We used a dataset that contains a few eggplant leaf images with proper labels, divided into six classes. Formally, the dataset consists of a set of input–output pairs defined as in equation (1).

D={(x_i,y_i)}_(i=1)^N (1)

Here, x_i is the i^th image and y_i is the corresponding label. N is the number of images, and each image falls in one of the six disease categories, K=6.

x_i ∈ R^H×W×C (2)

In equation (2), H is the height of the image, W is the width of the image, and C is the number of color channels, which in this study are the three channels of RGB. The representation of the images enables the model to learn spatial and color-based features that are critical in distinguishing different patterns of diseases. As represented in Equation (3), each image in the case studies has a corresponding disease.

(3)

In this representation, K is the number of classes. For this representation, we can say that Categorical y_i represents the y_i^th class from the K total classes of the system. To get from the modeling layer to the application layer, the classes are represented in the form of one-hot encoding, as shown in equation (4).

(4)

This then allows us to say that y_ik the image is a case of the class; otherwise, it is not (i.e., y_iK = 1 or y_iK = 0). As stated, the representation allows for the application of the probabilistic loss functions to the system during the optimization. The input images are subject to a minor transformation, as stated in equation (5), to increase the likelihood that the model does not overfit.

x_i'=T(x_i) (5)

In this case, T (∙) indicates the transformation function applied to the original image data. The transformation function, in this case, involves a sequence of operations, as described in Equation (6).

T(x)=T_flip (T_rot (T_HSV (x))) (6)

With this formulation, it is understood that, in the transformation of an input image, a set of operations of flipping, rotating, and adjusting the image to the hue-saturation-value color space is performed. Such operations help address the model's performance in different orientations and lighting conditions and image degradation caused by atmospheric phenomena. Therefore, the training is expressed, considering the transformed training set, as equation (7).

min_θ⁡ E_(x,y)~D [L(f(T(x);θ),y)] (7)

Where, in this case, f(x;θ) is the deep learning model, and L is the loss function. Specifically, Equation (7) implies that the model should minimize the expected loss, concerning not only the original samples but also the augmented samples, thus enhancing robustness and improving classification. Therefore, considering the equations from (1) to (7) and their respective sequence of operations, a comprehensive augmented training dataset aimed at improving the learning of the model concerning the disease-related features in the eggplant leaves is proposed.

In order to be more effective and use less learning time, pre-trained YOLOv8 classification models are used. YOLOv8n, YOLOv8s, YOLOv8m, YOLOv8l, and YOLOv8x models are chosen, each with a different degree of model depth and complexity. Transfer learning involves loading weights that have been learned on additional, large datasets and initializing these models.

(8)

Let θ be the parameter set for the study model and θ_pretrained be the parameters from a large benchmark dataset. Equation (8) shows the process of embedding learned representations like the edges, textures, and shapes of the images. This process speeds up training as it provides a starting point for the pre-trained model on the eggplant disease data. Since the feature representations pre-trained on external data show the model where it should end up, the optimization process becomes more isotropic and requires fewer epochs to reach the desired model function. Also, the approach entails fine-tuning the pre-trained parameters with a data set for the target tasks.

(9)

Here, the set of parameters optimized after training is the model, and ℒ denotes the loss function. Equation (9) suggests that the pre-trained parameters are fine-tuned with respect to classification error on a new dataset. Model initialization as per Equation (8), and then after that, optimize this as per Equation (9). The proposed method converges faster with more accuracy and generalizes better. This makes transfer learning with YOLOv8 an excellent choice for eggplant leaf disease classification when the datasets cannot be as large as the benchmarks of a larger scope.

3.3. YOLOv8m Architecture

The YOLOv8m architecture is composed of three main components: first, the Backbone, second, the Neck, and finally, the Head. These parts operate in a pipeline, simplifying the extraction of features, fusing multi-scale information, and exporting classification outputs. The backbone performs the steps of extracting deep feature representations from the input image.

(10)

Here x is the input image, f_b( • ) the backbone network, θ_b are the learnable parameters of the backbone, and z_b is its feature map. As defined in Equation (10), given the raw input, the backbone will convert the input into a salient representation that captures spatial patterns, including edge textures and disease specificity. Next, the neck integrates features from different scales by fusing multiple scales to improve its representation capacity.

(11)

Here f_n( • ), instead of the neck module, parameters are provided θ_n. The produced output z_n incorporates enhanced feature representations, combining low-level and high-level features. As described in Equation (11), at the same stage, it enhances the model learning towards both fine-grained and global patterns for better highlighting to identify relevant disease changes from various leaf images. The fused features are then passed on to the head, which outputs the final classification.

(12)

Here, f_h(•) the classification head θ_h is its parameters, and z is the vector of logits for each class. According to Equation (12), the head maps the fused features to class-specific scores, which get translated into probabilities. Combining these three elements, the model can be constructed as a function of composition.

(13)

Here θ = {θ_b,θ_n,θ_h) corresponds to each of the model parameters. Equation (13) represents the sequential flow of picture processing starting from the input image to the last resulting output, including feature extraction, feature fusion, and the classification process. The layered structure assists the YOLOv8m model in learning the various levels of image representations to identify features and leaf patterns of the eggplants. The Backbone component extracts essential features, the neck improves the representation of features, and the head accomplishes significant classification, resulting in superior Classification capabilities.

The classification head of YOLOv8m yields a vector of logits, with each entry corresponding to a disease class. The logits then undergo softmax activation, resulting in normalized probabilities.

(14)

Here, P(y = k|x) represents the predicted probability that the image x belongs to the class k, and

zk refers to the logit pertaining to class k in a total of K classes. The denominator of (14) constitutes the sum of the exponentials of the class logits, and thus the predicted probabilities are bound to [0,1].

The inverse of Equation (14) is that the softmax function inherently transforms raw outputs from the model into more comprehensible probability distributions. A higher logit value will yield a high probability score, signifying higher confidence in the class prediction. This enables the model to give probability scores for several different disease classes. The top class with the highest probability value gives us the final predicted class. This process is expressed as equation (15).

ŷ = arg max_k P(y = k|x) (15)

Here ŷ represents the predicted class label. The model classifies the input image with respect to the class that it estimates is more probable. Two key advantages are provided by the Softmax function in the case of multi-class classification. So first, it provides numerical stability and normalized output values like predicted probabilities. Second, it supports efficient optimization using probabilistic loss functions such as categorical cross-entropy at training time. These features enhance the model in learning discriminative feature representations to classify eggplant leaf diseases correctly.

YOLOv8m classification model is trained with a categorical cross-entropy loss function, which can be defined as the difference between the predicted probability distribution and the true class labels. The loss for a single training example is given by equation (16).

(16)

Here, K is the classification task, y_k is the ground truth for class k, and P(y = k|x) is the predicted probability from the Softmax function in Equation (14). In Equation (16) y_k =1 if that class is the correct class, and otherwise 0. One with its logarithm term that penalizes a poor prediction.

The categorical cross-entropy loss measures how well the predicted distribution indicates the actual one. When the value of predicted probability for the correct class gets to 1, then this means the loss becomes small, and vice versa. On the other hand, if the predictions are not correct, then the loss value will be higher, so the model needs to make changes to its parameters. The overall loss is calculated as the average of sample losses for the entire dataset, as represented in equation (17).

(17)

Here, N is the number of training samples, and ℒ_i is the loss on the i^th sample. Since we want optimization not to be biased towards individual samples, it encourages performance across all training samples. Training aims at minimizing the total loss introduced and thus increasing the classification ability of the model. The YOLOv8m model can learn discriminative features with increasing accuracy for classifying eggplant leaf diseases by continuously reducing the loss value during training.

The goal of the training is to find model parameters that minimize the total loss function. Here

θ* are the best model parameters after training, and the total categorical cross-entropy loss is denoted as ℒtotal. In fact, Equation (18) tells the training process to find some values of parameters so that the whole dataset has a smaller classification error.

θ* = arg min_θ ℒ_total (18)

This optimization is achieved using the general gradient-based learning approach. Gradient descent, as defined in Equation (19), is used iteratively to update the parameters of the model. Here, θ_t indicates the parameter values at iteration t, and so on, θ_t + 1 are the updated parameters,

η is the learning rate, and ∇θℒ is obtained from the losses as gradients related to model parameters. Gradient gives us information on how to change our parameters so that our loss will decrease.

(19)

The learning rate determines the size of parameter updates during optimization. Finding an appropriate learning rate leads to good convergence, preventing the training from diverging or converging too slowly. The gradients are being calculated and backpropagated for each iteration, so the model can learn and extract important and discriminative features from the training data on its own. The training in this study was done for 20 epochs on the augmented data samples created by flipping and rotating images, as well as HSV transformation. Using augmented information supplies better scale power as it lowers the network in unique rotations, lighting, enabling YOLOv8m to generalize very well to unseen eggplant leaf images and have a better classification performance in real-state applications. The model gradually reduces the loss function as it progresses through training and enhances the accuracy of predictions. This entire optimization is passed down to a trained model that can discriminate between healthy and diseased eggplant leaves.

Once the training process is finished, the YOLOv8m model categorizes given input images into one of the disease categories. Given an input image x, the model computes probability scores for all possible classes by applying the Softmax function shown in Equation (14). The final predicted class gets calculated, and it picks the class that is highest in probability.

ŷ = arg max_k P(y = k|x) (20)

Hete ŷ is the predicted class label, P(y = k|x) is the probability that the input image belongs to class k, and K is the number of classes. In Equation (20), the class corresponding to the highest probability value among all predicted classes is identified. During the prediction process, the test image is passed through the trained YOLOv8m network along with large-scale feature extraction, followed by multiplied feature fusion and classification. For each category, the model calculates confidence scores, and the classes that have the highest confidence scores are predicted. This way, the model can identify healthy and diseased eggplant leaves based on what it learned visually. The prediction method takes the maximum probability value. This helps achieve further consistent and understandable results. The predicted class label is applied for disease diagnosis in the running real-time application.

The performance of each model variant is logged and evaluated based on standard classification metrics. In our work, we establish the metrics of evaluation in Equation (21)

R = {Accuracy, Precision, Recall, F1_Score} (21)

In this case, R is the set of computational metrics and defines the model classification score. In equation (21), the R metrics offer insight into a model's potential and overall performance based on multiple angles. The Accuracy metric is focused on answer correctness across the entire output set. Precision is based on the correctness of the positive predicted cases. Recall is modeled based on the sensitivity of the model to identify all of the diseased aspects, and the F1_Score is meant to quantify the balance of Precision and Recall. Collectively, the R metrics offer a summary and ample insight into model performance across all classification levels of the various diseases. After every single epoch of training, evaluations get logged for the YOLOv8n, YOLOv8s, YOLOv8m, YOLOv8l, and YOLOv8x model combinations. The training runs record evaluations in log files to track performance and analyze combinations. The process of comparison is captured in Equation (22).

M* = arg max_MR(M) (22)

Here, M denotes a given YOLOv8 model variation, and M* is used to indicate an optimal model during evaluation. This means that the model with the best overall metric performance is selected as the final configuration. The results allow comparison of various YOLOv8 architectures in terms of accuracy, compute efficiency, and stability while training them. As demonstrated by the experimental results, YOLOv8m was found to be promising in offering an efficient solution combining high-performance accuracy and real-time efficiency for eggplant leaf disease classification.

The proposed YOLOv8m Model is evaluated based on standard classification metrics such as accuracy, precision, recall, and F1-score. These metrics give a clear idea about how well the model can classify eggplant leaf diseases correctly. Accuracy is the overall percentage of samples that are correctly classified with respect to the total predictions made. Here, TP, TN, FP, and FN refer to true positive prediction, true negative prediction, false-positive prediction, and false-negative prediction, respectively. Equation (23) Accuracy measures the overall correctness of the classification model.

(23)

It quantifies the accuracy of positive predictions by measuring how many predicted samples are truly positive; it’s the precision. According to Equation (24), we can say that high precision means fewer true positive classifications. High precision in eggplant disease Classification implies that predicted disease labels are very reliable.

(24)

Recall measures the fraction of relevant disease instances that are identified by the model and is calculated as in equation (25). Recall measures the ratio of true positive samples correctly identified by the model. A higher recall value shows effective Classification of diseased leaf samples with a lesser number of false negatives.

(25)

F1-score gives out one number by taking the harmonic mean of precision and recall. