# Trunk-Constrained and Tree Structure Analysis Method for Individual Tree Extraction from Scanned Outdoor Scenes

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## Abstract

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## 1. Introduction

- (1)
- A comprehensive framework combining semantic segmentation with trunk-constrained and tree structure analysis is constructed for individual tree extraction. It can solve the problem whereby trees are often distributed in multiple rows, and there are overlaps between the canopies.
- (2)
- A new method for locating tree position and crown center based on the local tree trunk method is proposed. The real local tree trunks are identified by restricting the height, the number of points and the angle between the trunk and the ground, the crown centers are located by circle fitting, and complete trunks are extracted according to region growing in relation to the proposed candidate trunk region.
- (3)
- A novel individual tree extraction method based on distance difference and centroid deflection angle is proposed. Exploiting tree point classification and the effective instance segmentation strategy, the proposed method can obtain more satisfactory individual tree extraction results.

## 2. Materials and Methods

#### 2.1. Tree Trunks Extraction

#### 2.1.1. Local Tree Trunks Extraction

#### 2.1.2. Tree Trunk Locating

#### 2.1.3. Trunks Extracted by Region Growing

- (1)
- For a trunk $tr{u}_{1}$, take ${o}_{1}$ as its center and expand the range of $\mathsf{\Delta}r\times {r}_{1}$ in the horizontal direction to construct the trunk candidate region. The radius of the candidate region is $\mathsf{\Delta}r$ ($\mathsf{\Delta}r=5$) times the trunk’s radius ${r}_{1}$. Therefore, for all tree points ${t}_{i}\in T$, if the horizontal distance from ${t}_{i}$ to ${o}_{1}$ satisfies ${d}^{H}\left({t}_{i},{o}_{1}\right)\le \mathsf{\Delta}r\times {r}_{1}$, then ${t}_{i}$ is added to the candidate region $bu{f}_{1}$, and ${d}^{H}$ is calculated via Equation (9):$${d}^{H}({t}_{i},o)=\sqrt{{({t}_{ix}-{o}_{x})}^{2}+{({t}_{iy}-{o}_{y})}^{2}}$$
- (2)
- The eigenvalue $({\lambda}_{1}>{\lambda}_{2}>{\lambda}_{3}\ge 0)$ and eigenvector $\left({v}_{1},{v}_{2},{v}_{3}\right)$ of the point in $bu{f}_{1}$ are obtained from the PCA and ${e}_{3}$ represents the normal vector. The curvature ${\sigma}_{1}$ is calculated by Equation (10), and the curvature is sorted in ascending order.$${\sigma}_{1}=\frac{{\lambda}_{1}}{{\lambda}_{1}+{\lambda}_{2}+{\lambda}_{3}}$$
- (3)
- We create an empty sequence $S$ of seed points and an empty cluster $Clu$, and then select the point with the smallest curvature from $bu{f}_{1}$ and place it in set $S$.
- (4)
- Take the first seed point from $S$ and search for its neighboring points. If the angle between the normal vector of the neighborhood point and the normal vector of the seed point is less than the smooth threshold ${S}_{th}=1/9\pi $, the current point is added to the $cl{u}_{1}$, and then we judge whether the curvature of the neighboring points is less than the curvature threshold ${C}_{th}=0.12$. If it is lower, it will be added to $S$ until all neighborhood points are processed.
- (5)
- Delete the first seed point from $S$ and repeat step (4). Cluster $cl{u}_{1}$ is segmented when $S$ is empty.
- (6)
- Select the first unsegmented point from the sorted curvature data to act as the seed point, and then repeat the above steps until all the points are segmented, to derive cluster $Clu=\left\{cl{u}_{i}|i=1,2,\dots ,{N}_{clu}\right\}$. In this way, the extraction of complete tree trunks in the trunk candidate region is obtained.

