# An Automated Hierarchical Approach for Three-Dimensional Segmentation of Single Trees Using UAV LiDAR Data

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## Abstract

**:**

## 1. Introduction

^{2}values ranging from 0.49–0.61 for key response variables such as canopy cover, stand height, basal area, and stem volume. Allouis et al. [3] estimated stem volume and aboveground biomass from the single-tree metrics derived from full-waveform LiDAR data by using regression models and improved the accuracy of aboveground biomass estimates. Matsuki et al. [4] obtained a tree species classification accuracy of 82% by integrating spectral features obtained from hyperspectral data and tree-crown features derived from LiDAR data with a support vector machine classifier. However, it is still difficult to detect single trees automatically from airborne LiDAR data due to the various shapes of trees and their periodic changes with the seasons, especially to segment trees with complex and heterogeneous crowns.

## 2. Test UAV LiDAR Data

^{2}on 24–26 July 2017, by a VLP16 (Velodyne 16E) laser scanner system produced by Velodyne LiDAR. The full specifications of VLP16 are listed in Table 2. Note that, in this study, the LiDAR data accuracy, which usually requires being evaluated based on the ground control points measured by a total station and creating a reference dataset [36,37], was unavailable; therefore, the data accuracy was directly reflected by the system’s ranging accuracy.

^{2}, respectively. Within each plot, the location and the diameter at breast height (DBH) of each tree were recorded.

## 3. Methodology

#### 3.1. Data Pre-processing

_{RI}), steep slope fit factor (F

_{ST}), grid resolution (F

_{GR}), and time step (F

_{DT}). The first two parameters are the key parameters, which control the filtering results, and vary with terrain types. The last two parameters are usually fix-valued and universally applicable to all LiDAR datasets. The detailed description of the CSF algorithm can be found in [38]. The ground points were then interpolated into a digital terrain model (DTM) by linear interpolation. Afterward, to reduce the influence of undulating terrain on single-tree recognition and tree height extraction, the non-ground points were normalized according to the produced DTM with a spatial resolution of 0.5 m. Moreover, low-rise shrubs in the forests were removed by a given height threshold (Γ

_{h}).

#### 3.2. Voxel-Based Mean Shift

_{s}). The voxel size depends on the point density of the UAV LiDAR points to be processed. We statistically counted the number of points and determined the center of all the points for each voxel. The voxelization for UAV LiDAR points contributes to improving the computational efficiency and maintaining feature details of objects, which has been widely used for point cloud registration, surface reconstruction, shape recognition, etc.

_{c}= (x

_{c}, y

_{c}, z

_{c}), in the non-ground voxels and obtaining all its neighboring voxels, X

_{i}= (x

_{i}, y

_{i}, z

_{i}) (i = 1, 2, 3, …, n), where n is the number of voxels within a given radius, R. Next, we calculated the offset vector by summing the vectors between the voxel and its neighboring voxels. To converge voxels within each crown toward the corresponding crown apex, a 3D space was separated into horizontal and vertical directions. The horizontal kernel was defined for searching local density maxima, and the vertical one for local height maxima [29]. Therefore, the offset vector of voxel X

_{i}to voxel X

_{c}is defined by:

_{c}

^{s}and x

_{c}

^{r}are the horizontal and vertical vector components of voxel X

_{c}, respectively. x

_{i}

^{s}and x

_{i}

^{r}are the horizontal and vertical vector components of voxel X

_{i}, respectively. The horizontal and vertical bandwidths (h

^{s}, h

^{r}) represent the width and depth of a canopy.

^{s}is the horizontal kernel function that follows a Gaussian function:

^{r}, is specially-designed for assigning a larger weight to the highest voxel:

_{c}

^{r}, x

_{i}

^{r}) represents a mask of foreground object; dist(x

_{c}

^{r}, x

_{i}

^{r}) is the distance between X

_{i}and the boundary of the mask. They are defined by,

_{c}moves along the offset vector until it reaches the density and height maxima and labels all voxels visited during this process as the same cluster. The proposed voxel-based mean shift method repeats the above steps until all voxels in the non-ground points are visited and labeled into specific clusters. Afterward, the nearby clusters, whose distances are less than a given distance threshold, Γ

_{d}, are merged together. In the study, to increase the similarity of all voxels belonging to a single tree, the proposed method compresses (m, a multiple of height compression) the point height to improve the clustering results.

_{1}and d

_{2}). According to the ratio of d

_{1}to d

_{2}, the clusters will be classified into two groups: well-detected and under-segmentation clusters. Here, we defined that a well-detected cluster is a single tree with circular-shaped canopy, while an under-segmentation cluster is an irregularly-shaped one containing more than two trees. Thus, if the ratio of d

_{1}to d

_{2}was close to 1, the cluster was labeled as well-detected (i.e., a single tree), otherwise the cluster was labeled as under-segmentation.

