# A Method to Obtain Orange Crop Geometry Information Using a Mobile Terrestrial Laser Scanner and 3D Modeling

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Description of Data Acquisition and Processing

#### 2.1.1. The Equipment and Data Acquisition

#### 2.1.2. Data Processing

**dx**and

**dy**deviations for each point (Equations (1) and (2)).

**x**and

_{p}**y**are UTM coordinates of the laser impact (point) (m);

_{p}**x**and

_{s}**y**are UTM coordinates of the sensor (m); and

_{s}**dx**and

**dy**are deviations in x and y axes between the sensor and the point (m).

**dxy**, the distance between the sensor and the laser impact in the x, y plane (m);

**α**, angle of the direction of the measurement in relation to the north (degrees);

**β**, angle from LiDAR scanning (0 to 180°);

**d**, the distance value from the LiDAR scanning (m);

**z**, coordinate z (height) of the point (m); and

_{p}**z**, coordinate z (height) of the sensor (m).

_{s}**dx**and

**dy**were calculated based on the distance between the sensor and the laser impact in the x, y plane (

**dxy**) and the angle

**α**(Figure 2a; Equations (3) and (4)).

**α**corresponded to the direction of the measurement in relation to north, counted clockwise. This angle is the subtraction of 90° from the vehicle direction (θ) in relation to north (the LiDAR sensor was arranged perpendicularly to the vehicle longitude, facing the left side). The direction of the vehicle (θ) at a given moment is defined by the median values of direction from 30 consecutive points along the vehicle track, which is equivalent to a time interval of 0.5 s approximately. Finally,

**dxy**was calculated based on the original polar coordinates of the laser impacts (distance

**d**and angle

**β**) (Figure 2b) (Equation (5)). The z coordinate (point height) is also derived from the polar coordinates as exposed in Equation (6). The sensor height (

**z**) was 1.4 m, being the reference to the point height (

_{s}**z**) calculation.

_{p}**d**) for the LiDAR readings. A minimum distance value was also set to exclude obstacles that were too close to the sensor (the GNSS antenna, for example). The points which represented the soil were excluded by establishing a minimum threshold for the height (z coordinate) of each point. The output data after filtering was a point cloud representing only the crowns of the trees for a single tree row (Figure 3b).

#### 2.2. Demonstrating and Evaluating the Proposed Method

#### 2.2.1. Validation of the Point Cloud Accuracy—Laboratory Testing

#### 2.2.2. Data Acquisition in a Commercial Orange Grove

^{−1}, scanning one side of the tree row at a time. The data were saved separately for each tree row.

#### 2.2.3. Evaluating Point Cloud Classification and 3D Modeling Options

#### 2.2.4. Mapping of Canopy Volume and Height of a Commercial Orange Grove

**a**, fuzzy value in pixel i from map 1;

_{i}**b**, fuzzy value in pixel i from map 2; and

_{i}**s**(

**a**,

**b**)

_{i}, fuzzy similarity index in pixel i between the two maps.

## 3. Results and Discussion

#### 3.1. Validation of the Point Cloud Accuracy—Laboratory Testing

#### 3.2. Data Acquisition in a Commercial Grove

^{−1}speed) the distance between each scan was around 4 cm. The total grove accounted for approximately 175 million points, which corresponds to approximately 700 points m

^{−2}(approximately 12,100 points per plant). Airborne LiDAR scanning applied over urban or forest areas usually produces point clouds with 0.5 to 5 points m

^{−2}. Escolà et al. [7] reported a density of 8000 points per m

^{−2}using a multi-echo LiDAR device on a MTLS on an olive grove but they were using a sensor with higher angular resolution traveling at a slower forward speed.

#### 3.3. Modeling of 3D Objects from the Point Cloud

^{3}per plant using an average of approximately 6600 points as references for measurements, whereas the convex-hull, considered a good option when trees were divided into sections, resulted in an average canopy volume of 12.8 m

^{3}using approximately 3400 points in 10 sections. Canopy volumes from manual measurements based on the cube-fit and the cylinder-fit were 22.6 m

^{3}and 11.9 m

^{3}, respectively (Table 2), using a significantly reduced amount of reference points. The difference in canopy volume obtained from the different methods is evidence of the importance of the adoption of a reference method. At this stage, it is reasonable to consider that the method of canopy volume computation based on the MTLS and 3D modeling is clearly more capable of capturing the geometry of the canopy than the current available manual methods based on regular geometries such as cubes or cylinders because it employs a remarkably greater number of reference points for measurements. Thorough investigation over the algorithms is still needed before changing to a new standardized system. Nevertheless, the LiDAR-based methods are applicable in the field and should be considered as a possible standard for canopy volume computation.

