# 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

- Turner, M.G. Landscape ecology: The effect of pattern on process. Annu. Rev. Ecol. Syst.
**1989**, 20, 171–197. [Google Scholar] [CrossRef] - Marquer, L.; Gaillard, M.-J.; Sugita, S.; Poska, A.; Trondman, A.-K.; Mazier, F.; Nielsen, A.B.; Fyfe, R.M.; Jöhnsson, A.M.; Smith, B.; et al. Quantifying the effects of land use and climate on Holocene vegetation in Europe. Quat. Sci. Rev.
**2017**, 171, 20–37. [Google Scholar] [CrossRef] - Bailly, J.S.; Lagacherie, P.; Millier, C.; Puech, C.; Kosuth, P. Agrarian landscapes linear features detection from lidar: Application to artificial drainage networks. Int. J. Remote Sens.
**2008**, 29, 3489–3508. [Google Scholar] [CrossRef] - Meyer, B.C.; Wolf, T.; Grabaum, R. A multifunctional assessment method for compromise optimisation of linear landscape elements. Ecol. Indic.
**2012**, 22, 53–63. [Google Scholar] [CrossRef] - Van der Zanden, E.H.; Verburg, P.H.; Mücher, C.A. Modelling the spatial distribution of linear landscape elements in Europe. Ecol. Indic.
**2013**, 27, 125–136. [Google Scholar] [CrossRef] - Aguirre-Gutiérrez, J.; Kissling, W.D.; Carvalheiro, L.G.; WallisDeVries, M.F.; Franzén, M.; Biesmeijer, J.C. Functional traits help to explain half-century long shifts in pollinator distributions. Sci. Rep.
**2016**, 6. [Google Scholar] [CrossRef] - Spellerberg, I.F.; Sawyer, J.W. An Introduction to Applied Biogeography; Cambridge University Press: Cambridge, UK, 1999. [Google Scholar] [CrossRef]
- Croxton, P.; Hann, J.; Greatorex-Davies, J.; Sparks, T. Linear hotspots? The floral and butterfly diversity of green lanes. Biol. Conserv.
**2005**, 121, 579–584. [Google Scholar] [CrossRef] - Burel, F. Hedgerows and their role in agricultural landscapes. Crit. Rev. Plant Sci.
**1996**, 15, 169–190. [Google Scholar] [CrossRef] - Jongman, R.G.H. Landscape linkages and biodiversity in Europe. In The New Dimensions of the European Landscape; Jongman, R.G.H., Ed.; Springer: Dordrecht, The Netherlands, 1996; pp. 179–189. [Google Scholar]
- Gobster, P.H.; Nassauer, J.I.; Daniel, T.C.; Fry, G. The shared landscape: What does aesthetics have to do with ecology? Landsc. Ecol.
**2007**, 22, 959–972. [Google Scholar] [CrossRef] - Boutin, C.; Jobin, B.; Bélanger, L.; Baril, A.; Freemark, K. Hedgerows in the Farming Landscapes of Canada. Hedgerows of the World: Their Ecological Functions in Different Landscapes. Available online: https://www.researchgate.net/publication/264670164_Hedgerows_in_the_farming_landscapes_of_Canada (accessed on 31 January 2019).
- Stoate, C.; Boatman, N.; Borralho, R.; Carvalho, C.R.; De Snoo, G.; Eden, P. Ecological impacts of arable intensification in Europe. J. Environ. Manag.
**2001**, 63, 337–365. [Google Scholar] [CrossRef] - Aksoy, S.; Akcay, H.G.; Wassenaar, T. Automatic mapping of linear woody vegetation features in agricultural landscapes using very high resolution imagery. IEEE Trans. Geosci. Remote Sens.
**2010**, 48, 511–522. [Google Scholar] [CrossRef] - Thornton, M.W.; Atkinson, P.M.; Holland, D. Sub-pixel mapping of rural land cover objects from fine spatial resolution satellite sensor imagery using super-resolution pixel-swapping. Int. J. Remote Sens.
**2006**, 27, 473–491. [Google Scholar] [CrossRef] - Vannier, C.; Hubert-Moy, L. Multiscale comparison of remote-sensing data for linear woody vegetation mapping. Int. J. Remote Sens.
**2014**, 35, 7376–7399. [Google Scholar] [CrossRef] - Tansey, K.; Chambers, I.; Anstee, A.; Denniss, A.; Lamb, A. Object-oriented classification of very high resolution airborne imagery for the extraction of hedgerows and field margin cover in agricultural areas. Appl. Geogr.