#### 2.2. Individual Tree Extraction

#### 2.2.1. Tree Crown Center Calculation

#### 2.2.2. Individual Tree Extraction by Distance Difference and Centroid Deflection Angle

- (1)
- The set of unsegmented points is $C=\left\{{c}_{i}|i=1,2,\dots ,{N}_{c}\right\}$, and ${N}_{c}$ is the number of unsegmented points. The spatial distance ${d}_{1i}$ from point ${c}_{1}\left({c}_{1}^{x},{c}_{1}^{y},{c}_{1}^{z}\right)\in C$ to each crown center ${e}_{i}\left({e}_{i}^{x},{e}_{i}^{y},{e}_{i}^{z}\right)\in E$ is achieved according to Equation (11). All distances are sorted in ascending order—the minimum distance is ${d}_{11}$, the sub minimum distance is ${d}_{12}$, and the corresponding crown centers are ${e}_{1}\left({e}_{1}^{x},{e}_{1}^{y},{e}_{1}^{z}\right)$ and ${e}_{2}\left({e}_{2}^{x},{e}_{2}^{y},{e}_{2}^{z}\right)$.$${d}_{1i}=\sqrt{{({c}_{1}^{x}-{e}_{i}^{x})}^{2}+{({c}_{1}^{y}-{e}_{i}^{y})}^{2}+{({c}_{1}^{z}-{e}_{i}^{z})}^{2}}$$
- (2)
- The distance difference is ${D}_{12}={d}_{12}-{d}_{11}$. If ${D}_{12}>{D}_{th}$, assign ${c}_{1}$ to the tree with ${e}_{1}$. If ${D}_{12}<{D}_{th}$, add ${c}_{1}$ to the remaining unsegmented point set $U=\left\{{u}_{i}|i=1,2,\dots ,{N}_{u}\right\}$. ${N}_{u}$ is the number of remaining unsegmented points. Repeat steps (1) and (2) for all points in set $C$, and obtain the segmentation results of all core points.
- (3)
- For $U$, the neighborhood points are obtained using the search radius $Rs$. If the number of neighborhood points is less than $MinPts$, the point is added to the boundary point set $B=\left\{{b}_{i}|i=1,2,\dots ,{N}_{b}\right\}$, and then the centroids of the boundary points are calculated from the neighborhood points. The centroids set is defined as $K=\left\{{k}_{i}|i=1,2,\dots ,{N}_{k}\right\}$, where ${N}_{k}$ is the number of centroids.
- (4)
- The vector $\overrightarrow{D\left({e}_{1},{b}_{1}\right)}={e}_{1}-{b}_{1}$, and $\overrightarrow{D\left({k}_{1},{b}_{1}\right)}={k}_{1}-{b}_{1}$. The angle ${\theta}_{11}$ of $\overrightarrow{D\left({e}_{1},{b}_{1}\right)}$ and $\overrightarrow{D\left({k}_{1},{b}_{1}\right)}$ is computed according to Equations (12) and (13).$${\theta}_{11}={\mathrm{cos}}^{-1}(\frac{\overrightarrow{D({e}_{1},{b}_{1})}\xb7\overrightarrow{D({k}_{1},{b}_{1})}}{\Vert \overrightarrow{D({e}_{1},{b}_{1})}\Vert \Vert \overrightarrow{D({k}_{1},{b}_{1})}\Vert})$$$${\theta}_{11}=\frac{{\theta}_{11}\times 180.0}{\pi}$$
- (5)
- The intermediate point set $Q=\left({q}_{i}|i=1,2,\dots ,{N}_{q}\right)$ is obtained by deleting the core points and boundary points, and the distance ${d}_{11}$ from ${q}_{1}$ to ${e}_{1}$ is calculated by step 1). The distance ${d}_{12}$ from ${q}_{1}$ to ${e}_{2}$, and the angles ${\theta}_{11}$ between $\overrightarrow{{q}_{1}{k}_{1}}$ and $\overrightarrow{{q}_{1}{e}_{1}}$ and ${\theta}_{12}$ between $\overrightarrow{{q}_{1}{k}_{1}}$ and $\overrightarrow{{q}_{1}{e}_{2}}$ are determinedrespectively based on 4). Normalize the distance and angle using Equations (14) and (15).$${d}_{11}=\frac{{d}_{11}}{{d}_{11}+{d}_{12}},{d}_{12}=\frac{{d}_{12}}{{d}_{11}+{d}_{12}}$$$${\theta}_{11}=\frac{{\theta}_{11}}{{\theta}_{11}+{\theta}_{12}},{\theta}_{12}=\frac{{\theta}_{12}}{{\theta}_{11}+{\theta}_{12}}$$

## 3. Results

#### 3.1. Paris-Lille-3D Dataset

#### 3.2. Analysis of Individual Tree Extraction Results

#### 3.3. Comparative Analysis of Experimental Results

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**Crown center from different views. (

