Introduction
Yellow rust is one of the most important wheat diseases, caused by the Puccinia striiformis f. sp. tritici (Pst) fungus, substantially reducing yield and quality. Studies indicate that yellow rust reduces wheat production by approximately 15% on average. This disease periodically becomes epidemic, causing severe damage to wheat crops.
One of the most crucial aspects of combating yellow rust is identifying affected areas and foci within the field. If spraying is conducted in the early stages, the spread of the disease and its associated damage can be effectively mitigated. Initially, disease detection relied on visual inspection, which, despite its practicality, is time-consuming, costly, and prone to errors. Additionally, visual inspection can contribute to disease spread, further complicating control efforts. Due to these limitations, researchers have been striving to develop more precise and faster methods to enable accurate and timely identification, thereby minimizing the damage caused by this disease. In recent years, chemical and molecular techniques, such as polymerase chain reaction (PCR), have been employed
for plant disease detection.While these methods provide high accuracy, they are destructive, time-consuming, and require specific chemical reagents.
With advancements in agricultural technology, image processing techniques have emerged as non-destructive and rapid approaches for detecting various plant diseases. Some of these methods include multispectral and hyperspectral imaging, infrared spectroscopy, and color imaging. Thus, the present study aims to identify yellow rust in wheat samples under laboratory conditions using visible image processing methods.

Method
For laboratory sample preparation, the Bolani variety was used. After planting, inoculation of yellow rust fungus was performed on the leaves at the seedling stage. Once the samples were prepared, 50 leaves were cut from each wheat sample with a specific disease severity. For imaging, a Canon (PowerShot G9, Made in Japan) visible camera was utilized. The shooting angle was set at 90 degrees relative to the leaves, and images were captured from a distance of 20 cm. To execute the image processing procedure, pre-processing techniques such as Gaussian low-pass filtering and histogram expansion were applied using MATLAB software. A total of nine color indices were extracted based on the average RGB color components. Then, various vegetation indices were evaluated for visible images, and the most suitable index for diagnosing yellow rust disease was introduced.

Results
A stepwise discriminant function analysis (DFA) method was employed to select and rank color indices and vegetation metrics. In this approach, the index that produces the lowest Wilks' lambda value in a univariate model is selected first, followed by the identification of additional indices that, when included, further reduce the Wilks' lambda value. A lower Wilks' lambda at the end of the analysis indicates higher model accuracy and classification quality. Indices that do not contribute to reducing Wilks' lambda are eliminated during this process. To implement this methodology, data from extracted indices of each image were recorded using SPSS 18 and analyzed via stepwise discriminant analysis. The indices were examined separately for wheat leaf samples with distinct infection levels (H: healthy, S10: tenth day of infection, ST: fully infected).The results of the stepwise discriminant analysis for pairwise differentiation of wheat leaf samples showed that the reflectance indices of the red and green components ranked first and second in the S-H10 and H10-ST comparisons. For the S-ST sample, the blue reflectance index ranked highest, followed by VDI, Blue, and RED indices in second to fourth place. Consequently, the red reflectance index was identified as the optimal metric for distinguishing between samples. Additionally, NGDBA, NDGI, and TGI were ranked sixth to seventh across all three sample groups. The lowest Wilks' lambda values calculated for the S-H10, S-ST, and H10-ST comparisons were 0.098, 0.088, and 0.085, respectively, indicating relatively high classification accuracy.
In this study, several neural network classifiers were applied to classify wheat yellow rust, including the self-organizing map (SOM), learning vector quantization (LVQ), radial basis function (RBF), support vector machine (SVM), multilayer perceptron (MLP), k-nearest neighbor (KNN), and k-means clustering. The evaluation of these neural networks revealed that their accuracy during the training phase exceeded 86.05%. Among them, SVM, MLP, and KNN demonstrated the highest performance in training. Similarly, in the testing phase, all studied neural networks achieved accuracy rates above 87.06%, with SVM, RBF, and LVQ showing the best classification performance. Overall, the SVM model exhibited the highest accuracy across both the training and testing stages, achieving a maximum accuracy of 98.06% during training and 95.44% during testing.

Conclusions
The findings of this study indicate that the use of an RGB imaging system is an effective method for detecting yellow rust infection in wheat. Stepwise discriminant analysis for ranking color reflectance indices revealed that the red and green components play a crucial role in distinguishing between S-H10 and H10-ST samples. Furthermore, the evaluation of classification models demonstrated that the SVM neural network achieved the highest accuracy in both training and testing phases for visible images, with an accuracy of 98.06% in training and 95.44% in testing. Thus, SVM was identified as the most effective model for detecting yellow rust in wheat. The proposed method can serve as a precise and non-invasive system for monitoring crop health. Additionally, leveraging artificial intelligence models such as SVM and selected vegetation indices can facilitate the development of automated and intelligent systems for early detection of plant diseases, significantly improving disease management and reducing agricultural losses.

Author Contributions
Mohammad Hossein Saeidirad was responsible for conceptualization, methodology, writing review & editing, supervision, and project administration.
Farzad Afshari contributed to validation and laboratory sample preparation.
Reyhaneh Pakdel contributed to data curation, writing-original draft, image processing using software and visualization.
Jalal Baradaran Motie contributed to pre-processing techniques.
Saeed Zarifneshat contributed to analyzeing via stepwise discriminant analysis.
Naim Lovaimi contributed to laboratory sample photographing.

Data Availability Statement
The datasets generated and/or analyzed during the current study are available from the corresponding author upon reasonable request.

Acknowledgements
This optional section acknowledges individuals or organizations that significantly contributed to the research beyond author contributions or funding. This may include administrative, technical support, or in-kind donations.

Ethical Considerations
This section states ethical approval details (e.g., Ethics Committee, ethical code) and confirms adherence to ethical standards, including avoidance of data fabrication, falsification, plagiarism, and misconduct.