#### 3.3. Improved Normalized Cut Single-Tree Segmentation

#### 3.3.1. Normalized Cut

**w**

_{ij}as the similarity between a pair of nodes {i,j} ϵ V. It is computed as follows:

_{ij}

^{XY}, D

_{ij}

^{Z}, and D

_{ij}

^{S}represent the horizontal, vertical, and shortest distances, respectively, between nodes i and j. σ

^{XY}, ${\sigma}^{XY},{\sigma}^{Z},$ σ

^{Z}, and σ

^{S}are coefficients, set to be 0.05-times the maximum of D

_{ij}

^{XY}, D

_{ij}

^{Z}, and D

_{ij}

^{S}, for controlling the sensitivity of the impact factors, respectively. Γ

_{R}represents the maximum horizontal distance threshold between nodes.

**w**

_{ij}= 0, if the horizontal distance between nodes {i,j} exceed the threshold, Γ

_{R}. NCut aims to divide the graph G into two disjoint voxel groups A and B by maximizing the similarity within each voxel group and minimizing the similarity between two voxel groups A and B. The corresponding cost function is as follows:

**W**is an n × n weighting matrix representing the weights between all nodes of graph G.

**D**is an n × n diagonal matrix, and

_{1}, to Equation (8) corresponds to the second smallest eigenvalue, λ

_{1}[23].

#### 3.3.2. Improved NCut

_{s}. The profiles generated both in the x- and y-direction help reduce the occlusions. For each profile in the x- and y-direction, respectively, we calculate the maximum height for generating shape curves by cubic spline data interpolation. Figure 5 shows two clusters and their corresponding shape curves. Figure 5a,d show two clusters in the form of 3D points, Figure 5b,e their corresponding shape curves in the x–direction and Figure 5c,f the shape curves in the y-direction. The peaks of the generated shape curves both in the x- and y-direction are found to determine tree apices, which means the number of peaks in the shape curves determines the number of potential single trees to be segmented in the under-segmentation cluster.

## 4. Experimental Results and Discussion

_{RI}, F

_{ST}, F

_{GR}, F

_{DT}, and Γ

_{h}—were used. F

_{RI}represented the terrain type and was set to three according to the flat terrain. F

_{ST}decided whether the post-processing of steep slopes was required. F

_{GR}and F

_{DT}were respectively set to 0.5 and 0.65, which were adapted to most of the scenes. F

_{GR}represented the horizontal distance between two neighboring points, and F

_{DT}controlled the displacement of points from gravity during each iteration. Low-rise shrub height threshold, Γ

_{h}, was set to 5.0 m according to the tree height in the test site. In the voxel-based mean shift algorithm, six parameters—V

_{s}, m, R, Γ

_{d}, h

_{s}, and h

_{r}—were used to obtain a set of clusters. The voxel size, V

_{s}, was set according to the point density. To increase the similarity in vertical distance, m was set to four. The search radius, R, and the minimum distance between clusters, Γ

_{d}, were both set to 2.0 m according to the average width of canopies in the study. h

_{s}and h

_{r}were two bandwidths of the horizontal and vertical kernels, which represented the range where the local density and local maxima existed. h

_{s}and h

_{r}were set to 1.5 m and 5.0 m, respectively, according to the average width and depth of the tree canopies in the test site. In the improved NCut-based single-tree segmentation stage, Γ

_{s}, the profile size in the x- and y-direction was set to 0.5 m based on the defined voxel size. The maximum horizontal distance threshold between the cluster nodes, Γ

_{R}, was empirically set to 4.5 m according to the average width of tree canopies.

_{cor}), completeness (E

_{cpt}), and F-score (E

_{f}). E

_{cor}indicates what percentage of the segmented single trees were valid, whereas E

_{cpt}describes how complete the detected single trees were. E

_{cor}is defined as E

_{cor}= C

_{p}/E

_{p}, and E

_{cpt}is expressed as E

_{cpt}= C

_{p}/Rf, where C

_{p}denotes the number of real single trees, Rf is the number of single trees in the reference data, and E

_{p}represents the number of single trees segmented by our method. E

_{f}evaluates the overall accuracy, which is defined as:

#### 4.1. Overall Performance

_{f}value of 0.89, respectively. For Metasequoia (Plots 1, 2, and 3), the E

_{cor}values were greater than 0.96, the E

_{cpt}values were higher than 0.88, and the E

_{f}values ranged from 0.93–0.94. The quantitative results indicate that the proposed method was greatly suitable for detecting the deciduous Metasequoia with the cone-shaped canopies, sparse branches, and leaves. For Poplar (Plots 4, 5, 6, and 7) with the irregularly-shaped canopies and staggered-like stems, the values of E

_{cor}, E

_{cpt}, and E

_{f}ranged from 0.81–0.9, slightly lower than those of the Metasequoia trees. Overall, the experiments indicate that our approach was robust to different tree species.

