# Integrating Real Tree Skeleton Reconstruction Based on Partial Computational Virtual Measurement (CVM) with Actual Forest Scenario Rendering: A Solid Step Forward for the Realization of the Digital Twins of Trees and Forests

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## Abstract

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## 1. Introduction

#### 1.1. Form Tree Models to Digital Twin of Forests

#### 1.2. A Step Forward for the Realization of the Digital Twin of Trees

## 2. Material and Methods

#### 2.1. Study Area and Field Measurements

#### 2.2. Data Preprocessing

#### 2.2.1. Conventional Data Preprocessing

#### 2.2.2. Amelioration of the Quality of the Wood Points with Gap Filling

#### 2.3. Analysis of Physical Scenario of Diameter Tapes

#### 2.4. Design of Physical Scenario of Virtual Diameter Tape (VDT)

#### 2.5. VDT Implementation

Algorithm 1: VDT measurement process |

while (termination_condiation is false) |

VDT_Move(direction) |

SaveFootprint(); |

if CollisionDetected(); |

direction.new(random); |

end |

end |

End |

#### 2.6. Retrieval of DBH from Raw VDT Measurement Outcome

#### 2.7. 3D Tree Skeleton Reconstruction and Actual Forest Scenario Rendering

#### 2.8. Reference Methods

## 3. Results and Discussion

#### 3.1. VDT Measurements on Ideal Point Clouds

#### 3.2. VDT Measurements on Point Clouds of Medium Completeness

#### 3.3. VDT Measurements on Point Clouds of Low Completeness

^{2}than the circle fitting (Hough) algorithm, as a representative of mathematical methods, with a decrement (approximately 0.27 cm in the ideal point cloud and 0.26 cm in point clouds of medium completeness) in RMSE for our method. Due to the diversity of forests and ecological environments, circle fitting algorithms always greatly depend on the parameter tuning operations and iteratively seeking optimized solutions. Conversely, the VDT method did not make these demands. Free from stem shape variations, VDT has the capability to measure any shape of branch cross-sections. We expect that the proposed method has strengthened universality with improved contour portrayal accuracy. This was also the initial ideological connotation when we conceived the CVM theory.

#### 3.4. Rubber Tree Model Reconstruction Based on the Derived Growth Parameters

#### 3.5. Sources of Error in CVM Procedure

^{0}to 10

^{−13}(in different physical units, e.g., N·m·s and meter). Therefore, with an appropriate setting in a physic engine, the simulation accuracy could be orders of magnitude higher than the error in the data collected by measuring instruments in reality. Under these circumstances, we believed that the error in the simulation of basic physical laws could be neglected.

#### 3.6. Forward for the Realization of the Digital Twin of Trees

#### 3.7. Contribution of Digital Twin Technology to Rubber Tree Management

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The study area and field measurements: (

**a**) schematic layout of rubber trees, scanning positions; (

**b**) point clouds of the five-year-old rubber trees—points in black refer to the classified ground points, points in brown refer to the classified stem/branches points, and points in green refer to the classified leaves points; (

