# Calibration and Validation of a Detailed Architectural Canopy Model Reconstruction for the Simulation of Synthetic Hemispherical Images and Airborne LiDAR Data

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Main Goals and Applicability

**Hypothesis**

**1.**

**Hypothesis**

**2.**

**Hypothesis**

**3.**

#### 1.2. Overview

## 2. Datasets

#### 2.1. Airborne LiDAR Data

^{2}in flat terrain, leading to point densities between 24 and 30 pts/m

^{2}in triple overlapping strips. Within the tree crowns, a maximum of seven returns per pulse has been recorded.

#### 2.2. Terrestrial LiDAR Data

#### 2.3. Digital Hemispherical Photographs

## 3. Methods

#### 3.1. Derivation of Branch and Foliage Model

#### 3.1.1. Tree Modelling Approach

#### 3.1.2. Foliage Modelling

^{2}). For more realism, complexity can easily be increased by using complex leaf and needle shape templates for branch colonization (see [35,36,37,38]), which was not realized in the study at hand.

_{voxel}(m

^{2}/m

^{3}). Following Cote et al. [35], a voxel edge length of 30 cm is implemented, which shows the best agreement between computational effort and plausibility of the results.

_{voxel}is the path length of the ray through the voxel and G

_{voxel}= 0.5 is the projection coefficient assuming a spherical distribution of canopy material. If P is larger than a random variable U in the interval [0, 1], the ray is occluded. If the number of occluded rays in the interval [0, 9] was smaller than a light threshold of four rays (found by automatic calibration), the branch segment was spirally colonized with leaves as described above.

#### 3.2. Calibration and Validation of Tree Modelling Approach Using DHPs

#### 3.3. Data Analysis Approaches

#### 3.3.1. aLiDAR-Simulation (Step 1)

_{step}) and the pulse repetition rate (PRR): trajectory data, v and θ were locked and the θ

_{step}was consecutively changed in the interval [0.005°, 0.04°] with an increment of 0.001°. As the cross track point distance (d

_{cross}) below the flight trajectory on the flat ground is defined by Equation (2), we guaranteed a homogeneous scan pattern on the ground by adapting PRR to v and θ

_{step}following the criteria given in Equation (3).

#### 3.3.2. Generation of Ray Interceptions and Leaf Centroids (Steps 2 and 3)

#### 3.3.3. Spatial Analysis (Step 4)

^{2}.

_{intercept}). On the other hand, the rays, defined by each ray-interception point and its associated emission point (along the aircraft flight path), were intersected with the voxel cells. For each cell the number of intersecting rays was stored. This represents the number of rays theoretically passing through a voxel (theo_point

_{intercept}). For rays which only defined theo_point

_{intercept}for the voxel, we tested if the associated interception point was before (before_point

_{intercept}) the voxel intersection or after. For each cell the number of before_points

_{intercept}was stored. AC is defined by Equation (8).

_{LiDAR}, theo_points

_{LiDAR}and before_points

_{LiDAR}as described above. For the aLiDAR data in the 3D grid, LIR and the AC_L are defined by Equations (9) and (10). According to Durrieu et al. [23], the AC_L is defined by Equation (10) and includes an attenuation correction with depth into canopy.

## 4. Results

#### 4.1. 3D Modelling Results

#### 4.2. Correlation between Simulated and Real aLiDAR Point Cloud

^{2}of 0.81. Regression lines were fitted separately for each tree. It can be shown that the regression functions show strong similarities. The scatter plot of the correlation with separate regression lines per tree is shown in Figure 9. The average RMSE between the fitted single-tree regression lines was less than 0.4 pts/m

^{3}.

#### 4.3. Correlation between aLiDAR Penetration Metrics and 3D Model Densities

#### 4.3.1. 2D Pixel Approach

^{2}the rLAI value per cell is 2.49 m

^{2}/m

^{2}.

^{2}of the correlation between LIR and the number of leaves is in the same range for multiple and single strip coverage (0.79, 0.81).

^{2}decreases to a value of 0.74 (single strip) and 0.68 (triple strip overlap).

^{2}of the correlation between AC_L and the true AC at 0° incidence angle is higher than 0.98 (single and overlapping strips). The fitted regression line for 2 m cell size setup follows the function given in Figure 10b.

#### 4.3.2. 3D Voxel Approach

^{2}the rLAI value per cell is 0.7 m

^{2}/m

^{2}.

^{2}of the correlation between LIR and the number of leaves is 0.40 (single strip) and 0.60 (triple strip overlap). The derived correlation function is given In Figure 10c.

^{2}values of 0.6. For incidence angles ≥60°, the R

^{2}decreases to values between 0.5 and 0.4.

