# Broadacre Crop Yield Estimation Using Imaging Spectroscopy from Unmanned Aerial Systems (UAS): A Field-Based Case Study with Snap Bean

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## Abstract

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## 1. Introduction

- Asses yield prediction of snap bean, at various points during the growing season, using hyperspectral imagery and descriptive models;
- Identify discriminating spectral features explaining yield; and
- Evaluate the most accurate time (growth period) for yield prediction, prior to harvest.

## 2. Methods

#### 2.1. Study Area

#### 2.2. Assessment of Plant Growth Characteristics

#### 2.3. Data Collection

#### 2.4. Data Preprocessing

#### 2.4.1. Calibration to Reflectance

#### 2.4.2. Vegetation Detection

`thresh_initial`), where

`thresh_initial`was fed to global thresholding algorithm [58] to compute the final threshold (

`thresh_final`). From the RENDVI image, values above and below the calculated

`thresh_final`were chosen as vegetation and background, respectively, and a mask was created. A median blur filter of size $7\times 7$ was used to remove any unwanted noise from the generated mask. Finally, the generated mask was applied to all plots.

#### 2.4.3. Spectral Denoising

#### 2.5. Data Analysis

#### 2.5.1. Jostar: Feature Selection Library in Python

#### 2.5.2. Feature Selection Procedure

`max_evals`= 200 as the maximum number of evaluations, to search the defined space and

`n_iter`= 20 iterations for the optimization model, at each evaluation. Subsequently, the test mode is run with the optimal parameter identified from the param. tuning mode, with

`n_iter`= 100. For both modes, the following steps were conducted: (i) PLSR was selected as the regressor for this study’s objective, given its capability for handling multicollinearity and its low computational cost; (ii) GA, SA, PSO, and ACO, embedded in Jostar, were selected as four feature selection optimization models; (iii) the defined number of selected features was set as five (i.e., ${n}_{f}=5$) for all sets and cross-validation Leave-One-Out $RMSE$ value was selected as the scoring parameter and minimized for (

`weight`= −1); (iv) the top 20 decorrelated features were retained, in order to ensure a consistent search space across all tests; (v) all features were scaled to the 0–1 range; (vi) the optimization model was then “fit” with the defined arguments and values. The test mode takes advantage of averaging output rankings from the four optimization models. The last step allows for a more holistic ranking, since there is a possibility of an optimization algorithm falling in a local minimum. The defined search spaces for the hyperparameter tuning step are tabulated in Table 2. More information on each parameter’s explanation can be found in Jostar’s documentation.

#### 2.6. Software

## 3. Results

#### 3.1. Descriptive Statistics

#### 3.2. Pod Weight

#### 3.2.1. 2019 Data Set

#### 3.2.2. 2020 Data Set

#### 3.3. Seed Length

#### 3.3.1. 2019 Data Set

#### 3.3.2. 2020 Data Set

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ACO | ant colony optimization |

DAP | days after planting |

ELM | empirical line method |

FWHM | full-width-half-maximum |

GA | genetic algorithm |

GDP | gross domestic product |

GPU | graphics processing unit |

GSD | ground sampling distance |

KNN | K-nearest neighbors |

LiDAR | light detection and ranging |

LRS | plus-L minus-R |

MAP | minimum average partial |

NIR | near infrared |

NSGAII | non-dominated sorting genetic algorithm-II |

PA | precision agriculture |

PC | principal component (PC) |

PCA | principal component analysis |

PLSR | partial least squares regression |

PSO | particle Swarm Optimization |

${R}^{2}$ | coefficient or determination |

RE | red edge |

RENDVI | red-edge normalized difference vegetation index |

RF | random forests |

RFE | recursive feature elimination |

$RMSE$ | root mean square error |

RS | remote sensing |

SA | simulated annealing |

SAM | spectral angle mapper |

SBS | sequential backward search |

SFS | sequential forward search |

SVR | support vector regression |

UAS | unmanned aerial systems |

VIs | vegetation indices |

VIS | visible |

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**Figure 1.**RGB representation of the data and the designated plots for (

**a**) 2019 and (

**b**) 2020 experimental designs. Note the plots’ bounds in blue.

**Figure 2.**Outlined plots and matching cultivars along with field and plot design dimensions for (

**a**) 2019 and (

**b**) 2020 experimental designs. Listed here are the Venture (large cultivar variety 1; L1), Huntington (large cultivar variety 2; L2), Colter (four sieve cultivar 1; F1), Cabot (four sieve cultivar 2; F2), Flavor-sweet (whole bean cultivar 1; W1), and Denver (whole bean cultivar 2; W2). Schematics are not to scale.

**Figure 3.**Maturity gauge used for determining seed length and pods’ sieve sizes. On the upper part, pod sieve size is determined by sliding pods across the cavities. On the bottom part, ten seeds are put alongside each other and the total length is recorded.

**Figure 4.**Flowchart of the steps employed for preprocessing raw hyperspectral data to evaluate snap bean yield components.

**Figure 6.**Ground truth yield values for pod weight and seed length for 2019 and 2020 data: (

**a**) pod weight 2019 data, (

**b**) pod weight 2020 data, (

**c**) seed length 2019 data, and (

**d**) seed length 2020 data.

**Figure 7.**A comparison of signal-to-noise (SNR) across wavelengths before and after spectral denoising. Note the increase in the average estimated SNR.

**Figure 8.**The first 10 principal components of a random flight from the 2019 data set. Please note that the first few PC’s contribute to the largest amount explained variability.

**Figure 9.**Results for coefficient of determination (${R}^{2}$) for snap bean 2019 pod weight data set, for (

**a**) early and (

**b**) late harvest stage, as determined via two different vegetation approaches, SAM and RENDVI, as tested on PLSR.

**Figure 10.**Regression results for snap bean 2019 data set on (

**a**) the ACO-RENDVI model at 46 DAP for the early harvest stage and (

**b**) the SA-SAM model at 48 DAP for the late harvest stage.

**Figure 11.**Snap bean pod weight 2019 data set average rankings at (

**a**) the early harvest stage and (

**b**) the late harvest stage, based on the SAM vegetation model. The corresponding days after planting (DAP) and heat unit for the collected data are shown to the left of each ranking belt, while the top five features, with the first one having the highest score, are listed to the right.

**Figure 12.**Coefficient of determination (${R}^{2}$) results for snap bean 2020 pod weight data set, for (

**a**) early and (

**b**) the late harvest stage via PLSR model and two different vegetation approaches, SAM and RENDVI.

**Figure 13.**Regression results for snap bean 2020 data set on (

**a**) the ACO-SAM model at 44 DAP for early harvest stage and (

**b**) the ACO-SAM model at 58 DAP for the late harvest stage.

**Figure 14.**Snap bean pod weight the 2020 data set average rankings across all four optimization models for SAM model at (

**a**) the early harvest stage and (

**b**) the late harvest stage. The corresponding days after planting (DAP) and heat unit for the collected data are shown to the left of each ranking belt, while the top five features, with the first one having the highest score, are listed to the right.

**Figure 15.**Results for the coefficient or determination (${R}^{2}$) for snap bean 2019 seed length data set, for (

**a**) the early and (

**b**) the late harvest stage, via two different vegetation approaches, namely SAM and RENDVI, as tested via PLSR.

**Figure 16.**Regression results for snap bean 2019 seed length data set on (

**a**) the GA-RENDVI model at 50 DAP for the early harvest stage and (

**b**) the SA-RENVI model at 56 DAP for the late harvest stage.

**Figure 17.**Snap bean seed length 2019 average rankings across all four optimization models for SAM model at (

**a**) the early harvest stage and (

**b**) the late harvest stage. The corresponding days after planting (DAP) and heat unit for the collected data are shown to the left of each ranking belt, while the top five features, with the first one having the highest score, are listed to the right.

**Figure 18.**Coefficient or determination metric for snap bean 2020 seed length data set, for (

**a**) early and (

**b**) the late harvest stage via two SAM and RENDVI, tested with PLSR.

**Figure 19.**Regression results for snap bean 2020 seed length data set on (

**a**) SA-SAM model at 58 DAP for the early harvest stage and (

**b**) ACO-SAM model at 58 DAP for the late harvest stage.

**Figure 20.**The snap bean 2020 seed length average rankings across for SAM models at (

**a**) the early and (

**b**) the late harvest stages. The corresponding days after planting (DAP) and heat unit for the collected data are shown to the left of each ranking belt, while the top five features, with the first one having the highest score, are listed to the right.