**a**) Front view of crown center. (

**b**) Top view of crown center. The red dots represent the crown center.

**Figure 6.**Individual trees extraction result. The different colors represent different individual tree.

**Figure 10.**Individual tree extraction process of Scene 1, Scene 2 and Scene 3. (

**a**) The PCD of trees. (

**b**) Trunk extraction results. (

**c**) Crown center extraction results. (

**d**) Individual tree extraction results.

**Figure 11.**Individual tree extraction process of Scene 4. (

**a**) The PCD of trees. (

**b**) Trunk extraction result. (

**c**) Crown center extraction result. (

**d**) Individual tree extraction result.

**Figure 12.**Individual tree extraction process of Scene 5. (

**a**) The PCD of trees. (

**b**) Trunk extraction result. (

**c**) Crown center extraction result. (

**d**) Individual tree extraction result.

Scene | ${\mathit{D}}_{\mathit{t}\mathit{h}}$ | $\mathit{R}\mathit{s}$ | $\mathit{M}\mathit{i}\mathit{n}\mathit{P}\mathit{t}\mathit{s}$ | $\mathit{\alpha}$ | $\mathit{\beta}$ |
---|---|---|---|---|---|

Scene1 | 1.8 | 3.0 | 1800 | 0.8 | 0.2 |

Scene2 | 1.8 | 3.0 | 1800 | 0.8 | 0.2 |

Scene3 | 1.8 | 3.0 | 1800 | 0.8 | 0.2 |

Scene4 | 2.0 | 3.0 | 1800 | 0.8 | 0.2 |

Scene4 | 1.8 | 3.0 | 1800 | 0.8 | 0.2 |

Scene5 | 2.5 | 4.0 | 10,000 | 0.7 | 0.3 |

Scene5 | 2.5 | 2.0 | 400 | 0.9 | 0.1 |

Scene | Method | $\mathit{T}\mathit{P}$ | $\mathit{F}\mathit{N}$ | $\mathit{F}\mathit{P}$ | $\mathit{P}$ | $\mathit{R}$ | $\mathit{F}$ |
---|---|---|---|---|---|---|---|

Scene 2 | Clustering method [44] | 3 | 2 | 2 | 0.6000 | 0.6000 | 0.6000 |

3D Forest [30] | 5 | 0 | 2 | 0.7143 | 1 | 0.8333 | |

Ours | 5 | 0 | 0 | 1 | 1 | 1 | |

Scene 3 | Clustering method [44] | 6 | 0 | 0 | 1 | 1 | 1 |

3D Forest [30] | 5 | 1 | 3 | 0.6250 | 0.8333 | 0.7143 | |

Ours | 6 | 0 | 0 | 1 | 1 | 1 | |

Scene 4 | Clustering method [44] | 11 | 3 | 8 | 0.5789 | 0.7857 | 0.6666 |

3D Forest [30] | 5 | 9 | 9 | 0.3571 | 0.3571 | 0.3571 | |

Ours | 13 | 1 | 0 | 1 | 0.9286 | 0.9630 | |

Scene 5 | Clustering method [44] | 12 | 8 | 8 | 0.6000 | 0.6000 | 0.6000 |

3D Forest [30] | 12 | 8 | 8 | 0.6000 | 0.6000 | 0.6000 | |

Ours | 20 | 0 | 0 | 0.6000 | 1 | 1 | |

Average | Clustering method [44] | - | - | - | 0.6947 | 0.7464 | 0.7167 |

3D Forest [30] | - | - | - | 0.5741 | 0.7976 | 0.6262 | |

Ours | - | - | - | 0.9000 | 0.9822 | 0.9908 |

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## Share and Cite

**MDPI and ACS Style**

Ning, X.; Ma, Y.; Hou, Y.; Lv, Z.; Jin, H.; Wang, Z.; Wang, Y.
Trunk-Constrained and Tree Structure Analysis Method for Individual Tree Extraction from Scanned Outdoor Scenes. *Remote Sens.* **2023**, *15*, 1567.
https://doi.org/10.3390/rs15061567

**AMA Style**

Ning X, Ma Y, Hou Y, Lv Z, Jin H, Wang Z, Wang Y.
Trunk-Constrained and Tree Structure Analysis Method for Individual Tree Extraction from Scanned Outdoor Scenes. *Remote Sensing*. 2023; 15(6):1567.
https://doi.org/10.3390/rs15061567

**Chicago/Turabian Style**

Ning, Xiaojuan, Yishu Ma, Yuanyuan Hou, Zhiyong Lv, Haiyan Jin, Zengbo Wang, and Yinghui Wang.
2023. "Trunk-Constrained and Tree Structure Analysis Method for Individual Tree Extraction from Scanned Outdoor Scenes" *Remote Sensing* 15, no. 6: 1567.
https://doi.org/10.3390/rs15061567