

**b**) for Tree2: the “Exact” curves in black are the true LAD and the G-function computed from the three-dimensional (3D) tree model, respectively; the green curves are the LAD and G-function computed from the complete point clouds (CPC) with a grid point distance (GPD) of 5 mm, which can represent the accuracy of the method without the occlusion effect; TLS_SIM denotes simulated TLS point clouds. The scanning strategy is illustrated in Figure 1(d2).

**Figure 7.**The effects of the number of scans and the scanner height on the leaf angle distribution (LAD) (

**a**) and the G-function (

**b**) for Tree3: the “Exact” curves in black are the true LAD and G-function computed from the three-dimensional (3D) tree model; the green curve is the LAD and the G-function computed from the complete point clouds (CPC) with a grid point distance (GPD) of 5 mm, which can represent the accuracy of the method without the occlusion effect; TLS_SIM denotes simulated TLS point clouds. The scanning strategy is illustrated in Figure 1(d3).

**Figure 8.**Influence of the noise on the inclination angle calculation. (

**a**) Schematic diagram of original points (white) with a point spacing of 5 mm on a horizontal plane, and noised points (red) acquired by adding random values on Z coordinates of the original points; (

**b**) influences of different levels of noise (by adding random values with a mean of zero and a standard deviation ($\sigma $) of 0.5 mm and 1.5 mm) on the inclination angle calculation of point P using a least squares fitting technique. P is originally on a plane with an inclination angle of 0°; the estimated inclination angles of P on the fitted planes with different number of adjacent points increases with the noise level, and the error generally decreases with the increasing number of adjacent points when the noise level is fixed. A total of 100 datasets of the noised points for each noise level (with the same mean and standard deviation) were generated, and each angle shown in (

**b**) is the average angle calculated from the 100 datasets.

**Figure 9.**The occlusion effect in terrestrial laser scanning (TLS) and the effect of the scanner height (SH) (

**a**) on the scanned points (

**b**,

**c**). Leaf① and leaf② are horizontal, leaf③ and leaf④ are slanted. The leaves are represented by a straight line because they are illustrated from the side. Dashed lines represent pulses emitted by TLS: the black and blue dashed lines are the pulses emitted by Scan I and Scan II, respectively. α and β are the angles between the emitted pulses of Scan I and leaf② and between Scan II and leaf②, respectively, β $>$ α.

**Figure 10.**Hemispherical scanning of a tree using UAV laser scanning (UAVLS). Leaf① is horizontal, and leaf② and leaf③ are slanted. Dashed lines represent the pulses emitted by the laser scanner: A, B, C and D are parallel to the leaf, indicating that no point can be acquired in these cases, and the rest (in blue) represent pulses that intersect with the leaves, indicating that some points can be acquired through scanning.

Sensitivity Analysis | Comparisons | Data |
---|---|---|

Point density | Grid point distances (GPDs) of 2 mm, 5 mm, 1 cm, 2 cm, and 4 cm; they are equivalent to: a number of points per unit leaf area of 26.6 cm ^{−2}, 4.6 cm^{−2}, 1.4 cm^{−2}, 0.4 cm^{−2}, and 0.2 cm^{−2} | Complete point clouds (CPC) |

Number of scans | One scan and the merged point clouds of two, four, and eight scans | Simulated TLS data |

Scanner height | 1.5 m, 3 m | Simulated TLS data |

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**MDPI and ACS Style**

Jiang, H.; Hu, R.; Yan, G.; Cheng, S.; Li, F.; Qi, J.; Li, L.; Xie, D.; Mu, X.
Influencing Factors in Estimation of Leaf Angle Distribution of an Individual Tree from Terrestrial Laser Scanning Data. *Remote Sens.* **2021**, *13*, 1159.
https://doi.org/10.3390/rs13061159

**AMA Style**

Jiang H, Hu R, Yan G, Cheng S, Li F, Qi J, Li L, Xie D, Mu X.
Influencing Factors in Estimation of Leaf Angle Distribution of an Individual Tree from Terrestrial Laser Scanning Data. *Remote Sensing*. 2021; 13(6):1159.
https://doi.org/10.3390/rs13061159

**Chicago/Turabian Style**

Jiang, Hailan, Ronghai Hu, Guangjian Yan, Shiyu Cheng, Fan Li, Jianbo Qi, Linyuan Li, Donghui Xie, and Xihan Mu.
2021. "Influencing Factors in Estimation of Leaf Angle Distribution of an Individual Tree from Terrestrial Laser Scanning Data" *Remote Sensing* 13, no. 6: 1159.
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