**Figure 21.**A comparison of the vegetation detection results for cases where (

**a**) vegetation canopy and the background are distinguishable and (

**b**) canopy closure has commenced, i.e., a dense canopy is present.

**Table 1.**Growth calendar of 2019 and 2020 experimental designs along with the captured ground sampling distance (GSD) of a snap bean field in Geneva, New York, USA. Please note that the first date is the sowing date and no data were collected.

Model | Date | Stage | Days after Planting (DAP) | Heat Unit (${}^{\circ}$) * | GSD (cm) |
---|---|---|---|---|---|

2019 | 06/27/2019 | Sowing | 0 | 0 | N/A |

08/01/2019 | Flowering | 35 | 794 | 3 | |

08/05/2019 | Flowering | 39 | 865 | 3 | |

08/12/2019 | Pod formation | 46 | 997 | 1.5 | |

08/14/2019 | Pod formation | 48 | 1040 | 3 | |

08/16/2019 | Pod formation | 50 | 1074 | 3 | |

08/20/2019 | Pod formation (early harvest) | 54 | 1158 | 3 | |

08/22/2019 | Pod formation (late harvest) | 56 | 1205 | 3 | |

2020 | 06/27/2020 | Sowing | 0 | 0 | N/A |

07/28/2020 | Budding | 31 | 760 | 3 | |

07/31/2020 | Flowering | 34 | 822 | 3 | |

08/06/2020 | Flowering | 40 | 945 | 3 | |

08/10/2020 | Pod formation | 44 | 1022 | 3 | |

08/14/2020 | Pod formation | 48 | 1116 | 3 | |

08/21/2020 | Pod formation | 55 | 1239 | 3 | |

08/24/2020 | Pod formation (early harvest) | 58 | 1306 | 3 | |

08/26/2020 | Pod formation (late harvest) | 60 | 1346 | 3 |

**Table 2.**Optimization models, corresponding parameters, and associated value ranges identified for hyperparameter tuning.

Optimization Model | Parameter | Description | Sampling Method | Low Bound | High Bound |
---|---|---|---|---|---|

GA ${}^{1}$ | $Cros{s}_{perc}$ | Crossover percentage | Uniform logarithmic | ${10}^{-2}$ | 0.5 |

$Mu{t}_{perc}$ | Mutation percentage | Uniform logarithmic | ${10}^{-2}$ | 0.2 | |

$Mu{t}_{rate}$ | Mutation rate | Uniform logarithmic | ${10}^{-2}$ | 0.2 | |

$\beta $ | Selection pressure | Random integer | 1 | 10 | |

${N}_{pop}$ | Population size | Random integer | 20 | 200 | |

SA ${}^{2}$ | $\alpha $ | Cooling factor | Uniform logarithmic | 0.8 | 0.99 |

${T}_{0}$ | Initial temperature | Uniform logarithmic | ${10}^{-1}$ | 500 | |

${N}_{iter-sub}$ | Number of sub-iterations | Random Integer | 20 | 200 | |

PSO ${}^{3}$ | $\alpha $ | Information elicitation factor | Uniform logarithmic | ${10}^{-5}$ | 0.5 |

${C}_{1}$ | Cognitive parameter | Uniform logarithmic | ${10}^{-2}$ | 2 | |

${C}_{2}$ | Social parameter | Uniform logarithmic | ${10}^{-2}$ | 2 | |

W | Inertia weight | Uniform logarithmic | ${10}^{-2}$ | 1.2 | |

${W}_{damp}$ | Inertia weight damping factor | Uniform logarithmic | ${10}^{-2}$ | 0.5 | |

${N}_{pop}$ | Number of particles | Random integer | 20 | 200 | |

ACO ${}^{4}$ | $\alpha $ | Information elicitation factor | Uniform logarithmic | ${10}^{-5}$ | 0.5 |

$\rho $ | Pheromone evaporation coefficient | Uniform logarithmic | ${10}^{-5}$ | 0.5 | |

${\tau}_{0}$ | Initial pheromone intensity | Uniform logarithmic | ${10}^{-5}$ | 1 | |

Q | Pheromone intensity | Uniform logarithmic | ${10}^{-5}$ | 1 | |

${N}_{ant}$ | Number of ants | Random integer | 20 | 200 | |

$\beta $ | Meta-heuristic factor | Random integer | 1 | 5 |

**Table 3.**Snap bean outperforming models and their corresponding prominent spectral regions with respect to DA (“Zones”) identified distinguishing wavelengths, and the drop in accuracy (“Dip”) in terms of temporal variability.

