# High-Throughput Legume Seed Phenotyping Using a Handheld 3D Laser Scanner

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data Acquisition and Processing Environment

#### 2.2. Automatic Measurement of Legume Seed Traits

#### 2.2.1. Single-Seed Extraction

_{1}, λ

_{2}, and λ

_{3}(λ

_{1}> λ

_{2}> λ

_{3}), can be obtained. Then the dimensions of each point cloud are calculated as follows:

_{1D}is a one-dimensional linear feature, a

_{2D}is a 2D planar feature, a

_{3D}is a 3D scattered point feature, and a

_{1D}+ a

_{2D}+ a

_{3D}= 1. Using these dimensional features of a point cloud, we can classify the point clouds as linear, planar, or 3D. A point cloud is linear when a

_{1D}is the largest and λ

_{1}>> λ

_{2}, λ

_{3}. A point cloud is planar when a

_{2D}is the largest and λ

_{1}, λ

_{2}>> λ

_{3}. A point cloud is 3D when a

_{3D}is the largest and λ

_{1}≈ λ

_{2}≈ λ

_{3}. This classification of the points using dimensional features allows us to remove the table points (Figure 3d).

#### 2.2.2. Pose Normalization

**e**

_{g1},

**e**

_{g2}, and

**e**

_{g3}) and the eigenvectors of the seed point cloud (

**e**

_{v1},

**e**

_{v2}, and

**e**

_{v3}) are obtained. Then the coordinate rotation matrix

**R**= [

**r**

_{1},

**r**

_{2},

**r**

_{3}] can be calculated, where

**r**

_{1}=

**e**

_{v1}×

**e**

_{g2}×

**e**

_{g2},

**r**

_{2}=

**e**

_{g3}and

**r**

_{3}=

**e**

_{v1}×

**e**

_{g2}.

#### 2.2.3. 3D Reconstruction

_{1}, D

_{2}, …, D

_{20}, are obtained by cutting PC into 20 pieces along the Y-axis, as shown in Figure 5b. Here, PC = {D

_{1}, D

_{2}, …, D

_{20}}. Then each point cloud (D

_{i}) in PC is detected by the axis-aligned bounding box (AABB box) [42], as shown in Figure 5c. The length (l) and width (w) of the box are obtained and used to compute the box area a = lw. A series of cross-sectional AABB box area values, a

_{1}, a

_{2}, …, a

_{20}, can be obtained, as shown in Figure 6. Then the position of the point cloud with the maximum AABB box area is the position of the symmetry plane. As shown in Figure 5d, the blue plane parallel to the XOZ plane is the symmetry plane.

_{1}, PC

_{2}}, where PC

_{1}is the point cloud with the values of y greater than or equal to the symmetry plane (the magenta point cloud in Figure 5e) and PC

_{2}is the point cloud with the values of y smaller than the symmetry plane (the yellow point cloud in Figure 5e). The mirror point cloud of PC

_{1}based on the symmetry plane is PM (the blue point cloud in Figure 5f). Then the 3D reconstructed seed point cloud is PR = {PC

_{1}, PM}. It is worth noting that the center of the scanned point cloud and the real geometric center of the seed do not overlap due to the lack of seed bottom data during scanning. Therefore, the reconstructed point cloud is centered (Figure 5g) so that the geometric center of the seed overlaps with the origin of the coordinate system. Here, the recentered point cloud is denoted as PR’.

#### 2.2.4. Trait Estimation

_{i}) is the projected volume of the i-th triangle. The projected volume of a triangle can be seen as a convex pentahedron. Supposing a projection plane that does not intersect with all triangles in the mesh model, the projected volume is the volume of the convex pentahedron enclosed by the triangles and the projection plane. As shown in Figure 7b, a convex pentahedron, P

_{1}P

_{2}P

_{3}P

_{01}P

_{02}P

_{03}, can be divided into three tetrahedrons, and the volume of the convex pentahedron is:

_{1}, P

_{2}, and P

_{3}are the three vertices of the i-th triangle, and P

_{01}, P

_{02}, and P

_{03}are the projection vertices of P

_{1}, P

_{2}, and P

_{3}on the projection plane. If (x

_{1}, y

_{1}, z

_{1}), (x

_{2}, y

_{2}, z

_{2}), (x

_{3}, y

_{3}, z

_{3}), and (x

_{4}, y

_{4}, z

_{4}) are four vertices of a tetrahedron, the volume of the tetrahedron can be calculated by:

_{i}is the area of the i-th triangle.

