# Virtual Laser Scanning Approach to Assessing Impact of Geometric Inaccuracy on 3D Plant Traits

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## Abstract

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## 1. Introduction

- To what extent progressive inaccuracy of 3D plant reconstruction simulated by different types of geometric noise affects the resulting 3D plant traits?
- Can partially inaccurate measurements of 3D plant traits provide consistent quantitative description of plant morphology and physiology by combining them with the results of computational simulations of synthetic plant models?

## 2. Methods

#### 2.1. Modelling Platform

#### 2.2. Synthetic Plant Models

#### 2.3. Simulation Scenarios

#### 2.3.1. Virtual Laser Scanner

#### 2.3.2. Light Simulation

#### 2.3.3. Geometrical Perturbation Scenarios and Simulations

#### 2.3.4. Data Analysis

**Height.**Total plant height in metre defined as highest Z-coordinate of the point cloud above the ground.**PCA1.**The length of the largest PCA axis of the scanned point cloud in [m].**PCA2.**The length of the smallest PCA axis of the scanned point cloud in [m]. ize Convex_Hull_Volume. The 3D volume [m${}^{3}$] of the convex hull (Figure 5) enclosing all points of the scanned point cloud.

**Plant_AbsorbedRadiation.**Total amount of radiation absorbed by the plant structure in Watt [W].**Plant_SurfaceArea.**Total surface area [m${}^{2}$] of the plant structure, computed as a sum of areas of all single-side faces.**Visible_Plant_SurfaceArea.**The visible surface area [m${}^{2}$] is defined as the sum of areas all single-side faces that are “visible” to the virtual laser scanner and obtained an intersection with at least one virtual light ray emitted by the scanner.**Number_ScanPoints.**Total number of scanner points, i.e., number of points within the point cloud, generated by the virtual laser scanner.

## 3. Experimental Results

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Screenshots of rendered images of the four plant shoot models used within this study including (

**a**) tomato, (

**b**) arabidopsis, (

**c**) greenhouse cucumber, and (

**d**) maize.

**Figure 2.**Screenshots of the 3D tomato plant model as described in Zhang et al. [35]. (

**a**) a rendered image of the whole virtual plant (uniformly coloured), (

**b**) a detail enlargement of leaf with rank 13 with the underlying wireframe triangulation, and (

**c**) an image of a single leaflet with the overlay of the wireframe triangulation. A leaflet is modelled of eight vertical mirror symmetric arranged faces (triangles), making it in total 16 faces for one single leaflet. The whole plant consists roughly of 25.7 k vertices forming a triangulation of about 8.5 k faces.

**Figure 3.**Top- (

**a**) and side-view (

**b**) of the virtual scanner hemisphere with the synthetic 3D tomato plant model in the centre of the scene. Blue spheres indicate the position of spatial points from where the 3D scanning is performed. The scanning sphere consists of 13 layers with 25 measuring points on each layer, resulting in 325 measuring points used for each scan. The thin yellow lines—length set to 30 centimetres for visualization only—represent a small fraction of the rays used for the scanning.

**Figure 4.**Top-view visualization of the tomato plant model for the three thinning scenarios: (

**a**) the original complete plant, (

**b**) random thinning, (

**c**) inside to outside thinning, and (

**d**) outside to inside thinning, all at $30\%$.

**Figure 5.**Visualization of the scanned point cloud (green dots) of the complete (initial) plant and the convex hull drawn as transparent blue for all four plant species used in this study: (

**a**) tomato, (

**b**) arabidopsis, (

**c**) greenhouse cucumber, and (

**d**) maize.

**Figure 6.**Visualization of the hit density (ray hits/mm${}^{2}$) on the example of the full tomato model at zero perturbation in (

**a**) top-, and (

**b**) side-view, as well the the normalized histogram in sub-figure (

**c**). Each triangle of the mesh model is coloured according to the number of rays that had hit is and the resulting hit density.

**Figure 7.**Visualization of the surrounding half ellipsoid (

**a**), that is used to estimate the relation between triangle area and number of hits. As shown in (

**b**) the hit density per square millimeter triangle area [hit/mm${}^{2}$] is quite homogenise around the surface of the ellipsoid with a slight higher concentration on the north pole and a bit lower at the south pole as expected from the used geometry from the hemispherical shape of the scanner dome. The chart in (

**c**) shows the relation between the number of hits per triangle versus the area of it.

**Figure 8.**Statistics of hit density of half-ellipsoid triangles. Visualization of the median and mean hit density along 10 area classes from zero to a maximum of 250 mm${}^{2}$ and a bin width of 25 mm${}^{2}$. The low variance between the individual mean and median values to the overall values proves that there is—as expected—a constant relation relation between the size of the triangles and the observed hit density. The hit density of a “fully visible” triangle is ${\rho}_{m}=0.0959$ hits/mm${}^{2}$.