**2009**, 29, 145–157. [Google Scholar] [CrossRef] - Kissling, W.D.; Seijmonsbergen, A.C.; Foppen, R.; Bouten, W. eEcolidar, eScience infrastructure for ecological applications of LiDAR point clouds: Reconstructing the 3d ecosystem structure for animals at regional to continental scales. Res. Ideas Outcomes
**2017**, 3, e14939. [Google Scholar] [CrossRef] - Lim, K.; Treitz, P.; Wulder, M.; St-Onge, B.; Flood, M. Lidar remote sensing of forest structure. Prog. Phys. Geogr.
**2003**, 27, 88–106. [Google Scholar] [CrossRef] - Lefsky, M.A.; Cohen, W.B.; Parker, G.G.; Harding, D.J. Lidar remote sensing for ecosystem studies: Lidar, an emerging remote sensing technology that directly measures the three-dimensional distribution of plant canopies, can accurately estimate vegetation structural attributes and should be of particular interest to forest, landscape, and global ecologists. AIBS Bull.
**2002**, 52, 19–30. [Google Scholar] - Eitel, J.U.; Höfle, B.; Vierling, L.A.; Abellán, A.; Asner, G.P.; Deems, J.S.; Glennie, C.L.; Joerg, P.C.; LeWinter, A.L.; Magney, T.S.; et al. Beyond 3-d: The new spectrum of lidar applications for earth and ecological sciences. Remote Sens. Environ.
**2016**, 186, 372–392. [Google Scholar] [CrossRef] - Song, J.-H.; Han, S.-H.; Yu, K.; Kim, Y.-I. Assessing the possibility of land-cover classification using lidar intensity data. Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci.
**2002**, 34, 259–262. [Google Scholar] - Weinmann, M.; Jutzi, B.; Hinz, S.; Mallet, C. Semantic point cloud interpretation based on optimal neighborhoods, relevant features and efficient classifiers. ISPRS J. Photogramm. Remote Sens.
**2015**, 105, 286–304. [Google Scholar] [CrossRef] - PDOK. Available online: https://www.pdok.nl/viewer/ (accessed on 12 July 2018).
- AHN Inwinjaren AHN2 & AHN3. Available online: http://www.ahn.nl/common-nlm/inwinjaren-ahn2--ahn3.html (accessed on 12 July 2018).
- Yan, W.Y.; Shaker, A.; El-Ashmawy, N. Urban land cover classification using airborne LiDAR data: A review. Remote Sens. Environ.
**2015**, 158, 295–310. [Google Scholar] [CrossRef] - Van der Walt, S.; Colbert, S.C.; Varoquaux, G. The numpy array: A structure for efficient numerical computation. Comput. Sci. Eng.
**2011**, 13, 22–30. [Google Scholar] [CrossRef] - SciPy: Open source scientific tools for Python. Available online: http://www.scipy.org/ (accessed on 12 July 2018).
- McKinney, W. Data structures for statistical computing in python. In Proceedings of the 9th Python in Science Conference, Austin, TX, USA, 28 June–3 July 2010; pp. 51–56. [Google Scholar]
- Pedregosa, F.; Varoquaux, G.; Gramfort, A.; Michel, V.; Thirion, B.; Grisel, O.; Blondel, M.; Prettenhofer, P.; Weiss, R.; Dubourg, V.; et al. Scikit-learn: Machine learning in Python. J. Mach. Learn. Res.
**2011**, 12, 2825–2830. [Google Scholar] - CGAL Project. CGAL User and Reference Manual, 4.13th ed.; CGAL Editorial Board, 2018; Available online: https://doc.cgal.org/latest/Manual/packages.html (acceseed on 1 February 2019).
- PDAL. Available online: https://pdal.io/ (accessed on 12 July 2018).
- Cloud Compare. Available online: http://www.cloudcompare.org/ (accessed on 12 July 2018).
- Chehata, N.; Guo, L.; Mallet, C. Airborne lidar feature selection for urban classification using random forests. Remote Sens. Spat. Inf. Sci.
**2009**, 38, 207–2012. [Google Scholar] - Guo, L.; Chehata, N.; Mallet, C.; Boukir, S. Relevance of airborne LiDAR and multispectral image data for urban scene classification using random forests. ISPRS J. Photogramm. Remote Sens.
**2011**, 66, 56–66. [Google Scholar] [CrossRef] - Mallet, C.; Bretar, F.; Roux, M.; Soergel, U.; Heipke, C. Relevance assessment of full-waveform lidar data for urban area classification. ISPRS J. Photogramm. Remote Sens.