_{cor}values were achieved for Plots 2 and 3 with the highest forest densities of 0.060 trees/m

^{2}when compared to Plot 1 with a forest density of 0.032 trees/m

^{2}. On the contrary, the E

_{f}values of Plots 2 and 3 were slightly lower than that of Plot 1. For Poplar, Plots 4–6 with little differences in forest density achieved E

_{f}values ranging from 0.83–0.87. Compared to Plot 4 with the lowest forest density of 0.020, an improvement of the E

_{cor}, E

_{cpt}, and E

_{f}values of Plot 7 was achieved by 0.05, 0.02, and 0.03, respectively. This indicates that our approach was capable of processing dense forests with overlapped canopies.

#### 4.2. Comparative Tests

_{f}were 0.98, 0.92, and 0.92, respectively. A few trees were over-segmented or missed. The average E

_{f}value of the marker-controlled watershed segmentation algorithm was slightly lower than that of our approach. This is because the watershed segmentation algorithm was sensitive to noise, which leads to staggered stems probably being misclassified into tree seed points. Moreover, the watershed segmentation algorithm detects single trees from the 2D CHM data interpolated from 3D points, which means data interpolation might decrease the accuracies of canopy segmentation and cause the unreliability of delineating crown diameters. For the Poplar trees (Plots 4, 5, 6, and 7), Figure 9a,b shows a close segmentation example of Plot 5 by the watershed segmentation and our proposed approach. Green dots and black circles represent tree locations and canopy radii derived from watershed segmentation, respectively, and black crosses represent reference tree locations. As seen in Figure 9a, the single trees detected by local maxima in CHM data were over-segmented, which was mainly caused by staggered stems, and tree canopies were still overlapped with each other, indicating that the segmentation results were unsatisfactory. Quantitatively, as seen in Table 6, the E

_{cor}values greatly ranged from 0.75–0.91, the E

_{cpt}values changed from 0.83–0.90, and the values of E

_{f}for the four Poplar plots only attained 0.79, 0.80, 0.85, and 0.84, respectively. This is because the local maxima detection in 2D CHM data, which only contain height difference information, is unreliable for dealing with the trees with irregularly-shaped canopies and staggered-like branches, and thus, many Poplar trees were over-segmented and missed.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

UAV | Unmanned Aerial Vehicle |

NCut | Normalized cut segmentation |

LiDAR | Light detection and ranging |

2D | Two-dimensional |

3D | Three-dimensional |

CHM | Canopy height model |

CSF | Cloth simulation filtering |

DTM | Digital terrain model |

DBH | Diameter at breast height |

VLP16 | Velodyne 16E laser scanning system |

GPS | Global positioning system |

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**Figure 5.**Two-cluster examples and their corresponding shape curves both in the x- and y-direction: (

**a**,

**d**) two-cluster samples, (

**b**,

**e**) their shape curves in the x-direction, and (

**c**,

**f**) their shape curves in the y-direction.

**Figure 6.**An example of the improved NCut segmentation algorithm: (

**a**) a cluster containing multiple overlapped trees and (

**b**) improved NCut segmentation results (different colors representing different single trees).

**Figure 7.**Results of the voxel-based mean shift method for seven plots: (

**a**) Plot 1, (

**b**) Plot 2, (

**c**) Plot 3, (

**d**) Plot 4, (

**e**) Plot 5, (

**f**) Plot 6, and (

**g**) Plot 7.

**Figure 8.**The segmentation results of marker-controlled watershed segmentation for seven plots: (

**a**) Plot 1, (

**b**) Plot 2, (

**c**) Plot 3, (

**d**) Plot 4, (

**e**) Plot 5, (

**f**) Plot 6, and (

**g**) Plot 7.

**Figure 9.**An example of segmentation results for Plot 5: (

**a**) the watershed segmentation and (

**b**) our proposed approach.

Parameters | Value |
---|---|

Weight of loadings | 7 kg |

Take-off-weight | 17 kg |

Diagonal wheelbase | 1280 mm |

Maximum flying time | 32 min |

Maximum flying distance | 10 km |

Flying height | 86 m above ground in this research |

Flying speed | 3.6 m/s in this research |

Measurement range of gyroscope | ±400 degrees/s |

Gyroscope zero drift | 0.5 degrees/h |

Measurement range of accelerometer | ±10 g |

Measurement deviation of accelerometer | 0.05 mg |

Parameters | Value |
---|---|

Principle | Pulse ranging |

Laser wavelength | 905 nm |

Measurement distance range | 100 m |

Vertical scan angle | −15–+15 degrees |

Laser scan frequency | 16 lines/s |

Divergence | 3 mrad |

Swath overlap | 100% |

Amplitude | 500 m/s^{2} |

Vibration frequency | 5–2000 Hz, 3 Grms ^{1} |

Weight | 0.83 kg |

Ranging accuracy | <10 cm |

^{1}Grms is a unit for representing root mean square acceleration.