#### 4.4. Scan Parameter Simulation

^{2}per strip, AC_L and LIR were computed for both analysis approaches and correlated to true AC and LAI measures given by the 3D architectural tree models. In general, the correlation coefficients show an increase with increasing LiDAR point densities. This is true for both the correlation of rLAI vs. LIR and AC vs. AC_L. The R

^{2}values increase along a saturation curve (Figure 11).

^{2}values for the whole test case is very low (0.05 rLAI vs. LIR; 0.01: AC vs. AC_L). R

^{2}values for 2 m cell size are high for both low and high point densities (0.80: rLAI vs. LIR; 0.98: AC vs. AC_L).

^{2}values of the rLAI-LIR relationship are very low for small point densities (0.21: 2.1 pts/m

^{2}) and reach a maximum of 0.6 at 30 pts/m

^{2}with a triple strip overlap. The maximum for a single nadir strip is also reached at 30 pts/m

^{2}but is limited to a maximum of about 0.50.

^{2}ranges from 0.30 (2.1 pts/m

^{2}) to 0.83 (20 pts/m

^{2}) with triple strip overlap and a penetration incidence angle of 0°. After reaching the maximum, the R

^{2}value keeps almost constant. For larger incident angles the maximum R

^{2}value is increasingly damped. For incidence angles smaller than 50° the maximum R

^{2}values are still higher than 0.6. For incidence angles ≥60° the R

^{2}shows only a maximum of about 0.5.

## 5. Discussion

#### 5.1. Plausibility of Derived 3D Models (Validation of Hypotheses 1–2)

^{2}of 0.81 for the correlation between synthetic and real LiDAR data). This can approve the plausibility of the described setup. Thus, the described set of unknown error sources must show only a negligible influence, which validates the given hypotheses 1 and 2. As the average correlation coefficient was 0.81, Hypothesis 3 could also be validated, stating that the derived 3D model setup is suitable for the systematic simulation of aLiDAR sensors. As the simulated aLiDAR point cloud shows strong similarities to the real data, we can assume a correct representation of the interactions of real foliage densities and the aLiDAR acquisition physics for our model.

#### 5.2. Prediction of Foliage Densities by Simulated aLiDAR Data

^{2}.

#### 5.3. Comparison of Data Structures for Analysis

#### 5.4. Comparison of Scan Settings and Point Densities for Analysis

^{2}reaches its maximum already at a first return density of 5 pts/m

^{2}. For AC, which shows no vertical clumping, this leads to almost perfect predictions. The R

^{2}of rLAI prediction did never exceed 0.8. This suggests that the quality has reached a saturation level. Sampling density and additional flight strips have a negligible effect onto the quality of the predictions. Only a capturing technique, which is able to sample the inner crown in a homogeneous manner, would be able to further improve the R

^{2}.

^{2}. For rLAI in particular, this is not enough in order reach an R

^{2}higher than 0.6, which can also be explained by the limitations of the object–sensor relationship.

^{2}are already suitable for 2D LAI description (not significantly improvable with increased point densities). Nevertheless, it has to be stated that with only 4 pts/m

^{2}, LiDAR based height estimates show errors of up to 1 m, which can lead to errors of aboveground biomass estimates of 80–125 Mg·ha

^{−1}[50]. The 3D grid approach aims at a three dimensional mapping of LAI, which is more ambitious and can only be achieved with moderate predictive power. This suggests the exploitation of more advanced sensing techniques, such as full-waveform LiDAR, which has already been proofed for vertical LAI mapping [29,30].

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Basic concept. The virtual domain (3D Models) is the digital reconstruction of the physical one. A comparison of model and physical domain can only be done in the appearance domain. The assessment of the physical domain is restricted to a limited set of sensing/measuring techniques that can be simulated in the virtual domain (DHP, tLiDAR, aLiDAR).

**Figure 2.**(

**a**) Surroundings of the experimental test site, showing the trajectories of the aLiDAR flight strips; and (

**b**) experimental test site showing the tree positions of Fraxinus excelsior (fe [tree 1]), Robinia (r [tree 1,2]) and Platanus (p [tree 1–6]). Scan positions and DHP positions are indicated by the instrument symbols (image source: tiris maps).

**Figure 3.**Overview of the derivation of the 3D Models: (1) In a leaf-off situation, in the physical domain, a point cloud is acquired using tLiDAR. (2) Based on the point cloud appearance, the data are pre-processed and a 3D branch model and an initial 3D foliage model is generated. (3) Using ray tracing/RTM, a synthetic hemispherical image (SHI) appearance is derived from the model. (4) In a leaf-on situation, in the physical domain, a DHP is acquired. (5) By comparing SHI and DHP, the 3D modelling parameters are iteratively calibrated. (6) After calibration, the models are validated by additional DHPs and simulations.

**Figure 4.**Overview of the analysis workflow: (1) Simulation of a test point cloud via ray tracing/RTM (including plausibility check with real aLiDAR data). (2) Simulation of a reference ray-interception point cloud via ray tracing (0.01 m resolution). (3) Reference leaf centroid derivation from polygonal model; (4) Data analysis in a 3D grid and 2D grid.

**Figure 5.**(

**a**) Schematic overview of the scanning parameters used for aLiDAR simulation; and (

**b**) principle of the multi-return simulation discretizing the cone-shaped laser beam into nine rays.

**Figure 6.**Example for the comparison of vertical hemispherical image from 3D tree models and digital hemispherical photograph. Red areas are building models, available for the city of Innsbruck, zenith angles where buildings occur were not analysed: (

**a**) leaf-off SHI; (

**b**) leaf-off DHP; (

**c**) leaf-on SHI; and (

**d**) leaf-on DHP.

**Figure 7.**Oblique view onto the modelled tree architecture results, demonstrating the 3D foliage arrangements, which were input to the aLiDAR and SHI simulations: (

**a**) leaf-off; and (

**b**) leaf-on.

**Figure 8.**Example for the generation of synthetic hemispherical images directly from the leaf-off tLiDAR data [21]: (

**a**) tLiDAR point radii are scaled by intensity between 0 and 0.02 m. SHI corresponds to a GFD of 0.15; and (

**b**) tLiDAR point radii are scaled by intensity between 0 and 0.05 m. SHI corresponds to a GFD of 0.35.

**Figure 9.**Scatterplot correlating the simulated point densities (simulation) per voxel cell with the real point density (aLiDAR) per voxel cell. Observations per tree are indicated in different colours: red = robinia [tree 1,2], blue = platanus [tree 1–6], and green = fraxinus excelsior. Individual regression lines per single tree are shown in black.

**Figure 10.**Scatterplots with correlation functions for the 2D and 3D grid approach. LiDAR metrics (LIR, AC_L) as predictor variables predicting rLAI and AC values: (

**a**) rLAI prediction by LIR (2D grid); (

**b**) AC prediction by AC_L (2D grid); (

**c**) rLAI prediction by LIR (3D grid); and (

**d**) AC prediction by AC_L (3D grid).

**Figure 11.**Behaviour of R

^{2}for the correlations between aLiDAR derived canopy density measures (LIR, AC_L) and reference canopy density measures (rLAI, AC) with an increasing point density of aLiDAR data. Single strip curves are shown in red and multi strip curves in blue: (

**a**) R

^{2}behaviour for the correlation of AC and AC_L (2D grid); (

**b**) R

^{2}behaviour for the correlation of rLAI and LIR (2D grid); (

**c**) R

^{2}behaviour for the correlation of AC (with different incidence angles) and AC_L (3D grid); and (

**d**) R

^{2}behaviour for the correlation of rLAI and LIR (3D grid).

Input Parameter | Used Setting |
---|---|

PCAmin ^{1} | 0.1 m |

PCAmax ^{1} | 1.0 m |

edge length ^{2} | 0.1 m |

segment resolution ^{2} | 0.2 m |

step width ^{3} | 0.04 m |

light threshold ^{3} | 4 |

^{1}defined by expected tree characteristics,

^{2}defined by point cloud quality,

^{3}calibrated by DHPs.

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Bremer, M.; Wichmann, V.; Rutzinger, M.
Calibration and Validation of a Detailed Architectural Canopy Model Reconstruction for the Simulation of Synthetic Hemispherical Images and Airborne LiDAR Data. *Remote Sens.* **2017**, *9*, 220.
https://doi.org/10.3390/rs9030220

**AMA Style**

Bremer M, Wichmann V, Rutzinger M.
Calibration and Validation of a Detailed Architectural Canopy Model Reconstruction for the Simulation of Synthetic Hemispherical Images and Airborne LiDAR Data. *Remote Sensing*. 2017; 9(3):220.
https://doi.org/10.3390/rs9030220

**Chicago/Turabian Style**

Bremer, Magnus, Volker Wichmann, and Martin Rutzinger.
2017. "Calibration and Validation of a Detailed Architectural Canopy Model Reconstruction for the Simulation of Synthetic Hemispherical Images and Airborne LiDAR Data" *Remote Sensing* 9, no. 3: 220.
https://doi.org/10.3390/rs9030220