#### 2.3. Accuracy Analysis

_{_scan}) and segmentation accuracy (R

_{_seg}) are calculated as follows:

_{1}, N

_{2}, and N

_{3}are the numbers of total seeds, scanned seeds, and automatically extracted seeds, respectively.

_{closest}(P

_{i}, P

_{mj}) is the distance between the true point P

_{i}and the closest reconstructed point P

_{mj}. The value of d

_{closest}(P

_{i}, P

_{mj}) can reflect the deviation between the true point cloud and the reconstructed point cloud. If the point cloud is perfectly symmetrical, then P

_{i}and P

_{mj}are completely coincident, and d

_{closest}(P

_{i}, P

_{mj}) = 0.

## 3. Results

#### 3.1. Visualization of Scanning and Segmentation Results

#### 3.2. Visualization of 3D Reconstruction

#### 3.3. Results of Trait Estimation

#### 3.4. Time Cost

## 4. Discussion

#### 4.1. Accuracy of Data Scanning and Segmentation

#### 4.2. Accuracy of 3D Reconstruction

#### 4.3. Comparison of Surface Reconstruction Methods

#### 4.4. Accuracy of Trait Estimation

^{2}of these kernel traits are presented in detail. The average absolute measurement accuracy and root mean square error are in submillimeter, the average relative measurement accuracy is within 3%, and R

^{2}is above 0.9983 for the 11 morphological traits. The average relative measurement accuracy is within 4%, and R

^{2}for the 11 morphological traits is above 0.8343 for 11 scale factors and 12 shape factors. The experiments show that the measurement accuracy of the proposed method is comparable to previous work in this area [6,44,50]. Moreover, the proposed method shows the viability and effectiveness of automatic estimation and batch extraction of seeds’ geometric parameters, especially their 3D traits.

#### 4.5. Advantages, Limitations, Improvements, and Future Work

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

## Appendix B

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**Figure 2.**Data acquisition process: (

**a**) data scanning using the RigelScan Elite scanner, (

**b**) details of soybean scanning (blue laser crosses are laser beams, and white points are marker points), and (

**c**) real-time rendering visualization of the obtained soybean point clouds.

**Figure 3.**The process of single-seed segmentation: (

**a**) the scanned point cloud of the soybean seeds, (

**b**) the removal of table points after RANSAC plane detection, (

**c**) the clusters after Euclidean segmentation, (

**d**) the clusters after dimensional feature detection, and (

**e**) single-seed segmentation result of several samples (the incomplete scanned point cloud without seed data facing the table).

**Figure 4.**Pose normalization. The red (

**a**) and blue (

**b**) point clouds are the point cloud before and after rotation in the world coordinate system with the viewpoint (4, 1, 40). The red-, green-, and blue-axis are the X-, Z-, and Y-axis, respectively.

**Figure 5.**The 3D model reconstruction process: (

**a**) the scanned point cloud after pose normalization; (

**b**) the sliced point clouds; (

**c**) the AABB box of one sliced point cloud; (

**d**) the symmetry plane; (

**e**) the point clouds on both sides of the symmetry plane; (

**f**) the reconstructed point cloud; (

**g**) the centered reconstructed point cloud; and (

**h**–

**j**) the wireframe, triangle mesh, and surface visualization of the soybean seed’s 3D model built by the Poisson surface reconstruction method.

**Figure 6.**The symmetry plane detection based on the box area of the sliced point clouds. The position of the red point with the maximum box area is the position of the symmetry plane.

**Figure 7.**Visualization of the morphological traits of one soybean seed sample: (

**a**) the triangulated Poisson mesh, (

**b**) the projected volume of a triangle, (

**c**) the AABB box, (

**d**) the horizontal profile, (

**e**) the transverse profile, and (

**f**) the longitudinal profile.

**Figure 8.**Visualization of scanning and segmentation results: (

**a**) legume seeds on the table ready for data scanning, (

**b**) rendered visualization of the obtained point clouds, (

**c**) detailed display of the red box area in (

**b**), (

**d**) segmentation results, and (

**e**) detailed display of the red box area in (

**d**).

**Figure 9.**Partial visualization of 3D reconstruction results. From first to last, the rows are soybean, pea, black bean, red bean, and mung bean seeds, respectively.