Parameters | Value |
---|---|

Weight | 5.8 kg |

Working time | 2.5 h each battery |

Laser scanning system | Velodyne 16E |

Measurement distance range | 100 m |

Vertical field angle | −15–+15 degrees |

Data accuracy | <5 cm |

Stage | Parameter | Definition | Value |
---|---|---|---|

Data preprocessing | Γ_{h} | Low-rise shrubs height threshold | 5.0 m |

F_{RI} | Terrain types | 3 | |

F_{ST} | Steep slope fit factor | False | |

F_{GR} | Grid resolution | 0.5 | |

F_{DT} | Time step | 0.65 | |

Voxel-based mean shift | V_{s} | Voxel size | 0.2 m |

m | Height compression | 4 | |

R | Search radius | 2.0 m | |

h^{s} | Horizontal bandwidth | 1.5 m | |

h^{r} | Vertical bandwidth | 5.0 m | |

Γ_{d} | Minimum distance between clusters | 2.0 m | |

Improved NCut segmentation | Γ_{s} | Profile size in the x- and y-direction | 0.5 m |

Γ_{R} | Maximum horizontal distance | 4.5 m |

Forest Density (trees/m^{2}) | E_{cor} (%) | E_{cpt} (%) | E_{f} | |
---|---|---|---|---|

Plot 1 | 0.032 | 0.96 | 0.93 | 0.94 |

Plot 2 | 0.060 | 0.98 | 0.93 | 0.93 |

Plot 3 | 0.060 | 0.98 | 0.88 | 0.93 |

Plot 4 | 0.020 | 0.84 | 0.88 | 0.86 |

Plot 5 | 0.022 | 0.89 | 0.85 | 0.87 |

Plot 6 | 0.023 | 0.81 | 0.85 | 0.83 |

Plot 7 | 0.047 | 0.89 | 0.9 | 0.89 |

Average accuracy | 0.90 | 0.88 | 0.89 |

^{1}E

_{cor}indicates what percentage of the segmented single trees are valid; E

_{cpt}describes how complete the detected single trees are; and E

_{f}evaluates the overall accuracy.

Forest Density (trees/m^{2}) | E_{cor} (%) | E_{cpt} (%) | E_{f} | |
---|---|---|---|---|

Plot 1 | 0.032 | 0.96 | 1.00 | 0.98 |

Plot 2 | 0.060 | 0.92 | 0.92 | 0.92 |

Plot 3 | 0.060 | 0.94 | 0.91 | 0.92 |

Plot 4 | 0.020 | 0.75 | 0.83 | 0.79 |

Plot 5 | 0.022 | 0.75 | 0.90 | 0.80 |

Plot 6 | 0.023 | 0.90 | 0.82 | 0.85 |

Plot 7 | 0.047 | 0.91 | 0.81 | 0.84 |

Average accuracy | 0.87 | 0.88 | 0.87 |

^{1}E

_{cor}indicates what percentage of the segmented single trees are valid; E

_{cpt}describes how complete the detected single trees are; and E

_{f}evaluates the overall accuracy.

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**MDPI and ACS Style**

Yan, W.; Guan, H.; Cao, L.; Yu, Y.; Gao, S.; Lu, J.
An Automated Hierarchical Approach for Three-Dimensional Segmentation of Single Trees Using UAV LiDAR Data. *Remote Sens.* **2018**, *10*, 1999.
https://doi.org/10.3390/rs10121999

**AMA Style**

Yan W, Guan H, Cao L, Yu Y, Gao S, Lu J.
An Automated Hierarchical Approach for Three-Dimensional Segmentation of Single Trees Using UAV LiDAR Data. *Remote Sensing*. 2018; 10(12):1999.
https://doi.org/10.3390/rs10121999

**Chicago/Turabian Style**

Yan, Wanqian, Haiyan Guan, Lin Cao, Yongtao Yu, Sha Gao, and JianYong Lu.
2018. "An Automated Hierarchical Approach for Three-Dimensional Segmentation of Single Trees Using UAV LiDAR Data" *Remote Sensing* 10, no. 12: 1999.
https://doi.org/10.3390/rs10121999