#### 3.4. Mapping of Canopy Volume and Height in a Commercial Orange Grove

^{3}and 12.13 m

^{3}for Methods 1 and 2, respectively—Table 3), which was not the case when 25 trees were analyzed separately (14.1 and 12.8 m

^{3}for Methods 1 and 2, respectively—Table 2). It should also be noted that, when analyzing results from the entire grove, a range of different targets (gaps, trees with different size, shape and density, etc.) are being scanned which was not the case for the selected 25 trees. The different algorithms and classifications options might perform differently depending on the target characteristics, and, for that reason, further investigations are needed in order to better understand what aspects can affect the results.

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Dworak, V.; Selbeck, J.; Ehlert, D. Ranging sensors for vehicle-based measurement of crop stand and orchard parameters: A review. Trans. ASABE
**2011**, 54, 1497–1510. [Google Scholar] [CrossRef] - Rosell-Polo, J.R.; Sanz, R. A review of methods and applications of the geometric characterization of tree crops in agricultural activities. Comput. Electron. Agric.
**2012**, 81, 124–141. [Google Scholar] [CrossRef] - Berk, P.; Hocevar, M.; belsak, A. Development of alternative plant protection product application techniques in orchards, based on measurement sensing systems: A review. Comput. Electron. Agric.
**2016**, 124, 273–288. [Google Scholar] [CrossRef] - Gil, E.; Arnó, J.; Llorens, J.; Sanz, R.; Llop, J.; Rosell-Polo, J.R.; Gallart, M.; Escolà, A. Advanced technologies for the improvement of spray application techniques in Spanish viticulture: An overview. Sensors
**2014**, 14, 691–708. [Google Scholar] [CrossRef] [PubMed][Green Version] - Underwood, J.P.; Hung, C.; Whelan, B.; Sukkarieh, S. Mapping almond orchard canopy volume, flowers, fruit and yield using lidar and vision sensors. Comput. Electron. Agric.
**2016**, 130, 83–96. [Google Scholar] [CrossRef] - Underwood, J.P.; Jagbrant, G.; Nieto, J.I.; Sukkarieh, S. Lidar-Based Tree Recognition and Platform Localization in Orchards. J. Field Robot.
**2015**, 32, 1056–1074. [Google Scholar] [CrossRef] - Escolà, A.; Martínez-Casasnovas, J.A.; Rufat, J.; Arnó, J.; Arbonés, A.; Sebé, F.; Pascual, M.; Gregorio, E.; Rosell-Polo, J.R. Mobile terrestrial laser scanner applications in precision fruticulture/horticulture and tools to extract information from canopy point clouds. Precis. Agric.
**2017**, 18, 111–132. [Google Scholar] [CrossRef] - Escolà, A.; Rosell-Polo, J.R.; Planas, S.; Gil, E.; Pomar, J.; Camp, F.; Llorens, J.; Solanelles, F. Variable rate sprayer. Part 1—Orchard prototype: Design, implementation and validation. Comput. Electron. Agric.
**2013**, 95, 122–135. [Google Scholar] [CrossRef] - Chen, Y.; Zhu, H.; Ozkan, H.E. Development of a variable-rate sprayer with laser scanning sensor to synchronize spray outputs to tree structures. Trans. ASABE
**2012**, 55, 773–781. [Google Scholar] [CrossRef] - Rosell-Polo, J.R.; Gregorio, E.; Gené, J.; Llorens, J.; Torrent, X.; Arnó, J.; Escolà, A. Kinect v2 sensor-based mobile terrestrial laser scanner for agricultural outdoor applications. IEEE/ASME Trans. Mech.
**2017**. [Google Scholar] [CrossRef] - Méndez, V.; Rosell-Polo, J.R.; Sanz, R.; Escolà, A.; Catalán, H. Deciduous tree reconstruction algorithm based on cylinder fitting from mobile terrestrial laser scanned point clouds. Biosyst. Eng.
**2014**, 124, 78–88. [Google Scholar] [CrossRef] - Del-Moral-Martínez, I.; Rosell-Polo, J.R.; Company, J.; Sanz, R.; Escolà, A.; Masip, J.; Martínez-Casasnovas, J.A.; Arnó, J. Mapping vineyard leaf area using mobile terrestrial laser scanners: should rows be scanned on-the-go or discontinuously sampled? Sensors
**2016**, 16, 119. [Google Scholar] [CrossRef] [PubMed] - Arnó, J.; Escolà, A.; Rosell-Polo, J.R. Setting the optimal length to be scanned in rows of vines by using mobile terrestrial laser scanners. Precis. Agric.
**2017**, 18, 145–151. [Google Scholar] [CrossRef] - Lee, K.H.; Ehsani, R. A laser scanner based measurement system for quantification of citrus tree geometric. Appl. Eng. Agric.
**2009**, 25, 777–788. [Google Scholar] [CrossRef] - Rosell-Polo, J.R.; Llorens, J.; Sanz, R.; Arnó, J.; Ribes-Dasi, M.; Masip, J.; Escolà, A.; Camp, F.; Solanelles, F.; Gràcia, F.; et al. Obtaining the three-dimensional structure of tree orchards from remote 2D terrestrial LIDAR scanning. Agric. For. Meteorol.