**c**) a scan position in the field measurement using Leica ScanStation C10; (

**d**) locations of three sample plots; (

**e**) the scaffolding system of branches measurements.

**Figure 2.**Two sections in data preprocessing: (

**a**) conventional data preprocessing employed for LiDAR field scanning; (

**b**) data preprocessing for VDT measurement. In the figure, VDT refers to virtual diameter tape.

**Figure 3.**The workflow of the amelioration process: (

**a**) a stem disk; (

**b**) the demonstration of the recorded points (in purple) and the missing points (in white); (

**c**) the fitted circle (in red); (

**d**) partial enlargement of the boundary area between the recorded and missing points; (

**e**) using of buffer to generate the breakpoint, the red color point; (

**f**) enclosing the area between the recorded (purple) point and the breakpoint; (

**g**) finishing the synthetic ideal point cloud; (

**h**) applying VDT method, the VDT detector is in green; photo of stem disk: Freeimages.com/Artur Łuczka.

**Figure 4.**Mathematical processes for determining the optimal fitting circle in amelioration; (

**a**) example of non-ideal points; (

**b**) the determination of the long and short axes of the fitted ellipse; (

**c**) determination of the rotation angle of the fitted ellipse.

**Figure 5.**Comparison of physical scenarios between diameter tape (

**a**–

**d**) and virtual diameter tape (VDT) (

**e**–

**h**); (

**a**) a stem disk naturally divided space into the internal area and the external area; (

**b**) the diameter tape enclosed an area in space; (

**c**) the enclosed area decreased with the measurement processed; (

**d**) the termination condition of the diameter tape measurement process; (

**e**) point clouds as the boundary; (

**f**) a VDT detector was released in a distant and arbitrary area region in space; (

**g**) the movements of the VDT detector are denoted as green circles, which iteratively collide with the edge scanned points of each branch slice and bounce back to depict the actual edge of the branches; the positions of the VDT detector were represented using i, ii, iii, and i’; (

**h**) the theoretical accessed area of the VDT detector over time. Photo of stem disk: Freeimages.com/Artur Łuczka.

**Figure 6.**Retrieval of DBH from raw VDT measurement data: (

**a**) a raw VDT measurement outcome of a cross-section of trees; (

**b**) the line of perimeter and DBH were extracted using image segmentation.

**Figure 7.**The results of VDT measurement compared with reference methods. (

**a**) VDT measurement; (

**b**) cylinder fitting method; (

**c**) circle fitting method; (

**d**) a revised circle fitting method. In the figure, VDT refers to virtual diameter tape; R

^{2}refers to the coefficient of determination; RMSE refers to the root mean square error.

**Figure 8.**The results of VDT estimations of stem diameter at an arbitrary height along a tree bole: (

**a**) VDT measurement; (

**b**) cylinder fitting (Hough) method. In the figure, VDT refers to virtual diameter tape; R

^{2}refers to the coefficient of determination; RMSE refers to the root mean square error.

**Figure 9.**The results of estimations for the base diameter of the first order branches of three sample plots. (

**a**) VDT measurement of a 5-year-old sample plot; (

**b**) cylinder fitting (Hough) processing of a 5-year-old sample plot; (

**c**) VDT measurement of a 10-year-old sample plot; (

**d**) cylinder fitting (Hough) processing of a 10-year-old sample plot; (

**e**) VDT measurement of a 20-year-old sample plot; (

**f**) cylinder fitting (Hough) processing of a 20-year-old sample plot. In the figure, VDT refers to virtual diameter tape; R

^{2}refers to the coefficient of determination; RMSE refers to the root mean square error.

**Figure 10.**The modeling results of rubber tree skeletons of different ages based on the scanned points. (

**a**) Original scanned points of rubber tree branches and (

**b**) the reconstructed rubber tree models of 5 years old. (

**c**,

**d**) The equivalent figures for rubber trees of 10 years old. (

**e**,

**f**) The equivalent figures for rubber trees of 10 years old. (

**g**) Detailed images of the resulting tree trunks and first order branches. (

**h**) Overview of rubber tree models of various years.

**Figure 11.**The modeling results with twilight as the background. (

**a**) Point clouds of 5-year-old rubber trees; (

**b**) branching models of 5-year-old rubber trees; (

**c**) models of 5-year-old-rubber trees with branches and leaves; (

**d**) overview of branching models of rubber trees; (

**e**) overview of branching models of rubber trees with branches and leaves.

**Figure 12.**The random error in VDT measurement. (

**a**) The same VDT detector colliding with points of different gaps; (

**b**) the accessed area after collision; (

**c**) the large VDT detector colliding with smooth and coarse points; (

**d**) the missing area marked using red. In the figure, purple points refer to the points in a point cloud; big circles refer to VDT detectors; raster refers to a data storage architecture, the matrix.

