# Identification of Linear Vegetation Elements in a Rural Landscape Using LiDAR Point Clouds

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}resolution through spatial modeling of 200,000 ground observations [5]. However, these maps strongly depend on spatial interpolation methods as well as regional environmental and socio-economic variation and therefore contain a considerable amount of uncertainty in the exact spatial distribution of linear vegetation elements in the landscape. High-resolution measurements of 2D and 3D ecosystem structures derived from cross-national remote sensing datasets are therefore needed to identify and map linear vegetation elements across broad spatial extents [18].

## 2. Data and study area

#### 2.1. LiDAR and Orthophoto Data

^{2}and includes multiple discrete return values (which can result into effective point densities between 10 and 20 points/m

^{2}) as well as intensity data. The dataset is collected in the first quarter of each year when deciduous vegetation is leafless [25]. Nevertheless, the return signal is sufficiently strong to retrieve a useful scan of the vegetation cover. Freely available very high resolution (VHR) true color orthophotos [24] with a resolution of 25 cm were consulted for location purposes.

#### 2.2. Study Area

## 3. Method

#### 3.1. Feature Extraction

#### 3.1.1. Point-Based Features

_{1}, p

_{2}, …, p

_{n}} $\left(\in {R}^{\mathbb{3}}\right)$, where each point p

_{i}has x, y and z coordinates. In addition, an intensity value (I), a return number (R), and a number of returns (R

_{t}) of the returned signal are stored. We used R

_{t}as well as the normalized return number R

_{n}as echo-based features (Table 1). The R

_{n}highlights vegetation, since vegetation can be characterized by multiple returns [35]. Since the available LiDAR data were available without the information such as flying height, plane trajectory data and sensor-related parameters, required to do a radiometric correction of the intensity data, we omitted this feature for the classification [40].

#### 3.1.2. Neighborhood-Based Features

_{i}of points {q

_{1}, q

_{2}, …, q

_{k}} was defined for each point p

_{i}, where q

_{1}= p

_{i}, by using the k-nearest neighbors method with k = 10 points. We used a spherical neighborhood search with a fixed number of points instead of a fixed radius to calculate the features in Table 1, because of the homogeneous point density across our study area [23,39]. In this way a k of 10 results in a neighborhood of 10 points, one of which is the focal point itself. Based on these neighborhoods we then computed four geometric features: Height difference, height standard deviation, local radius and local point density (Table 1).

_{1}, λ

_{2}, λ

_{3}, where λ

_{1}> λ

_{2}> λ

_{3}) of this covariance matrix. Hence, the magnitude of the eigenvalues of the matrix describe the spread of points in the direction of the eigenvector. The eigenvector belonging to the third eigenvalue is equal to the normal vector ($\overrightarrow{N}$ = (N

_{x}, N

_{y}, N

_{z})) [39]. The points are linearly distributed if the eigenvalue of the first principle direction is significantly larger than the other two (λ

_{1}>> λ

_{2}≈ λ

_{3}), and planarly distributed if the eigenvalues of the first two principle directions are about equal and significantly larger than the third (λ

_{1}≈ λ

_{2}>> λ

_{3}). The points are scattered in all directions if all eigenvalues are about equal (λ

_{1}≈ λ

_{2}≈ λ

_{3}). These properties (linearity, planarity, and scatter), as well as some additional features (omnivariance, eigenentropy, sum of eigenvalues, and curvature), were quantified using the formulas in Table 1.

#### 3.2. Vegetation Classification

#### 3.2.1. Preprocessing

_{λ}< 0.03) were removed. This threshold was very conservative, but substantially contributed to reduction of the point data size, while still preserving all points that characterize tall vegetation.

#### 3.2.2. Supervised Classification

#### 3.2.3. Accuracy Assessment

#### 3.3. Linear Object Segmentation

#### 3.3.1. Preprocessing

#### 3.3.2. Rectangularity-Based Region Growing

#### 3.3.3. Object Merging

#### 3.3.4. Elongatedness

#### 3.3.5. Accuracy Assessment

## 4. Results

#### 4.1. Vegetation Classification

#### 4.2. Linear Object Segmentation

## 5. Discussion

#### 5.1. Feature Extraction

#### 5.2. Vegetation Classification

#### 5.3. Linear Object Segmentation

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Location of the rural landscape in the central part of the Netherlands. The true color aerial photograph [24] shows various objects identified as agricultural fields, grasslands, bare soil, and infrastructure such as paved and unpaved roads and farmhouses. The numbered photos show a selection of the variety of linear landscape elements such as (1) green lanes (2) planted tall tree lines along ditches, (3) low and high shrubs/copse, (4) hedges and (5) rows of fruit trees and willows.

**Figure 2.**Workflow detailing three routines for the identification of linear vegetation objects, 1. Feature extraction 2. Vegetation classification, and 3. Linear object segmentation. The computational steps are represented as rectangles and datasets as grey parallelograms.

**Figure 3.**Visualization of the region growing process based on rectangularity in three steps. Step a shows how a current region (in green) is grown in which the ratio between the concave hull and bounding box is above the threshold of 0.55. Step b considers a next point (in red) to be included to the region, which is also accepted. Step c considers a next point, which does not meet the rectangularity constraint of 0.55 and is not added to that region.