**2011**, 66, S71–S84. [Google Scholar] [CrossRef] - Niemeyer, J.; Rottensteiner, F.; Soergel, U. Contextual classification of LiDAR data and building object detection in urban areas. SPRS J. Photogramm. Remote Sens.
**2018**, 87, 152–165. [Google Scholar] [CrossRef] - Pauly, M.; Gross, M.; Kobbelt, L.P. Efficient simplification of point-sampled surfaces. In Proceedings of the Conference on Visualization, IEEE Visualization, Boston, MA, USA, 27 October–1 November 2002; pp. 163–170. [Google Scholar] [Green Version]
- West, K.F.; Webb, B.N.; Lersch, J.R.; Pothier, S.; Triscari, J.M.; Iverson, A.E. Context-driven automated target detection in 3d data. In Proceedings of the SPIE 5426, Automatic Target Recognition XIX, Orlando, FL, USA, 21 September 2004; pp. 133–143. [Google Scholar] [CrossRef]
- Kashani, A.G.; Olsen, M.J.; Parrish, C.E.; Wilson, N. A review of LiDAR radiometric processing: From ad hoc intensity correction to rigorous radiometric calibration. Sensors
**2015**, 15, 28099–28128. [Google Scholar] [CrossRef] - Hoppe, H.; DeRose, T.; Duchampt, T.; McDonald, J.; Stuetzle, W. Surface reconstruction from unorganized points. Comp. Graph.
**1992**, 26, 2. [Google Scholar] [CrossRef] - Breiman, L. Random forests. Mach. Learn.
**2001**, 45, 5–32. [Google Scholar] [CrossRef] - Ho, T.K. The random subspace method for constructing decision forests. IEEE Trans. Pattern Anal. Mach. Int.
**1998**, 20, 832–844. [Google Scholar] - Hsu, C.; Chang, C.; Lin, C. A Practical Guide to Support Vector Classification. Available online: https://www.csie.ntu.edu.tw/~cjlin/papers/guide/guide.pdf (accessed on 12 July 2018).
- He, H.; Garcia, E.A. Learning from imbalanced data. IEEE Trans. Knowl. Data Eng.
**2009**, 21, 1263–1284. [Google Scholar] [CrossRef] - Chen, C.; Liaw, A.; Breiman, L. Using Random Forest to Learn Imbalanced Data; Technik Report 666; Department of Statistics, UC Berkeley: Berkeley, CA, USA, 2004. [Google Scholar]
- Breiman, L.; Friedman, J.; Stone, C.J.; Olshen, R.A. Classification and Regression Trees; CRC Press: Boca Raton, FL, USA, 1984. [Google Scholar]
- Bradley, A.P. The use of the area under the roc curve in the evaluation of machine learning algorithms. Pattern Recogn.
**1997**, 30, 1145–1159. [Google Scholar] [CrossRef] - Matthews, B.W. Comparison of the predicted and observed secondary structure of t4 phage lysozyme. Biochim. Biophys. Acta (BBA) Protein Struct.
**1975**, 405, 442–451. [Google Scholar] [CrossRef] - Kubat, M.; Holte, R.C.; Matwin, S. Machine learning for the detection of oil spills in satellite radar images. Mach. Learn.
**1998**, 30, 195–215. [Google Scholar] [CrossRef] - Kohavi, R. A study of cross-validation and bootstrap for accuracy estimation and model selection. In Proceedings of the 14th International Joint Conference on Artificial Intelligence, Montreal, QC, Canada, 20–25 August 1995; pp. 1137–1145. [Google Scholar]
- Sun, Y.; Wong, A.K.; Kamel, M.S. Classification of imbalanced data: A review. Int. J. Pattern Recognit. Artif. Intell.
**2009**, 23, 687–719. [Google Scholar] [CrossRef] - López, V.; Fernandez, A.; García, S.; Palade, V.; Herrera, F. An insight into classification with imbalanced data: Empirical results and current trends on using data intrinsic characteristics. Inf. Sci.
**2013**, 250, 113–141. [Google Scholar] [CrossRef] - Ester, M.; Kriegel, H.-P.; Sander, J.; Xu, X. A density-based algorithm for discovering clusters in large spatial databases with noise. In Proceedings of the Kdd-96 Second International Conference on Knowledge Discovery and Data Mining, Portland, OR, USA, 2–4 August 1996; pp. 226–231. [Google Scholar]
- Rabbani, T.; Van Den Heuvel, F.; Vosselmann, G. Segmentation of point clouds using smoothness constraint. Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci.