**2009**, 149, 1505–1515. [Google Scholar] [CrossRef] - Tumbo, S.D.; Salyani, M.; Whitney, J.D.; Wheaton, T.A.; Miller, W.M. Investigation of laser and ultrasonic ranging sensors for measurements of citrus canopy volume. Appl. Eng. Agric.
**2002**, 18, 367–372. [Google Scholar] [CrossRef] - Wei, J.; Salyani, M. Development of a laser scanner for measuring tree canopy characteristics: Phase 1. Prototype development. Trans. ASABE
**2004**, 47, 2101–2108. [Google Scholar] [CrossRef] - Del-Moral-Martínez, I.; Arnó, J.; Escolà, A.; Sanz, R.; Masip-Vilalta, J.; Company-Messa, J.; Rosell-Polo, J.R. Georeferenced Scanning System to Estimate the LeafWall Area in Tree Crops. Sensors
**2015**, 15, 8382–8405. [Google Scholar] [CrossRef] [PubMed] - Auat Cheein, F.A.; Guivant, J.; Sanz, R.; Escolà, A.; Yandún, F.; Torres-Torriti, M.; Rosell-Polo, J.R. Real-time approaches for characterization of fully and partially scanned canopies in groves. Comput. Electron. Agric.
**2015**, 118, 361–371. [Google Scholar] [CrossRef] - Food and Agriculture Organization (FAO). Faostat. 2014. Available online: http://faostat.fao.org (accessed on 2 April 2017).
- Colaço, A.F.; Molin, J.P. Variable rate fertilization in citrus: A long term study. Precis. Agric.
**2017**, 18, 169–191. [Google Scholar] [CrossRef] - Processing v2, 2014. Available online: https://processing.org (accessed on 28 October 2014).
- SICK AG. Telegrams for Operating/Configuring the LMS2XX Laser Measurement Systems; Firmware Version V.2.10/X1.14; 2003. Available online: http://sicktoolbox.sourceforge.net/docs/sick-lms-telegram-listing.pdf (accessed on 28 October 2014).
- R v3.2.2—R Core Team. R: A Language and Environment for Statistical Computing; Software; R Foundation for Statistical Computing: Vienna, Austria, 2015; Available online: http://www.R-project.org (accessed on 13 May 2015).
- CloudCompare [GPL Software] v2.6.1. 2015. Available online: http://www.cloudcompare.org (accessed on 15 March 2015).
- Pateiro-López, B.; Rodríguez-Casal, A. Generalizing the convex-hull of a sample: The R package alphahull. J. Stat. Softw.
**2010**, 34. [Google Scholar] [CrossRef] - Edelsbrunner, H.; Mucke, E.P. Three-Dimensional alpha shapes. ACM Trans. Graph.
**1994**, 13, 43–72. [Google Scholar] [CrossRef] - Van der Zande, D.; Hoet, W.; Jonckheere, I.; van Aardt, J.; Coppin, P. Influence of measurement set-up of ground-based LiDAR for derivation of tree structure. Agric. For. Meteorol.
**2006**, 141, 147–160. [Google Scholar] [CrossRef] - Velázquez-Martí, B.; Estornell, J.; López-Cortéz, I.; Martí-Gavilá, J. Calculation of biomass volume of citrus trees from an adapted dendrometry. Biosyst. Eng.
**2012**, 112, 285–292. [Google Scholar] [CrossRef] - Mendel, K. Rootstock-scion relationships in Shamouti trees on light soil. Katavim
**1956**, 6, 35–60. [Google Scholar] - Schinor, E.H.; Cristofani-Yaly, M.; Bastianel, M.; Machado, M.A. Sunki Mandarin vs Poncirus trifoliate hybrids as rootstocks for Pera sweet orange. J. Agric. Sci.
**2013**, 5, 190–200. [Google Scholar] [CrossRef] - Scapin, M.S.; Behlau, F.; Scandelai, L.J.M.; Fernandes, R.S.; Silva, G.J., Jr.; Ramos, H.H. Tree-row-volume-based sprays of copper bactericide for control of citrus canker. Crop Prot.
**2015**, 77, 119–126. [Google Scholar] [CrossRef] - Silva, G.J., Jr.; Scapin, M.S.; Silva, F.P.; Silva, A.R.P.; Behlau, F.; Ramos, H.H. Spray volume and fungicide rates for citrus black spot control based on tree canopy volume. Crop Prot.
**2016**, 85, 38–45. [Google Scholar] [CrossRef] - QGIS v2.10—QGIS Development Team. QGIS Geographic Information System. Open Source Geospatial Foundation Project. 2015. Available online: http://www.qgis.org (accessed on 15 March 2015).
- Minasny, B.; McBratney, A.B.; Whelan, B.M. VESPER Version 1.62; Precision Agriculture Laboratory, Faculty of Agriculture and Environment, University of Sydney: Sydney, Australia, 2006. [Google Scholar]
- Map Comparison Kit v3.2. 2016. Available online: http://mck.riks.nl (accessed on 17 December 2016).
- Hagen, A. Fuzzy set approach to assessing similarity of categorical maps. Int. J. Geogr. Inf. Sci.
**2003**, 17, 235–249. [Google Scholar] [CrossRef] - Lee, W.S.; Ehsani, R. Comparison of two 2D laser scanners for sensing object distances, shapes, and surfaces patterns. Comput. Electron. Agric.
**2008**, 60, 250–262. [Google Scholar] [CrossRef]