**Figure 4.**Results of the supervised classification. The green class represents the tall vegetation. The two ‘other’ classes contained data points that were classified as grasslands, agricultural fields, bare soil and water bodies (grey class), or as infrastructure and ditches (blue class).

**Figure 5.**Results of vegetation classification. Green areas have been correctly classified as linear vegetation (light green) and non-linear vegetation (dark green). Red areas have been wrongly classified as linear vegetation (light red), while dark red areas have been wrongly classified as non-linear vegetation. Cross plots 1–6 illustrate the variation in linear vegetation elements (in yellow) and terrain points (in purple), as visible from the LiDAR point cloud.

**Table 1.**Overview of point-based and neighborhood-based features used in the vegetation classification. The point-based features are based only on return number information stored with each point (i.e., echo information) whereas neighborhood-based features are based on the local geometry and eigenvalue characteristics derived from the x, y and z coordinates of the point cloud.

Feature Group | Feature | Symbol | Formula | Reference |
---|---|---|---|---|

Point | ||||

Echo | Number of returns | R_{t} | - | - |

Normalized return number | R_{n} | R/R_{t} | [35] | |

Neighborhood | ||||

Geometric | Height difference | ∆_{z} | $\underset{j:{\mathcal{N}}_{i}}{\mathrm{max}}\left({q}_{{Z}_{j}}\right)-\underset{j:{\mathcal{N}}_{i}}{\mathrm{min}}\left({q}_{{Z}_{j}}\right)$ | [23] |

Height standard deviation | σ_{z} | $\sqrt{\frac{1}{k}{\displaystyle {\displaystyle \sum}_{j=1}^{k}}{\left({q}_{{z}_{j}}-\overline{{q}_{z}}\right)}^{2}}$ | [23] | |

Local radius | r_{l} | $\underset{j:{\mathcal{N}}_{i}}{\mathrm{max}}\left(\left|{p}_{i}-{q}_{j}\right|\right)$ | [23] | |

Local point density | D | $\frac{k}{\frac{4}{3}\mathsf{\pi}{r}_{{l}_{i}}^{3}}$ | [23] | |

Eigenvalue | Normal vector Z | N_{z} | [38] | |

Linearity | L_{λ} | $\frac{{\lambda}_{1}-{\lambda}_{2}}{{\lambda}_{1}}$ | [39] | |

Planarity | P_{λ} | $\frac{{\lambda}_{2}-{\lambda}_{3}}{{\lambda}_{1}}$ | [39] | |

Scatter | S_{λ} | $\frac{{\lambda}_{3}}{{\lambda}_{1}}$ | [39] | |

Omnivariance | O_{λ} | $\sqrt[3]{{\lambda}_{1}{\lambda}_{2}{\lambda}_{3}}$ | [39] | |

Eigentropy | E_{λ} | $-{\lambda}_{1}\mathrm{ln}\left({\lambda}_{1}\right)-{\lambda}_{2}\mathrm{ln}\left({\lambda}_{2}\right)-{\lambda}_{3}\mathrm{ln}\left({\lambda}_{3}\right)$ | [39] | |

Sum of eigenvalues | ∑_{λ} | ${\lambda}_{1}+{\lambda}_{2}+{\lambda}_{3}$ | [36] | |

Curvature | C_{λ} | $\frac{{\lambda}_{3}}{{\lambda}_{1}+{\lambda}_{2}+{\lambda}_{3}}$ | [38] |

Actual | ||||
---|---|---|---|---|

Vegetation | Other | User’s Accuracy | ||

Predicted | Vegetation | 974,177 | 8171 | 0.99 |

Other | 22,908 | 47,999 | 0.68 | |

Producer’s accuracy | 0.98 | 0.85 | Overall accuracy: 0.97 |

**Table 3.**Confusion matrix of the automatically segmented against the manually annotated set of linear and non-linear vegetation objects (m

^{2}).

Actual | ||||
---|---|---|---|---|

Linear | Non-Linear | Producer’s Accuracy | ||

Predicted | Linear | 116,483.76 | 20,201.53 | 0.85 |

Non-linear | 28,385.56 | 33,6754.65 | 0.92 | |

User’s accuracy | 0.80 | 0.94 | Overall accuracy: 0.90 |

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**MDPI and ACS Style**

Lucas, C.; Bouten, W.; Koma, Z.; Kissling, W.D.; Seijmonsbergen, A.C. Identification of Linear Vegetation Elements in a Rural Landscape Using LiDAR Point Clouds. *Remote Sens.* **2019**, *11*, 292.
https://doi.org/10.3390/rs11030292

**AMA Style**

Lucas C, Bouten W, Koma Z, Kissling WD, Seijmonsbergen AC. Identification of Linear Vegetation Elements in a Rural Landscape Using LiDAR Point Clouds. *Remote Sensing*. 2019; 11(3):292.
https://doi.org/10.3390/rs11030292

**Chicago/Turabian Style**

Lucas, Chris, Willem Bouten, Zsófia Koma, W. Daniel Kissling, and Arie C. Seijmonsbergen. 2019. "Identification of Linear Vegetation Elements in a Rural Landscape Using LiDAR Point Clouds" *Remote Sensing* 11, no. 3: 292.
https://doi.org/10.3390/rs11030292