**2006**, 36, 248–253. [Google Scholar] - Vosselman, G. Point cloud segmentation for urban scene classification. Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci.
**2013**, 1, 257–262. [Google Scholar] [CrossRef] - Rosin, P.L. Measuring rectangularity. Mach. Vis. Appl.
**1999**, 11, 191–196. [Google Scholar] [CrossRef] - Toussaint, G.T. Solving geometric problems with the rotating calipers. In Proceedings of the IEEE Melecon’83, Athens, Greece, 24–26 May 1983; pp. 1–8. [Google Scholar]
- Preparata, F.P.; Shamos, M. Computational Geometry: An Introduction; Springer-Verlag: New York, NY, USA, 1985; ISBN 978-0-387-96131-6. [Google Scholar]
- Freeman, H.; Shapira, R. Determining the minimum-area encasing rectangle for an arbitrary closed curve. Commun. ACM
**1975**, 18, 409–413. [Google Scholar] [CrossRef] - Edelsbrunner, H.; Kirkpatrick, D.; Seidel, R. On the shape of a set of points in the plane. IEEE Trans. Inf. Theory
**1983**, 29, 551–559. [Google Scholar] [CrossRef] - Delaunay, B. Sur la sphere vide. Izv. Akad. Nauk SSSR. Otdelenie Matematicheskii i Estestvennyka Nauk 7
**1934**, 1–2, 793–800. [Google Scholar] - Nagao, M.; Matsuyama, T. A Structural Analysis of Complex Aerial Photographs; Springer-Verlag: New York, NY, USA, 1980; ISBN13 9781461582960. [Google Scholar]
- Congalton, R.G.; Green, K. Assessing the Accuracy of Remotely Sensed Data: Principles and Practices, 2nd ed.; CRC Press: Boca Raton, FL, USA, 2008; ISBN 9781420055139. [Google Scholar]
- Eysn, L.; Hollaus, M.; Schadauer, K.; Pfeifer, N. Forest Delineation Based on Airborne LiDAR Data. Remote Sens.
**2012**, 4, 762–783. [Google Scholar] [CrossRef] - Yang, H.; Chen, W.; Qian, T.; Shen, D.; Wang, J. The Extraction of Vegetation Points from LiDAR Using 3D Fractal Dimension Analyses. Remote Sens.
**2015**, 7, 10815–10831. [Google Scholar] [CrossRef] [Green Version] - Pfeiffer, N.; Mandlburger, G.; Otepka, J.; Karel, W. OPALS—A framework for Airborne Laser Scanning data analysis. Comput. Environ. Urban Syst.
**2014**, 45, 125–136. [Google Scholar] [CrossRef] - Maes, J.; Teller, A.; Erhard, M.; Liquete, C.; Braat, L.; Berry, P.; Egoh, B.; Puydarrieux, P.; Fiorina, C.; Santos, F.; et al. Mapping and Assessment of Ecosystems and Their Services; Tech. Rep. EUR 27143 EN. Joint Research Center—Institute for Environment and Sustainability, 2013. Available online: http://ec.europa.eu/environment/nature/knowledge/ecosystem_assessment/pdf/102.pdf (accessed on 10 December 2018).
- Biała, K.; Condé, S.; Delbaere, B.; Jones-Walters, L.; Torre-Marín, A. Streamlining European Biodiversity Indicators 2020; Tech. Rep. 11/2012. European Environment Agency, 2012. Available online: https://www.eea.europa.eu/publications/streamlining-european-biodiversity-indicators-2020 (accessed on 10 December 2018).
- Paracchini, M.L.; Petersen, J.-E.; Hoogeveen, Y.; Bamps, C.; Burfield, I.; van Swaay, C. High Nature Value Farmland in Europe; Tech. Rep. EUR 23480 EN. Joint Research Center—Institute for Environment and Sustainability, 2008. Available online: http://agrienv.jrc.ec.europa.eu/publications/pdfs/HNV_Final_Report.pdf (accessed on 10 December 2018).
- Bouwma, I.; Sanders, M.; Op Akkerhuis, G.J.; Onno Knol, J.V.; de Wit, B.; Wiertz, J.; van Hinsber, A. Biodiversiteit Bekeken: Hoe Evalueert en Verkent Het PBL het Natuurbeleid? 2014. Available online: https://www.pbl.nl/sites/default/files/cms/publicaties/PBL_2014_Biodiversiteit%20bekeken_924.pdf (accessed on 10 December 2018).

**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