**Figure 1.**(

**a**) LiDAR (Light Detection and Ranging) sensor and GNSS (Global Navigation Satellite System) receiver mounted on an all-terrain vehicle; and (

**b**) diagram of LiDAR sensor 2D scanning and displacement along the alleys.

**Figure 2.**(

**a**)

**dx**and

**dy**deviations based on the angle

**α**and

**dxy**; and (

**b**)

**dxy**based on distance d and angle

**β**.

**Figure 3.**(

**a**) Original point cloud from one tree row; and (

**b**) point cloud after the filtering process.

**Figure 4.**(

**a**) Top view of a non-classified point cloud from orange trees; (

**b**) clustering classification into groups each representing an individual tree; and (

**c**) classification of points in transversal sections along the row.

**Figure 5.**Point clouds from objects scanned with a mobile terrestrial laser scanner mounted on an all-terrain vehicle: (

**a**) cylinder; (

**b**) body of cone; (

**c**) square; (

**d**) triangle; and (

**e**) circle.

**Figure 6.**3D georeferenced point cloud derived from the developed mobile terrestrial laser scanning system used in a 25 ha commercial orange grove.

**Figure 7.**Convex-hull and alpha-shape algorithms to model orange trees according to two approaches: clusters (individual trees) and transversal sections of the row (0.26 m long). The top picture is an image of the point cloud.

**Figure 8.**Detail of the convex-hull and alpha-shape models over a single 0.26 m long transversal section of a tree row.

**Figure 10.**3D canopy structure of a single tree modeled according to different algorithms. The top picture is an image of the point cloud.