**Figure 11.**Reconstructed point clouds (magenta point clouds) and real scanned point clouds (yellow point clouds). From left to right are soybean, pea, black bean, red bean, and mung bean seeds, respectively.

**Figure 12.**Average reconstruction errors and average standard deviations of soybeans, peas, black beans, red beans, and mung beans, respectively.

**Figure 13.**Surface reconstruction results. Each column shows a type of seed, from left to right: soybeans, peas, black beans, red beans, and mung beans. The rows show the mesh built by Poisson surface reconstruction, greedy triangulation, and marching cube surface reconstruction from top to bottom.

**Figure 15.**Three-dimensional models of one peanut obtained manually (

**a**) and reconstructed by our method (

**b**).

Types | Parameters | Types | Parameters |
---|---|---|---|

Weight | 1.0 kg | Accuracy | 0.010 mm |

Volume | 310 × 147 × 80 mm | Field depth | 550 mm |

Scanning area | 600 × 550 mm | Transfer method | USB 3.0 |

Speed | 1,050,000 times/s | Work temperatures | −20–40 °C |

Light | 11 laser crosses (+1 + 5) | Work humidity | 10–90% |

Light security | ΙΙ | Outputs | Point clouds/3D mesh |

NO. | Traits | Sym. |
---|---|---|

1 | Volume | V |

2 | Surface area | S |

3 | Length | L |

4 | Width | W |

5 | Thickness | H |

6 | Horizontal profile perimeter | C_{1} |

7 | Transverse profile perimeter | C_{2} |

8 | Longitudinal profile perimeter | C_{3} |

9 | Horizontal profile cross-section area | A_{1} |

10 | Transverse profile cross-section area | A_{2} |

11 | Longitudinal profile cross-section area | A_{3} |

NO. | Scale Factors | NO. | Shape Factors |
---|---|---|---|

1 | W/L | 1 | XZsf_{1} = 4πA_{1}/C_{1}^{2} |

2 | H/L | 2 | XZsf_{2} = A_{1}/L^{3} |

3 | H/W | 3 | XZsf_{3} = 4A_{1}/πL^{2} |

4 | L/S | 4 | XZsf_{4} = A_{1}/LW |

5 | L/V | 5 | XYsf_{1} = 4πA_{2}/C_{2}^{2} |

6 | W/S | 6 | XYsf_{2} = A_{2}/L^{3} |

7 | W/V | 7 | XYsf_{3} = 4A_{2}/πL^{2} |

8 | H/S | 8 | XYsf_{4} = A_{2}/LW |

9 | H/V | 9 | YZsf_{1} = 4πA_{3}/C_{3}^{2} |

10 | A/V | 10 | YZsf_{2} = A_{3}/L^{3} |

11 | V/LWH | 11 | YZsf_{3} = 4A_{3}/πW^{2} |

W/L | 12 | YZsf_{4} = A_{3}/WH |

Seeds | Points | T_scan | T_p |
---|---|---|---|

Soybeans | 2,390,308 | 220 | 20.43 |

Peas | 2,461,206 | 228 | 20.13 |

Black beans | 2,307,619 | 234 | 19.98 |

Red beans | 2,229,617 | 250 | 16.93 |

Mung beans | 2,150,969 | 265 | 16.24 |

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**MDPI and ACS Style**

Huang, X.; Zheng, S.; Zhu, N.
High-Throughput Legume Seed Phenotyping Using a Handheld 3D Laser Scanner. *Remote Sens.* **2022**, *14*, 431.
https://doi.org/10.3390/rs14020431

**AMA Style**

Huang X, Zheng S, Zhu N.
High-Throughput Legume Seed Phenotyping Using a Handheld 3D Laser Scanner. *Remote Sensing*. 2022; 14(2):431.
https://doi.org/10.3390/rs14020431

**Chicago/Turabian Style**

Huang, Xia, Shunyi Zheng, and Ningning Zhu.
2022. "High-Throughput Legume Seed Phenotyping Using a Handheld 3D Laser Scanner" *Remote Sensing* 14, no. 2: 431.
https://doi.org/10.3390/rs14020431