**Figure 9.**Summary of the simulated dependency of normalized phenotypic traits on the percentage of plant area loss for four different plant models and three different area perturbation scenarios including random (red), outside-to-inside (blue), and inside-to-outside (green) perturbation scenarios. The last row shows the dependency of the normalized visible plant area on the percentage of the total area loss for four plant models and the three alternative perturbation scenarios.

**Figure 10.**Visualization of the relative visible area for each perturbation scenario in different plant types.

**Figure 12.**Example of analysis and visualization of smoothness of tomato point clouds (PC). (

**a**) Histograms of smoothness factor (SF) from Equation (1)) of original and randomly perturbed tomato point clouds. The arrow in the histogram plot indicates the elevation of amount of corner/edge points with a larger smoothness factor (SF) in the randomly perturbed model. (

**b**) Visualization of original vs. randomly perturbed full and boundary point clouds of the tomato plant. Boundary points were detected using the smoothness factor values larger than 0.5. The colour map indicates the SF values ranging in $[0,\phantom{\rule{3.33333pt}{0ex}}1]$.

**Figure 13.**Exemplary comparison of point cloud smoothness of different plants (A—arabidopsis, C—cucumber, M—maize, T—tomato) in dependency on random model perturbation. (

**a**) Average smoothness factor (SF) of different plants, (

**b**) stdev of SF distribution in different plants, (

**c**) fraction of boundary points in % detected by thresholding of SF values larger than >0.5, and (

**d**) t-test values computed from comparison of SF distributions of randomly perturbed plant point clouds vs. original (unperturbed) models.

**Table 1.**Summary of the plant model properties. Starting from the number of geometric primitive objects of the original 3D model, i.e., number of leaves and internodes and morphological traits like plant dimensions, to the number of vertices and faces of the triangulated mesh.

Plant | Number | Number of | Max | Max | Number | Number | Mean Face |
---|---|---|---|---|---|---|---|

Model | of Leaves | Internodes | Height [m] | Radius [m] | of Vertices | of Faces | Area [mm${}^{2}$] |

Tomato | 21 | 21 | 1.7 | 0.43 | 25,674 | 8558 | 142.53 |

Arabidopsis | 10 | 11 | 0.03 | 0.06 | 3600 | 1200 | 189.92 |

Maize | 14 | 15 | 2.5 | 0.97 | 15,450 | 5150 | 699.83 |

Cucumber | 17 | 18 | 2.0 | 0.43 | 5793 | 1931 | 12.74 |

**Table 2.**Overview of the faces (F) and areas (A) that are “visible” to laser scanner in original (unperturbed) plant models as relative ratios to their known full-plant values, i.e., ${F}_{vis}/{F}_{all}$ re. ${A}_{vis}/{A}_{all}$.

Species | Visible Faces [%] | Visible Area [%] |
---|---|---|

Tomato | 0.59 | 0.78 |

Arabidopsis | 0.79 | 0.81 |

Maize | 0.67 | 0.94 |

Cucumber | 0.48 | 0.94 |

**Table 3.**Summary of the linear correlation between the phenotypic features from Figure 11 and the visible plant area for all three geometry perturbation scenarios (random, inside-to-outside (i2o), and outside-to-inside (o2i)) in the range of 0–30% including correlation coefficients ($\rho $) and corresponding p-values. $NaN$ entries indicate a uncorrelated relationship between a feature and the visible plant area.

