# Semi-Automatic Method for Early Detection of Xylella fastidiosa in Olive Trees Using UAV Multispectral Imagery and Geostatistical-Discriminant Analysis

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Site Description

#### 2.2. Variables

#### 2.3. Methodology

- Extraction of canopies for each field from UAV images.

- ✓
- Pre-processing:
- To create a composite multispectral image from the individual spectral bands, the procedure of layer stacking has been applied, so individual image bands to have the same extent (no. of rows and columns).
- To enhance specific information about the landscape, which cannot easily be seen with a natural color image, as stress and vigor of vegetation, the false color composite has been applied. In this case, to emphasize the status of the plant, the following bands have been combined: Red → Red, Red-Edge → Green, Green → Blue, (Figure 4a).

- ✓
- Supervised Classification:
- Supervised classification was applied, which involves the use of training area data considered representative of the land cover types of the study areas. In this case three labels were identified: soil, canopy and shadow.As classifier algorithm, the maximum likelihood was used, which is based on maximizing the likelihood that the observed values follow a normal distribution (Figure 4b).
**Figure 4.**(**a**) An example, Oria Field: 4 layer stack at false colors. (**b**) An example, Oria Field: thematic map of classification. - To smooth the boundaries of small areas located near each other, or to aggregate these areas, a morphological filter [31,32,33], which uses the fundamental operations of erosion and dilation, was preferred to fill gaps in the contour lines. Subsequently, a format conversion has been applied to convert labelled raster image into vector data to extract closed spatial features (polygons) from the classification.

- ✓
- Exporting to GIS Environment:
- Each closed polygon, representing an individual plant, was then imported into GIS environment and an editing procedure was applied to generate a multipolygon product (Figure 5). This process allowed to modify the vertices of the selected spatial feature, to fill eventual holes in the polygon and/or to cut some parts.
- Each polygon was further subdivided into four quadrants (North, East, South, and West), to which to refer both visual and radiometric measurements (common support). The quadrants were generated by a procedure that has been implemented in C# language with ArcObjects libraries to be integrated into the ArcGIS environment. This procedure is based on segments that join the centroid of each polygon with the four points at 45°, 135°, 225°, 315° (defined above the horizon), to split the polygon into the north, east, south, and west sectors of the crown, respectively.
- Each shapefiles of quadrants has been imported in geostatistical environment.

- 2.
- Change of support: polygon cokriging.

_{s}different spatial scales [40,41,42]. All (both direct and cross-) variogram models are expressed as linear combinations of the same basic structures for each spatial scale (range), represented by variograms standardized to unit sill, and with the coefficients equal to partial sills [41]. These last ones reflect the influence of the specific spatial scale on the total spatial variation of the study variable.

#### 2.4. Construction of the Prediction Model: Statistical Analyses

- Selection of predictors. The first step in the statistical analysis was preliminary to determine which variables (bands) were significantly related to the response class variable (disease severity level), coded as shown above. For this purpose, a stepwise discriminant analysis was performed, which is a regression technique aimed to select a subset of the quantitative variables (predictors) for use in discriminating between the classes. The variables are chosen to enter or to leave the regression model on the basis of the significance level of an F test from an analysis of covariance, where the variables already chosen act as covariates and the variable under consideration is the response variable [39]. The analysis was performed using the STEPDISC procedure of SAS software in stepwise mode [39], and the significance levels for a variable to enter the subset and to stay in the subset were set to 0.1.
- Check of multivariate normality. The next step for implementing discriminant analysis was to check the multivariate normality in each of the two severity classes of Xfp symptoms, since the estimation of misclassification probabilities requires the assumption of multivariate normality. Since the condition of normality for each of the 16 quantitative variables is a necessary, but not sufficient, condition for multi-normality, first, the assumption of univariate normality was checked with three tests (Kolmogorov–Smirnov, Cramer–von Mises, and Anderson–Darling) [40].

_{i}) using Blom’s formula [41]:

_{i}is the rank of the i

^{th}observation, and n is the number of observations that have non missing values for the ranking variable.