Data Set | Yield Indicator | Across Yield Indicator WL (nm) Similarity | |||||
---|---|---|---|---|---|---|---|

Pod Weight | Seed Length | ||||||

Zone (DAP) | WL ${}^{\mathit{a}}$ (nm) | Dip | Zone (DAP) | WL (nm) | Dip | ||

2019 early | Blue: E. ${}^{b}$ 50 Green: T. ${}^{c}$ Red: E. 39, 46 RE: E. 48, 54 NIR: NA ${}^{d}$ | 3x: 451 2x: 478, 505, 516, 525 | at 39 DAP None | Blue: E. 39, 48 Green: E. 50, 54 Red: T. RE: E. 35, 48 NIR: O. ^{e} 50, 54 | 2x: 451, 585, 659, 710, 716 | at 40 DAP at 55 DAP | 451 |

2019 late | Blue: E. 35, 50 Green: T. Red: E. 39 RE: E. 46, 54, 56 NIR: O. 35, 56 | 4x: 525 3x: 451 2x: 505, 541, 659, 759, 819 | None at 56 DAP | Blue: E. 35, 50 Green: E. 54, 56 Red: E. 54 RE: O. 48 NIR: O. 54 | 3x: 451, 721 2x: 583, 585, 659, 716 | at 46 DAP at 56 DAP | 451, 659 |

2020 early | Blue: T. Green: E. 44 Red: E. 58 RE: T. NIR: NA | 5x: 451, 759 3x: 523 2x: 518, 607, 647 | at 34 DAP at 55 DAP | Blue: T. Green: E. 58 Red: E. 44, 55, 58 RE: E. 31, 48 NIR: O. 58 | 6x: 451 2x: 494, 518 | at 44 DAP None | 451, 518 |

2020 late | Blue: E. 58 Green: E. 44 Red: E. 40 RE: E. 31, 55, 60 NIR: NA | 4x: 451, 756 2x: 474, 500, 525, 654, 707 | at 34 DAP at 60 DAP | Blue: T. Green: E. 58 Red: E. 58, 60 RE: E. 31, 34 NIR: O. 58 | 7x: 451 2x: 494, 518, 670, 699, 759 | at 44 DAP at 60 DAP | 451, ∼500, ∼520, ∼700, ∼760 |

Across years WL (nm) similarity | 451, ∼500, ∼ 520, ∼650, ∼760 | 451, ∼520, ∼500, ∼585, ∼660, ∼720 | ∼451, ∼500, ∼520, ∼650, ∼700, ∼760 |

^{e}O.: Only.

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**MDPI and ACS Style**

Hassanzadeh, A.; Zhang, F.; van Aardt, J.; Murphy, S.P.; Pethybridge, S.J.
Broadacre Crop Yield Estimation Using Imaging Spectroscopy from Unmanned Aerial Systems (UAS): A Field-Based Case Study with Snap Bean. *Remote Sens.* **2021**, *13*, 3241.
https://doi.org/10.3390/rs13163241

**AMA Style**

Hassanzadeh A, Zhang F, van Aardt J, Murphy SP, Pethybridge SJ.
Broadacre Crop Yield Estimation Using Imaging Spectroscopy from Unmanned Aerial Systems (UAS): A Field-Based Case Study with Snap Bean. *Remote Sensing*. 2021; 13(16):3241.
https://doi.org/10.3390/rs13163241

**Chicago/Turabian Style**

Hassanzadeh, Amirhossein, Fei Zhang, Jan van Aardt, Sean P. Murphy, and Sarah J. Pethybridge.
2021. "Broadacre Crop Yield Estimation Using Imaging Spectroscopy from Unmanned Aerial Systems (UAS): A Field-Based Case Study with Snap Bean" *Remote Sensing* 13, no. 16: 3241.
https://doi.org/10.3390/rs13163241