# Analysis of Parameters for the Accurate and Fast Estimation of Tree Diameter at Breast Height Based on Simulated Point Cloud

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. In-Situ TLS and Simulation Data

#### 2.2. DBH Model Construction

- (a)
- Each trunk was a cylinder that was perpendicular to the horizontal ground.
- (b)
- The virtual TLS scanner was placed at a height of 1.3 m, which is the exact height where the breast diameter was measured.
- (c)
- The position of the virtual TLS scanner was the origin (0, 0, 0) of the local coordinate system.

#### 2.3. DBH Model Simulations

- The range of DBH values was 0.1 m $\sim $ 0.4 m. The diameter of a slice was randomly chosen from this range.
- The distance between the scanner and the real center of a slice was a random value in the range of 0.1 m $\sim $ 30 m.
- The thickness of the slices was 0.1 m.

#### 2.4. DBH Model Estimations

#### 2.5. Accuracy Assessment

## 3. Results

#### 3.1. Performances of the Two Circle Fitting Methods

#### 3.2. Impacts of the Error Parameters

#### 3.3. Impacts of the Angular Step Widths

#### 3.4. Impacts of the Slice Parameters

## 4. Discussion

#### 4.1. Circle Fitting Methods

#### 4.2. Error Parameters

#### 4.3. Scanning Parameters

#### 4.4. Slice Parameters

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Illustration of two simulated slices. (

**a**) Slice point cloud without errors. (

**b**) Slice point cloud with the range and angular errors.

**Figure 4.**Estimated results of the Levenberg–Marquardt (LM) method and the Taubin method when the angular errors in the vertical and horizontal directions were 0 degrees, and the angular step widths in the vertical and horizontal directions were 0.02 degrees. The results are shown when the range error was (

**a**) 0.02 m, (

**b**) 0.05 m, (

**c**) 0.10 m and (

**d**) 0.15 m.

**Figure 5.**Time cost of the LM method and Taubin method when the angular errors in the vertical and horizontal directions were 0 degrees, and the angular step widths in the vertical and horizontal directions were 0.02 degrees. The results are shown when the range error was (

**a**) 0.02 m, (

**b**) 0.05 m, (

**c**) 0.10 m and (

**d**) 0.15 m.

**Figure 6.**Illustration of the impacts of the range error on the relative error of the DBH estimation when the angular errors in the vertical and horizontal directions were 0 degrees, and the range error was set as 0.02 m, 0.05 m, 0.10 m, and 0.15 m in turn. The results are shown when the angular step widths in the vertical and horizontal directions were (

**a**) 0.02 degrees, (

**b**) 0.05 degrees, (

**c**) 0.10 degrees and (

**d**) 0.15 degrees.

**Figure 7.**Illustration of the impacts of the vertical angular error on the relative error of the DBH estimation when the range error was 0 m, the angular error in the horizontal direction was 0 degrees, the angular step widths in the vertical and horizontal directions were 0.10 degrees, and the angular error in the vertical direction was set as 0.02 degrees, 0.05 degrees, 0.10 degrees, and 0.15 degrees in turn. (

**a**) Plot on regular scale. (

**b**) Regional magnification of plot (

**a**).

**Figure 8.**Illustration of the impacts of the horizontal angular error on the relative error of the DBH estimation when the range error was 0 m, the angular error in the vertical direction was 0 degrees, and the angular error in the horizontal direction was set as 0.02 degrees, 0.05 degrees, 0.10 degrees, and 0.15 degrees in turn. The results are shown when the angular step widths in the vertical and horizontal directions were (

**a**) 0.02 degrees, (

**b**) 0.05 degrees, (

**c**) 0.10 degrees and (

**d**) 0.15 degrees.

**Figure 9.**Illustration of the impacts of the angular step widths on the relative error of the DBH estimation when the angular errors in the vertical and horizontal directions were 0 degrees, and the angular step widths in the vertical and horizontal directions were set as 0.02 degrees, 0.05 degrees, 0.10 degrees, and 0.15 degrees in turn. The results are shown when the range error was (

**a**) 0.02 m, (

**b**) 0.05 m, (

**c**) 0.08 m and (

**d**) 0.16 m.

**Figure 10.**Illustration of the impacts of distance on the relative error of the DBH estimation when the angular errors in the vertical and horizontal directions were 0 degrees, and the angular step widths in the vertical and horizontal directions were 0.02 degrees. The results are shown when the range error was (

