# Genetic Programming Approach for the Detection of Mistletoe Based on UAV Multispectral Imagery in the Conservation Area of Mexico City

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## Abstract

**:**

## 1. Introduction

## 2. Study Area

## 3. Materials and Methods

#### 3.1. Multispectral Image Collection

#### 3.2. Hardware and Software

#### 3.3. Image Preprocessing

#### 3.3.1. Image Registration

#### 3.3.2. Mask and Data Set Creation

#### 3.4. Algorithm to Detect Mistletoe

#### 3.4.1. Genetic Programming for Feature Extraction

#### 3.5. Comparison Methods

## 4. Experiments and Results

#### 4.1. Experimental Setup

#### 4.2. Structural Analysis of Gp Solutions

#### 4.3. Analysis of the Best Solution

#### 4.4. Comparison with Other Methods

#### 4.5. Mistletoe Map Detection

## 5. Discussion

## 6. Conclusions and Future Work

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

## References

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**Figure 1.**Location of the study area and flight polygon distribution for Unmanned Aerial Vehicle (UAV) image collection.

**Figure 2.**Complete diagram of the operation of the algorithm to detect mistletoe in multispectral images. In the Image Transformation stage, we illustrate, as an example, the internal nodes or functions and the leaf nodes or terminals required by the Genetic Programming (GP) algorithm to implement the NDVI index.

**Figure 4.**Frequency distribution of the use of terminals in the best individuals evolved by GP. The bar diagram shows how many of the best individuals have used the corresponding terminals; i.e., the $R,G,B,REG,$ and $NIR$ bands; the line graph shows the number of times that the terminals have been used in total within the best solutions individuals.

**Figure 5.**Frequency distribution of the use of functions in the best individuals evolved by GP. The bar diagram shows how many of the best individuals have used the corresponding functions (arithmetic operators), while the line graph shows the number of times that the functions have been used in total within the best-solution individuals.

**Figure 6.**Example of the partial results obtained by applying the first factor of the best solution, shown in Equation (4), on an image. The letters (

**a**–

**g**) show the performance (visual result) of each term in the equation that is expressed below the corresponding image.

**Figure 7.**Example of the partial results obtained by applying the second factor of the best solution, shown in Equation (4), on an image. The letters (

**a**–

**g**) show the performance (visual result) of each term in the equation that is expressed below the corresponding image.

**Figure 8.**Example of the result of the best solution, shown in Equation (4), when applied on an image. The letters (

**a**–

**c**) show the performance (visual result) of each term in the equation that is expressed below the corresponding image.

**Figure 9.**Classification map of Phoradendron velutinum (P. velutinum) with the best GP algorithm. A section of the Conservation Area of Mexico City is shown, in which the detection of Phoradendron velutinum was carried out employing the best individual generated from GP (Equation (4)). The main areas with infestation of P. velutinum are shown in red and P. velutinum in situ GPS sampling points are represented by blue circles.

Polygon | Area (ha) | Flying Height (m) | GSD (cm/px) | Number of Images |
---|---|---|---|---|

1 | 31.40 | 110 | 5.8 | 474 |

2 | 46.34 | 80 | 4.2 | 1244 |

3 | 49.14 | 90 | 4.8 | 522 |

4 | 20.37 | 110 | 5.8 | 325 |

Protected Function | Input Arguments | Output Argument |
---|---|---|

Division | a, b | a (if b $=0$) |

a/b (otherwise) | ||

Square root | a | 0 (if a ≤ 0 ) |

sqrt (a) (otherwise) | ||

Base 2 | a | 0 (if a $=0$) |

Logarithm | $log2\left(abs\right($a$\left)\right)$ (otherwise) | |

Base 10 | a | 0 (if a $=0$) |

Logarithm | $log10\left(abs\right($a$\left)\right)$ (otherwise) |

Feature | Feature | ||
---|---|---|---|

Generations | 50 | Selection | Lexictour |

Population size | 100 | Elitism criteria | Keepbest |

Initialization | Rampedinit | Functions set | +, $|+|$, $|-|$, ÷, ×, ${x}^{2}$, $\sqrt{x}$, ${e}^{x}$, ${log}_{2}$, ${log}_{10}$, $Ln$, ¬, $\left|x\right|$, $\lceil x\rceil $ |

Crossover | Probability 0.7 | Terminals set | $R,G,B,REG,NIR$ |

Mutation | Probability 0.3 | Fitness function | Weighted Cohen’s Kappa |

Predicted | |||
---|---|---|---|

Infested | Other | ||

Real | Infested | 0 | 1 |

Other | 2 | 0 |

**Table 5.**Classification performance obtained by the two best and the two worst algorithms produced by our GP implementation, in comparison with the Intensive Pigment Index of Structure 2 (SIPI2), and Support Vector Machine (SVM) methods, as well as the $|R-B|$ and ${log}_{2}\left(\frac{R}{B}\right)$ terms. The first column shows the different methods. The training column shows the results of the training stage of each method employing the Weighted Cohen’s Kappa metric; in the test columns, the results corresponding to the metrics Weighted Cohen’s Kappa (${k}_{w}$), Cohen’s Kappa (k), Overall Accuracy (OA), Precision (P), and Recall (R) are listed; in the Diff column, the difference between the ${k}_{w}$ coefficients in the training and testing stages is shown.

