# AdTree: Accurate, Detailed, and Automatic Modelling of Laser-Scanned Trees

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## Abstract

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## 1. Introduction

## 2. Overview

**Robust to tree species.**The method should be able to reconstruct common tree species with clear branch structures. The reconstructed models should convey the main topological branch structure of the real world trees represented by the point clouds. Vegetation that do not demonstrate skeleton structures (e.g., bushes) are not considered the target objects.**High fidelity.**The reconstructed tree models should be topologically faithful to the input and have acceptable geometrical accuracy. This is vital for applications where important tree attributes (i.e., stem location, stem thickness, tree height) are expected to be derived from the reconstructed models.**High efficiency.**The reconstruction process should not require user intervention, i.e., it is fully automatic and can produce 3D models of individual trees promptly regardless of the size of the input point clouds. This enables large scale tree modeling when, for instance, an instance segmentation of the trees is available [24].

**Skeleton initialization.**We triangulate the input points and apply the MST algorithm to extract the initial tree skeleton. Note that the main-branch points are identified and centralized beforehand to improve the quality of the skeleton;**Skeleton simplification.**The initial skeleton is iteratively simplified, resulting in a light-weight tree skeleton. We simplify the skeleton by retrieving and merging adjacent vertices if their distance is sufficiently small;**Branch fitting.**Based on the reconstructed tree skeleton, we fit a sequence of cylinders over the input points to approximate the geometry of the branches. We first apply non-linear least squares to obtain the accurate radius of the tree trunk. Then, we derive the radius of the subsequent branches from the main trunk geometry;**Adding realism.**We synthesize leaves at the end of tree branches and add texture to enhance realism.

## 3. Materials and Methods

#### 3.1. Skeleton Initialization

#### 3.2. Skeleton Simplification

#### 3.2.1. Assigning Vertex and Edge Importances

#### 3.2.2. Simplifying Adjacent Vertices and Edges

#### 3.3. Branch Fitting

**Input data:**position p of the input points;**Parameters to be solved:**the axis direction vector $\mathbf{a}$ of the cylinder, position ${p}_{a}$ of the endpoint on the axis, and the radius r of the cylinder;**Objective function:**sum of squared distance d from the points to the branch cylinder, i.e.,

#### 3.4. Adding Realism

#### 3.5. Implementation Details

#### 3.6. Test Datasets

## 4. Results and Discussion

#### 4.1. Visual Evaluation

#### 4.2. Reconstruction Accuracy

#### 4.3. Robustness

#### 4.4. Comparisons

#### 4.5. Limitations

#### 4.6. Potential Applications

## 5. Conclusions and Future Work

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

LiDAR | Light Detection and Ranging |

MST | Minimum Spanning Tree |

PCA | Principal Component Analysis |

QSM | Quantitative Structure Modelling |

SFM | Structure From Motion |

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**Figure 2.**Skeleton initialization for two trees. (

**a**) A valid tree skeleton structure (in red). (

**b**) An invalid tree skeleton structure (in red). The left column shows the input point clouds.

**Figure 3.**Skeleton extraction from the centralized points. (

**a**) Density map of the raw point cloud. Red indicates high density and blue indicates low density. (

**b**) Skeleton extracted after the main-branch point centralization.

**Figure 4.**Skeleton simplification. (

**a**) Initial skeleton. (

**b**) Importance value assigned to branches. Red indicates high importance and blue indicates low importance. (

**c**) Simplification by eliminating noisy small branches. (

**d**) Simplification by merging similar vertices and edges.

**Figure 6.**Bidirectional similarity indicators. (

**a**) Indicator computed from v

_{1}to v

_{2}. (

**b**) Indicator computed from v

_{2}to v

_{1}.

**Figure 8.**Branch fitting. (

**a**) Tree skeleton. (

**b**) Points segmented into different parts. (

**c**) Cylinder fitted to the main trunk. (

**d**) Geometry derived for the subsequent branches.

**Figure 11.**Five different trees (from (

**a**) to (

**e**)) reconstructed using our method. From left to right: point cloud, skeleton, tree branches, and final model.

**Figure 14.**Comparison between Livny’s method [23] and our method demonstrated on two trees.

**Table 1.**Statistics on the tree examples shown in Figure 11. This table summarizes the height, complexity, number of points, data source of the trees and the accuracy (mean distance from the points to the surface of the reconstructed models) and the standard deviation.

Figure | Height (m) | Complexity | Point Number | Sensor Type | Accuracy (cm) | Stardard Deviation |
---|---|---|---|---|---|---|

Figure 11a | 5.52 | Medium | 11,855 | Mobile scanning | 2.76 | 2 |

Figure 11b | 9.87 | Medium | 6992 | Mobile scanning | 10.04 | 8 |

Figure 11c | 15.99 | Difficult | 28,993 | Mobile scanning | 6.59 | 6 |

Figure 11d | 21.73 | Difficult | 137,407 | Static scanning | 6.50 | 6 |

Figure 11e | 13.13 | Easy | 2488 | Airborne scanning | 11.88 | 7 |

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**MDPI and ACS Style**

Du, S.; Lindenbergh, R.; Ledoux, H.; Stoter, J.; Nan, L. AdTree: Accurate, Detailed, and Automatic Modelling of Laser-Scanned Trees. *Remote Sens.* **2019**, *11*, 2074.
https://doi.org/10.3390/rs11182074

**AMA Style**

Du S, Lindenbergh R, Ledoux H, Stoter J, Nan L. AdTree: Accurate, Detailed, and Automatic Modelling of Laser-Scanned Trees. *Remote Sensing*. 2019; 11(18):2074.
https://doi.org/10.3390/rs11182074

**Chicago/Turabian Style**

Du, Shenglan, Roderik Lindenbergh, Hugo Ledoux, Jantien Stoter, and Liangliang Nan. 2019. "AdTree: Accurate, Detailed, and Automatic Modelling of Laser-Scanned Trees" *Remote Sensing* 11, no. 18: 2074.
https://doi.org/10.3390/rs11182074