Height | PCA1 | PCA2 | Volume | Absorption | Area | |
---|---|---|---|---|---|---|

$\mathit{\rho}$, p-Value | $\mathit{\rho}$, p-Value | $\mathit{\rho}$, p-Value | $\mathit{\rho}$, p-Value | $\mathit{\rho}$, p-Value | $\mathit{\rho}$, p-Value | |

Tomato | ||||||

Random | NaN, NaN | −0.75, $8.11\times {10}^{-4}$ | 0.87, $1.10\times {10}^{-5}$ | 0.94, $5.88\times {10}^{-8}$ | 1.00, $4.75\times {10}^{-19}$ | NaN, NaN |

i2o | NaN, NaN | 0.98, $1.26\times {10}^{-11}$ | 0.95, $2.57\times {10}^{-8}$ | 0.78, $3.46\times {10}^{-4}$ | 0.99, $1.90\times {10}^{-13}$ | 1.00, $2.00\times {10}^{-103}$ |

o2i | NaN, NaN | 0.98, $6.60\times {10}^{-12}$ | 0.98, $6.00\times {10}^{-12}$ | 1.00, $4.57\times {10}^{-18}$ | 1.00, $3.26\times {10}^{-20}$ | 1.00, $9.13\times {10}^{-107}$ |

Maize | ||||||

Random | NaN, NaN | 0.80, $1.69\times {10}^{-4}$ | 0.87, $1.15\times {10}^{-5}$ | 0.94, $9.83\times {10}^{-8}$ | 1.00, $3.03\times {10}^{-25}$ | 1.00, $4.98\times {10}^{-102}$ |

i2o | NaN, NaN | 0.95, $1.93\times {10}^{-8}$ | 0.87, $1.28\times {10}^{-5}$ | 0.97, $5.40\times {10}^{-10}$ | 0.99, $7.83\times {10}^{-14}$ | 1.00, $9.13\times {10}^{-107}$ |

o2i | NaN, NaN | 0.99, $3.19\times {10}^{-13}$ | 0.92, $3.67\times {10}^{-7}$ | 1.00, $1.34\times {10}^{-23}$ | 1.00, $1.12\times {10}^{-20}$ | 1.00, 0.00 |

Cucumber | ||||||

Random | NaN, NaN | −0.85, $3.44\times {10}^{-5}$ | −0.73, $1.34\times {10}^{-3}$ | 0.91, $8.62\times {10}^{-7}$ | 1.00, $4.25\times {10}^{-21}$ | NaN, NaN |

i2o | NaN, NaN | 0.43, $9.76\times {10}^{-2}$ | 0.42, $1.02\times {10}^{-1}$ | 0.75, $7.96\times {10}^{-4}$ | 0.98, $1.49\times {10}^{-11}$ | 1.00, $4.36\times {10}^{-106}$ |

o2i | NaN, NaN | 0.99, $1.18\times {10}^{-13}$ | 1.00, $4.57\times {10}^{-16}$ | 1.00, $1.97\times {10}^{-21}$ | 1.00, $2.20\times {10}^{-20}$ | 1.00, 0.00 |

Arabidopsis | ||||||

Random | 0.71, $1.91\times {10}^{-3}$ | 0.89, $3.51\times {10}^{-6}$ | 0.83, $5.80\times {10}^{-5}$ | −0.77, $5.00\times {10}^{-4}$ | 1.00, $2.70\times {10}^{-22}$ | 1.00, 0.00 |

i2o | NaN, NaN | −0.88, $5.59\times {10}^{-6}$ | 0.87, $9.27\times {10}^{-6}$ | 0.73, $1.44\times {10}^{-3}$ | 0.95, $1.74\times {10}^{-8}$ | 1.00, $7.14\times {10}^{-109}$ |

o2i | 0.82, $1.07\times {10}^{-4}$ | 0.98, $6.08\times {10}^{-12}$ | 0.99, $1.04\times {10}^{-14}$ | 1.00, $1.18\times {10}^{-21}$ | 1.00, $3.57\times {10}^{-23}$ | 1.00, 0.00 |

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**MDPI and ACS Style**

Henke, M.; Gladilin, E.
Virtual Laser Scanning Approach to Assessing Impact of Geometric Inaccuracy on 3D Plant Traits. *Remote Sens.* **2022**, *14*, 4727.
https://doi.org/10.3390/rs14194727

**AMA Style**

Henke M, Gladilin E.
Virtual Laser Scanning Approach to Assessing Impact of Geometric Inaccuracy on 3D Plant Traits. *Remote Sensing*. 2022; 14(19):4727.
https://doi.org/10.3390/rs14194727

**Chicago/Turabian Style**

Henke, Michael, and Evgeny Gladilin.
2022. "Virtual Laser Scanning Approach to Assessing Impact of Geometric Inaccuracy on 3D Plant Traits" *Remote Sensing* 14, no. 19: 4727.
https://doi.org/10.3390/rs14194727