Method | Training | Test | Diff. | ||||
---|---|---|---|---|---|---|---|

${\mathit{k}}_{\mathit{w}}$ | ${\mathit{k}}_{\mathit{w}}$ | k | OA | R | P | ||

${\mathrm{GP}}_{1}$ | 0.465 | 0.448 | 0.442 | 0.966 | 0.482 | 0.498 | −0.017 |

${\mathrm{GP}}_{2}$ | 0.436 | 0.416 | 0.395 | 0.964 | 0.389 | 0.524 | −0.021 |

${\mathrm{GP}}_{49}$ | 0.298 | 0.294 | 0.275 | 0.963 | 0.269 | 0.412 | −0.004 |

${\mathrm{GP}}_{50}$ | 0.296 | 0.282 | 0.284 | 0.952 | 0.357 | 0.319 | −0.014 |

SIPI2 | 0.0025 | −0.005 | -0.006 | 0.543 | 0.426 | 0.028 | −0.007 |

$|R-B|$ | 0.267 | 0.276 | 0.261 | 0.913 | 0.326 | 0.373 | 0.009 |

${log}_{2}\left(\frac{R}{B}\right)$ | 0.236 | 0.197 | 0.203 | 0.732 | 0.649 | 0.247 | −0.039 |

SVM | Validation | ||||||

0.198 | 0.168 | 0.207 | 0.881 | 0.146 | 0.704 | −0.030 |

**Table 6.**Classification of Phoradendron velutinum (P. velutinum) in multispectral images produced by GP, SIPI2 index, and SVM methods. The first column shows the original images evaluated, columns two, three, and four represent, respectively, the classification of P. velutinum in the original images using four of the best algorithms found by GP, SIPI2 index, and SVM methods. In these results, the correctly classified mistletoe can be seen in white color, the well-classified background in black color, while shown in green are the pixels that represent errors by omission (FN) and in magenta the errors by commission (FP).

Original Image | Testing Results | ||
---|---|---|---|

GP | SIPI2 | SVM | |

${k}_{w}=0.866$ OA $=0.991$ P $=0.886$ R $=0.839$ | ${k}_{w}=0.083$ OA $=0.796$ P $=0.090$ R $=0.566$ | ${k}_{w}=0.328$ OA $=0.932$ P $=0.285$ R $=0.707$ | |

${k}_{w}=0.796$ OA $=0.988$ P $=0.894$ R $=0.663$ | ${k}_{w}=0.011$ OA $=0.434$ P $=0.035$ R $=0.728$ | ${k}_{w}=0.433$ OA $=0.959$ P $=0.379$ R $=0.733$ | |

${k}_{w}=0.712$ OA $=0.991$ P $=0.795$ R $=0.598$ | ${k}_{w}=0.005$ OA $=0.550$ P $=0.019$ R $=0.551$ | ${k}_{w}=0.130$ OA $=0.885$ P $=0.106$ R $=0.838$ | |

${k}_{w}=0.687$ OA $=0.987$ P $=0.653$ R $=0.795$ | ${k}_{w}=-0.029$ OA $=0.366$ P $=0.002$ R $=0.046$ | ${k}_{w}=0.325$ OA $=0.951$ P $=0.268$ R $=0.777$ | |

**Table 7.**Visual term analysis from the best GP algorithm. This comparison is made with the same examples show in Table 6. The first column displays the original images evaluated, the second and third columns show the analysis of $|R-B|$ and ${log}_{2}\left(\frac{R}{B}\right)$ terms, respectively. Black color is the well-classified background, white is P. velutinum correctly classified, green and magenta indicate the omission and commission errors, respectively.

Original Image | Testing Results | |
---|---|---|

$|\mathbf{R}-\mathbf{B}|$ | ${log}_{\mathbf{2}}\left(\frac{\mathbf{R}}{\mathbf{B}}\right)$ | |

${k}_{w}=0.71$ OA $=0.98$ P $=0.91$ R $=0.51$ | ${k}_{w}=0.62$ OA $=0.98$ P $=0.98$ R $=0.36$ | |

${k}_{w}=0.16$ OA $=0.97$ P $=0.81$ R $=0.06$ | ${k}_{w}=0.58$ OA $=0.98$ P $=0.99$ R $=0.32$ | |

${k}_{w}=0.27$ OA $=0.98$ P $=0.39$ R $=0.17$ | ${k}_{w}=0.16$ OA $=0.96$ P $=0.15$ R $=0.26$ | |

${k}_{w}=0.49$ OA $=0.98$ P $=0.92$ R $=0.26$ | ${k}_{w}=0.84$ OA $=0.99$ P $=0.92$ R $=0.73$ | |

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**MDPI and ACS Style**

Mejia-Zuluaga, P.A.; Dozal, L.; Valdiviezo-N., J.C.
Genetic Programming Approach for the Detection of Mistletoe Based on UAV Multispectral Imagery in the Conservation Area of Mexico City. *Remote Sens.* **2022**, *14*, 801.
https://doi.org/10.3390/rs14030801

**AMA Style**

Mejia-Zuluaga PA, Dozal L, Valdiviezo-N. JC.
Genetic Programming Approach for the Detection of Mistletoe Based on UAV Multispectral Imagery in the Conservation Area of Mexico City. *Remote Sensing*. 2022; 14(3):801.
https://doi.org/10.3390/rs14030801

**Chicago/Turabian Style**

Mejia-Zuluaga, Paola Andrea, León Dozal, and Juan C. Valdiviezo-N.
2022. "Genetic Programming Approach for the Detection of Mistletoe Based on UAV Multispectral Imagery in the Conservation Area of Mexico City" *Remote Sensing* 14, no. 3: 801.
https://doi.org/10.3390/rs14030801