**Figure 11.**Shapefiles produced after either segmenting the row into transversal sections or into individual trees.

**Figure 12.**Canopy volume and height maps generated according to the two data processing methods: Method 1, classifying the point cloud into individual trees (cluster) and subsequently applying the alpha-shape algorithm (α = 0.75); and Method 2, dividing the rows into 0.26 m long sections and further applying the convex-hull algorithm.

**Table 1.**Object dimensions measured manually and by a mobile terrestrial laser scanner mounted on an all-terrain vehicle and on a platform running over a rail.

Objects | a | b | c | ||||||
---|---|---|---|---|---|---|---|---|---|

(i) | (ii) | (iii) | (i) | (ii) | (iii) | (i) | (ii) | (iii) | |

(cm) | |||||||||

Square | 98.60 | 98.29 | 100.00 | 94.23 | 100.25 | 100.00 | - | - | - |

Triangle | 98.22 | 98.33 | 100.00 | 84.64 | 88.48 | 87.00 | - | - | - |

Circle | 101.17 | 99.96 | 100.00 | - | - | - | - | - | - |

Cylinder I | 79.58 | 79.78 | 80.00 | 29.58 | 30.13 | 30.00 | - | - | - |

Cylinder II | 80.92 | 83.21 | 83.00 | 19.74 | 20.28 | 20.00 | - | - | - |

Body of cone | 62.65 | 63.31 | 64.00 | 44.95 | 45.05 | 45.00 | 31.15 | 30.90 | 31.00 |

**Table 2.**Mean canopy volume of 25 individual trees estimated by different methods and by dividing the trees into different number of sections.

Algorithm | Number of Sections Per Tree | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

1 | 3 | 5 | 7 | 10 | ||||||

Mean Canopy Volume of 25 Individual Trees (m^{3}) | ||||||||||

Cube-fit | 22.65 | a | - | - | - | - | ||||

Cylinder-fit | 11.90 | c | - | - | - | - | ||||

Convex-hull | 16.07 | b,a | 14.71 | a,ab | 13.97 | a,ab | 13.46 | a,ab | 12.86 | a,b |

α-shape (α = 0.75) | 14.31 | c,a | 11.57 | b,b | 10.02 | b,bc | 8.66 | b,cd | 7.34 | b,d |

α-shape (α = 0.50) | 12.16 | c,a | 9.77 | b,b | 8.19 | b,bc | 6.98 | c,cd | 5.72 | c,d |

α-shape (α = 0.25) | 6.19 | d,a | 5.32 | c,b | 4.47 | c,bc | 4.15 | d,c | 3.34 | d,d |

Canopy Variable | Method * | Mean | Minimum | Maximum | Coef. of Variation |
---|---|---|---|---|---|

m^{3} | |||||

Volume | 1 | 11.94 | 7.64 | 18.57 | 0.09 |

2 | 12.13 | 8.05 | 17.30 | 0.09 | |

m | |||||

Height | 1 | 2.85 | 2.47 | 3.39 | 0.03 |

2 | 2.87 | 2.44 | 3.43 | 0.04 |

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## Share and Cite

**MDPI and ACS Style**

Colaço, A.F.; Trevisan, R.G.; Molin, J.P.; Rosell-Polo, J.R.; Escolà, A. A Method to Obtain Orange Crop Geometry Information Using a Mobile Terrestrial Laser Scanner and 3D Modeling. *Remote Sens.* **2017**, *9*, 763.
https://doi.org/10.3390/rs9080763

**AMA Style**

Colaço AF, Trevisan RG, Molin JP, Rosell-Polo JR, Escolà A. A Method to Obtain Orange Crop Geometry Information Using a Mobile Terrestrial Laser Scanner and 3D Modeling. *Remote Sensing*. 2017; 9(8):763.
https://doi.org/10.3390/rs9080763

**Chicago/Turabian Style**

Colaço, André F., Rodrigo G. Trevisan, José P. Molin, Joan R. Rosell-Polo, and Alexandre Escolà. 2017. "A Method to Obtain Orange Crop Geometry Information Using a Mobile Terrestrial Laser Scanner and 3D Modeling" *Remote Sensing* 9, no. 8: 763.
https://doi.org/10.3390/rs9080763