- 3.
- Testing the sensitivity of multi-band data to the infection severity level. Univariate (ANOVA) and multivariate (MANOVA) analyses of variance were carried out on the UAV data, the former to test the hypothesis that the class means for each quantitative variable (band reflectivity) were equal, whereas the latter to compare multivariate class means across several variables. Four multivariate statistical tests were used: Wilks’ lambda, Pillai’s trace, Hotelling–Lawley trace, and Roy’s maximum root [42,43,44,45,46,47].
- 4.
- Determination of the parametric discriminant model. Assuming that each severity class had a multivariate normal distribution, firstly, a parametric method was performed, aimed at developing a discriminant mathematical function or classification, which best separated between the two classes of severity [44]. The classification criterion can be a linear function, assuming the same variance–covariance matrix of responses across the severity classes, or quadratic, assuming each class with a unique variance structure. A chi-square test of equal variance was then performed [43]. Using Bayes theorem, the posterior probability of each observation belonging to each class was calculated, taking into account the prior probabilities of the classes [45,46]. Each observation was placed in the class to which it had the highest posterior probability to belong. Therefore, as the final product of the model, for each observation the most probable class was assigned together with its posterior probability, which can be considered as a measure of the uncertainty associated with such assignation or prediction.
- 5.
- Determination of non-parametric discriminant model. Since multivariate normality might not be fully satisfied, a non-parametric approach was also estimated to be compared with the parametric one. Non-parametric discriminant methods are based on non-parametric estimates of class-specific probability densities. The non-parametric kernel method uses a fixed radius (r) and a specified kernel (k), which can be uniform, normal, Epanechnikov, biweight or triweight, to calculate the kernel density in each class [44]. The value of r and type of kernel, called smoothing parameters, determine the degree of irregularity in the estimate of the density function. Small values of r produce jagged density estimates, whereas large values produce smoother density estimates. Therefore, for each type of kernel, several (ten on average) r values were tested, and the optimal set of the smoothing parameters, which minimizes the error rates, was chosen.
- 6.
- Comparison between the two models. The performance of each model was evaluated using cross-validation [45,46]. Cross-validation uses n-1 out of n observations to determine the discriminant function for the classification of the one observation left out. This is repeated for each of the n observations. The error-rate estimates were calculated by counting the number of misclassified observations; the class-specific error-count estimate was determined as the proportion of misclassified observations in the class. [47,48,49]. The overall error rate was calculated as a weighted average of the individual class-specific error-rate estimates by using the prior probabilities as the weights [50,51,52,53,54].
- 7.
- Graphical display of infection status. Canonical discriminant analysis was also performed to extract one (number of classes (2) minus 1) linear combination of the quantitative variables, called canonical variable, which best revealed the differences between the classes and had the highest possible multiple correlation with the classes. The standardized canonical coefficients were estimated, which express the partial contribution of each quantitative variable (band) to the canonical variable, and were then used to interpret its meaning.
- 8.
- Prediction phase. The better classification model was then used in the prediction phase, by determining the more likely severity class for an independent data set not used in the previous phase of construction of the model. In particular, eight plants in the Torchiarolo field, for which the visual surveys were missing, were used for severity class prediction on August 2019. The estimated posterior probability of the predicted class was also provided as a measure of prediction uncertainty.

## 3. Results

#### 3.1. Geostatistical Analysis

#### 3.2. Statistical Analysis

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Localization of the three olive groves in the Apulia region (south–eastern Italy): Re field, Fella field, Torchiarolo field.

**Figure 3.**High resolution frame portion acquired by Unmanned Aerial Vehicle (UAV) at Oria field on September 2017.

**Figure 5.**An example of multipolygon product of the three fields on the date of September 2017: Re (

**a**), Fella (

**b**), and Torchiarolo (

**c**).

**Figure 8.**(

**a**) Temporal red-edge reflectivity maps at plant quadrant level for the Re field. In this figure, and the following ones, the color scale is on isofrequency classes to enhance the differences. (

**b**) Temporal red-edge reflectivity maps at plant quadrant level for the Fella field. (

**c**) Temporal red-edge reflectivity maps at plant quadrant level for the Torchiarolo field.

**Figure 10.**The prediction of the more probable severity class, together with its posterior probability at plant quadrant level, for eight plants at Torchiarolo field on August 2019. The brown color represents class1, blue color represents class 0.

Field | Type of Model | Range (m) | Spatial Variance Explained (%) |
---|---|---|---|

Re | Nugget effect | - | 32 |

Cardinal sinus | 18.64 | 68 | |

Fella | Nugget effect | - | 37 |

Cubic | 2.42 | 21 | |

Cardinal sinus | 31.18 | 42 | |

Torchiarolo | Nugget effect | - | 54 |

Cardinal sinus | 22.23 | 37 | |

Spherical | 88.62 | 9 |

Variable | D* | W-Qu* | A-Qu* | |||
---|---|---|---|---|---|---|

Statistics | Probability | Statistic | Probability | Statistic | Probability | |

GREEN | 0.281019 | <0.0100 | 105.9703 | <0.0050 | 585.016 | <0.0050 |

RED | 0.21957 | <0.0100 | 56.25436 | <0.0050 | 331.2315 | <0.0050 |

RED-EDGE | 0.164006 | <0.0100 | 17.94999 | <0.0050 | 123.1129 | <0.0050 |

NIR | 0.066529 | <0.0100 | 2.045712 | <0.0050 | 10.74146 | <0.0050 |

GREEN_std | 0.442217 | <0.0100 | 157.4172 | <0.0050 | 830.784 | <0.0050 |

RED_std | 0.391301 | <0.0100 | 126.0456 | <0.0050 | 728.0533 | <0.0050 |

RED-EDGE_std | 0.370405 | <0.0100 | 111.0805 | <0.0050 | 552.6192 | <0.0050 |

NIR_std | 0.281603 | <0.0100 | 65.14581 | <0.0050 | 323.1493 | <0.0050 |

Variable | F Value | Probability |
---|---|---|

R_GREEN | 134.09 | <0.0001 |

R_RED | 24.07 | <0.0001 |

R_RED-EDGE | 174.09 | <0.0001 |

R_NIR | 106.90 | <0.0001 |

R_GREEN_std | 50.57 | <0.0001 |

R_RED_std | 0.84 | 0.3580 |

R_RED-EDGE_std | 90.59 | <0.0001 |

R_NIR_std | 16.86 | <0.0001 |

Test | Statistic Value | F Value | Probability |
---|---|---|---|

Wilks’s lambda | 0.931 | 37.74 | <0.0001 |

Pillai’s trace | 0.069 | 37.74 | <0.0001 |

Hotelling–Lawley’s trace | 0.074 | 37.74 | <0.0001 |

Roy’s maximum root | 0.074 | 37.74 | <0.0001 |

**Table 5.**Confusion Matrix for X. fastidiosa subsp. pauca severity classes using the quadratic discriminant classification with the absolute counts and the accuracies.

Ground Truth | |||||

0 | 1 | Total # of classified samples | User’s accuracy | ||

ClassificationResults | 0 | 1405 | 498 | 1903 | 0.74 |

1 | 968 | 1224 | 2192 | 0.56 | |

Total #of ground truth samples | 2373 | 1722 | |||

Producer’s accuracy | 0.59 | 0.71 | 0.64 |

**Table 6.**Error rates for X. fastidiosa subsp. pauca severity classes using the quadratic discriminant classification.

Class | 0 | 1 | Average |
---|---|---|---|

Error Rate | 0.41 | 0.29 | 0.36 |

**Table 7.**Confusion Matrix for X. fastidiosa subsp. pauca severity classes using the non-parametric method with the absolute counts and the accuracies.

Ground Truth | |||||

0 | 1 | Total # of classified samples | User’s accuracy | ||

ClassificationResults | 0 | 1835 | 730 | 2565 | 0.72 |

1 | 538 | 992 | 1530 | 0.65 | |

Total #of ground truth samples | 2373 | 1722 | |||

Producer’s accuracy | 0.77 | 0.58 | 0.69 |

**Table 8.**Error rates for X. fastidiosa subsp. pauca severity classes using the non-parametric method.

Class | 0 | 1 | Average |
---|---|---|---|

Error rate | 0.23 | 0.42 | 0.31 |

Variable | Coefficients |
---|---|

R_GREEN | 0.034 |

R_RED | 0.652 |

R_RED-EDGE | 0.885 |

R_NIR | −0.247 |

R_GREEN_std | 0.171 |

R_RED_std | −0.689 |

R_RED-EDGE_std | 0.364 |

R_NIR_std | −0.154 |

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## Share and Cite

**MDPI and ACS Style**

Castrignanò, A.; Belmonte, A.; Antelmi, I.; Quarto, R.; Quarto, F.; Shaddad, S.; Sion, V.; Muolo, M.R.; Ranieri, N.A.; Gadaleta, G.;
et al. Semi-Automatic Method for Early Detection of *Xylella fastidiosa* in Olive Trees Using UAV Multispectral Imagery and Geostatistical-Discriminant Analysis. *Remote Sens.* **2021**, *13*, 14.
https://doi.org/10.3390/rs13010014

**AMA Style**

Castrignanò A, Belmonte A, Antelmi I, Quarto R, Quarto F, Shaddad S, Sion V, Muolo MR, Ranieri NA, Gadaleta G,
et al. Semi-Automatic Method for Early Detection of *Xylella fastidiosa* in Olive Trees Using UAV Multispectral Imagery and Geostatistical-Discriminant Analysis. *Remote Sensing*. 2021; 13(1):14.
https://doi.org/10.3390/rs13010014

**Chicago/Turabian Style**

Castrignanò, Annamaria, Antonella Belmonte, Ilaria Antelmi, Ruggiero Quarto, Francesco Quarto, Sameh Shaddad, Valentina Sion, Maria Rita Muolo, Nicola A. Ranieri, Giovanni Gadaleta,
and et al. 2021. "Semi-Automatic Method for Early Detection of *Xylella fastidiosa* in Olive Trees Using UAV Multispectral Imagery and Geostatistical-Discriminant Analysis" *Remote Sensing* 13, no. 1: 14.
https://doi.org/10.3390/rs13010014