Name | Virtual Diameter Tape | Circle Fitting (Hough) |
---|---|---|

Methodology | CVM | Mathematical modeling |

Prior knowledge | No need | Cross-section area is round-shaped |

Adoption of various shapes | Yes | No |

Role of data | Objects in virtual space | Elements to be processed |

Processing logic | Simulation of physical mechanism of diameter tape | Making prediction using presets |

Raw result | Cross-section area | Model of cross-section area |

Number of result (s) | Infinite | 1 |

Final result | Perimeter (DBH) | Perimeter (DBH) |

Need for validation | No (using ideal point clouds)/Yes | Yes |

R^{2} (in IDL ^{1}/Mid ^{2}/Low ^{3}) | 0.97/0.96/0.88 ^{4} | 0.94/0.94/0.85 ^{4} |

RMSE(cm) (in IDL ^{1}/Mid ^{2}/Low ^{3}) | 1.02/1.30/0.56 ^{4} | 1.29/1.56/0.55 ^{4} |

^{1}IDL refers to the inputted point clouds are the ideal point cloud;

^{2}Mid refers to the inputted point clouds are the point cloud of medium completeness;

^{3}Low refers to the inputted point clouds are the point cloud of low completeness;

^{4}the mean value from nine trees in three sample plots; CVM refers to computational virtual measurement; R

^{2}refers to determination coefficient; RMSE refers to root-mean-square deviation; DBH refers to diameter at breast height.

Age of Trees | Tree Height/m | Crown Width/m | Crown Volumes/m^{3} | Average Length of Primary Branches of Rubber Tree/m | Average Included Angles between Stem and Branches/° | Tilt Angles of Stem/° |
---|---|---|---|---|---|---|

Five years | 7.46 ± 0.61 | 3.02 ± 0.71 (N-S) 3.09 ± 0.97 (E-W) | 69.63 | 1.840 ± 0.44 | 39.53 ± 4.84 | 3.92 ± 3.33 |

Ten years | 9.18 ± 0.48 | 2.89 ± 0.95 (N-S) 4.21 ± 1.6 (E-W) | 85.39 | 2.49 ± 0.68 | 41.11 ± 10.66 | 7.86 ± 7.67 |

Twenty years | 14.47 ± 3.99 | 2.66 ± 1.55 (N-S) 5.22 ± 2.59 (E-W) | 146.52 | 2.57 ± 2.33 | 45.91 ± 18.75 | 14.22 ± 13.9 |

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## Share and Cite

**MDPI and ACS Style**

Wang, Z.; Lu, X.; An, F.; Zhou, L.; Wang, X.; Wang, Z.; Zhang, H.; Yun, T.
Integrating Real Tree Skeleton Reconstruction Based on Partial Computational Virtual Measurement (CVM) with Actual Forest Scenario Rendering: A Solid Step Forward for the Realization of the Digital Twins of Trees and Forests. *Remote Sens.* **2022**, *14*, 6041.
https://doi.org/10.3390/rs14236041

**AMA Style**

Wang Z, Lu X, An F, Zhou L, Wang X, Wang Z, Zhang H, Yun T.
Integrating Real Tree Skeleton Reconstruction Based on Partial Computational Virtual Measurement (CVM) with Actual Forest Scenario Rendering: A Solid Step Forward for the Realization of the Digital Twins of Trees and Forests. *Remote Sensing*. 2022; 14(23):6041.
https://doi.org/10.3390/rs14236041

**Chicago/Turabian Style**

Wang, Zhichao, Xin Lu, Feng An, Lijun Zhou, Xiangjun Wang, Zhihao Wang, Huaiqing Zhang, and Ting Yun.
2022. "Integrating Real Tree Skeleton Reconstruction Based on Partial Computational Virtual Measurement (CVM) with Actual Forest Scenario Rendering: A Solid Step Forward for the Realization of the Digital Twins of Trees and Forests" *Remote Sensing* 14, no. 23: 6041.
https://doi.org/10.3390/rs14236041