3.2.3. Extraction of Texture Features

Because of the redundant information in hyperspectral images, here texture features of images at the six selected sensitive wavelengths were extracted, for the further development of NDTIs. Eight texture features for each spectral band and in total 48 texture features were adopted. Figure 6 shows one of the texture images at the 533.5 nm wavelength. Texture images at same wavelength are various due to different texture features.

**Figure 6.** Texture images at wavelength of 533.5 nm. Note: MEA = mean; VAR = variance; HOM = homogeneity; CON = contrast; DIS = dissimilarity; ENT = entropy; SEM = second moment; COR = correlation).

The Pearson correlation coefficient r was used to examine the relationships between the texture features and the observed DS at different growth stages (Figure 7). The results showed that the texture features were poorly correlated with DS at the jointing stage but highly correlated at the booting stage. Whether it was at the jointing or the booting stage, 20 textures, namely homogeneity (HOM), dissimilarity (DIS), entropy (ENT), and second moment (SEM) at the wavelengths of 523.6, 528.5, 533.5, 659.2, and 661.7 nm were significantly correlated with DS.

**Figure 7.** Pearson correlation analysis between texture features and DS.

with DS.

### 3.2.4. Calculation of Normalized Difference Texture Indices (NDTIs)

NDTIs were constructed to improve the performance of texture analysis in disease recognition as the texture features did not exhibit consistent relationships to DS at two growth stages. Based on the aforementioned 48 texture features, 2256 NDTIs were realized by combining all two possible texture features, and the significance of those NDTIs were analyzed by correlation analysis. Among the 2256 NDTIs, only 10 NDTIs were sensitive to DS at different growth stages and throughout both growth stages, as listed in Figure 8. Ten best performing NDTIs were constructed by a combination of the following seven texture features, namely the second moment (SEM) at 659.2 nm and 661.7 nm and the homogeneity (HOM) at 523.6 nm, 528.5 nm, 533.5 nm, 659.2 nm, and 661.7 nm. Compared with texture features in Figure 7, the NDTIs are better correlated to disease severity. Thus, these NDTIs were selected for further construction of the disease detection model.

**Figure 8.** The correlation coefficient of the top 10 normalized difference texture indices (NDTI) which are highly

### *3.3. PLS-LDA Model for Classifying the Healthy and Diseased Leaves*

3.3.1. Evaluation of PLS-LDA Model Based on Different Selected Sensitive Features

The PLS-LDA model was built to evaluate the performance of different indices in terms of detecting wheat PM at different growth stages. The classification results were evaluated both for calibration and validation accuracies, as listed in Table 3. Regardless of growth stage, spectral vegetation indices achieved better classification accuracies than texture indices. However, the model based on the combination of VIs and NDTIs performed best in

 correlated comparison with that of VIs and NDTIs when used alone as input features. The combination of VIs and NDTIs significantly increased the classification accuracy, yielding calibration accuracies of 75.34%, 80.72%, and 76.46% and validation accuracies of 74.88%, 78.93%, and 76.23% at jointing stage, booting stage, and throughout both stages, respectively. The classification accuracies at booting stage were superior, followed by that at both stages and jointing stage, respectively.


**Table 3.** Classification results of PLS-LDA model based on different features.

 Note: VIs = vegetation indices; NDTIs = normalized difference texture indices; VIs & NDTIs = combination of VIs and NDTIs.

### 3.3.2. Classification of Healthy and Diseased Leaves at Early Stage after Inoculation

As demonstrated in Section 3.3.1 (Table 3), the model based on combination of VIs and NDTIs revealed better results. So, further for classification of healthy and diseased leaves as early as possible after inoculation, we established the PLS-LDA model based on combined features (VIs & NDTIs), on datasets of different days after inoculation (DAI) of each growth stage (Table 4). At the jointing stage, healthy and diseased leaves could be better distinguished on 6 DAI with an average DS of 3.9%, as the overall classification accuracy on this day approached more than 85% with a kappa value of 0.73 and the accuracies for healthy and diseased leaves were 82.35% and 100%, respectively. While, at booting stage, on 3 DAI the overall accuracy reached more than 85% with a kappa value of 0.73 and the accuracies for healthy and diseased leaves were recorded as 81.25% and 100%, respectively. The mean disease severity on this day was noted as 1.1%. Therefore, it can be concluded that wheat PM can be better diagnosed at an early-stage with a maximum of up to 3–6 DAI or at a mean DS of around 1–9%, by using combined (VIs & NDTIs) sensitive features as an input in classification model.


**Table 4.** PLS-LDA classification results of healthy and diseased leaves based on combined spectral and texture indices (VIs & NDTIs) at the jointing and booting stage.

Note: DAI indicates days after inoculation, T is mean temperature of green house in degree centigrade, DS is mean disease severity, Healthy and Diseased indicate classification accuracies of inoculated and non-inoculated wheat leaves, OA is overall classification accuracy.

### *3.4. PLSR Model for Estimating the Disease Severity*

For estimating the disease severity, the aforementioned six sensitive vegetation indices, 10 texture indices and 16 combined features (i.e., VIs & NDTIs) were used to construct the partial least square regression (PLSR) model with 10-fold cross-validation (Table 5). Across growth stages, the *R*<sup>2</sup> and *RMSE* results of booting stage were superior regardless of input features, followed by pooled data of both stages and then jointing stage, respectively. Based on input features, the model constructed by using VIs was comparatively better in the validation model than that of the model constructed by using NDTIs. However, the model constructed by using combined features (i.e., VIs & NDTIs) yielded significantly better results, both for calibration and validation, than the models separately based on VIs or NDTIs.


**Table 5.** Results of partial least-squares regression (PLSR) models based on different inputted features.

Figure 9 shows DS estimation models based on combined features (i.e., VIs & NDTIs), by using the validation datasets of different growth stages. It can be observed that the measured DS is close to the predicted DS which lies along line of concordance (1:1 solid line), confirming the accuracy of the DS estimation model. The performance of the estimation model at booting dataset was superior, i.e., the *R*<sup>2</sup> values between measured and estimated DS was 0.818 and *RMSE* was 11.320, followed by pooled data of both stages (*R*<sup>2</sup> = 0.722, *RMSE* = 13.356). While the model performance at jointing stage was relatively poor (*R*<sup>2</sup> = 0.532, *RMSE* = 15.32) and the predicted DS was overestimated. The above results sugges<sup>t</sup> that the PLSR model based on the combined features of VIs and NDTIs performed better for detecting wheat PM disease severity.

**Figure 9.** Comparison of measured and estimated wheat powdery mildew DS based on combined features of VIs & NDTIs, at both stages (**a**), jointing stage (**b**), and booting stage (**c**).