**a**) 0.02 m, (

**b**) 0.05 m, (

**c**) 0.10 m and (

**d**) 0.15 m.

**Figure 11.**Illustration of the impacts of thickness on the relative error of the DBH estimation when the range error was 0.02 m, the angular error in the vertical and horizontal directions were 0 degrees. The results are shown when the angular step widths in the vertical and horizontal directions were (

**a**) 0.02 degrees, (

**b**) 0.05 degrees, (

**c**) 0.10 degrees and (

**d**) 0.15 degrees.

**Figure 12.**Illustration of the impacts of the real DBH on the relative error of the DBH estimation when the range error was 0.02 m, the angular error in the vertical and horizontal directions were 0 degrees. The results are shown when the angular step widths in the vertical and horizontal directions were (

**a**) 0.02 degrees, (

**b**) 0.05 degrees, (

**c**) 0.10 degrees and (

**d**) 0.15 degrees.

**Figure 13.**Illustration of the relationship between the number of points and the relative error of the DBH estimation when the range error was 0.02 m, the angular error in the vertical and horizontal directions were 0 degrees. The results are shown when the angular step widths in the vertical and horizontal directions were (

**a**) 0.02 degrees, (

**b**) 0.05 degrees, (

**c**) 0.10 degrees and (

**d**) 0.15 degrees.

**Figure 14.**Illustration of the relationship between the scanning angular width and the relative error of the DBH estimation when the range error was 0.02 m, the angular error in the vertical and horizontal directions were 0 degrees. The results are shown when the angular step widths in the vertical and horizontal directions were (

**a**) 0.02 degrees, (

**b**) 0.05 degrees, (

**c**) 0.10 degrees and (

**d**) 0.15 degrees.

Group No. | ${\mathit{\sigma}}_{\mathit{r}}\text{}\left(\mathbf{m}\right)$ | ${\mathit{\sigma}}_{\mathit{\theta}}\text{}\left(\mathbf{deg}\right)$ | ${\mathit{\sigma}}_{\mathit{\phi}}\text{}\left(\mathbf{deg}\right)$ | ${\mathit{\theta}}_{\mathit{s}}\&{\mathit{\phi}}_{\mathit{s}}\text{}\left(\mathbf{deg}\right)$ | Purposes |
---|---|---|---|---|---|

1 | 0.02, 0.05, 0.10, 0.15 | 0 | 0 | 0.02 | Circle fitting methods, distance |

2 | 0.02, 0.05, 0.10, 0.15 | 0 | 0 | 0.02, 0.05, 0.10, 0.15 | Range error, angular step width |

3 | 0 | 0.02, 0.05, 0.10, 0.15 | 0 | 0.10 | Vertical angular errors |

4 | 0 | 0 | 0.02, 0.05, 0.10, 0.15 | 0.02, 0.05, 0.10, 0.15 | Horizontal angular errors |

5 | 0.02 | 0 | 0 | 0.02, 0.05, 0.10, 0.15 | Number of points, real diameters at breast height (DBH), scanning angular width |

6 | 0.02 | 0 | 0 | 0.02, 0.05, 0.10, 0.15 | Thickness |

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## Share and Cite

**MDPI and ACS Style**

Wang, P.; Gan, X.; Zhang, Q.; Bu, G.; Li, L.; Xu, X.; Li, Y.; Liu, Z.; Xiao, X. Analysis of Parameters for the Accurate and Fast Estimation of Tree Diameter at Breast Height Based on Simulated Point Cloud. *Remote Sens.* **2019**, *11*, 2707.
https://doi.org/10.3390/rs11222707

**AMA Style**

Wang P, Gan X, Zhang Q, Bu G, Li L, Xu X, Li Y, Liu Z, Xiao X. Analysis of Parameters for the Accurate and Fast Estimation of Tree Diameter at Breast Height Based on Simulated Point Cloud. *Remote Sensing*. 2019; 11(22):2707.
https://doi.org/10.3390/rs11222707

**Chicago/Turabian Style**

Wang, Pei, Xiaozheng Gan, Qing Zhang, Guochao Bu, Li Li, Xiuxian Xu, Yaxin Li, Zichu Liu, and Xiangming Xiao. 2019. "Analysis of Parameters for the Accurate and Fast Estimation of Tree Diameter at Breast Height Based on Simulated Point Cloud" *Remote Sensing* 11, no. 22: 2707.
https://doi.org/10.3390/rs11222707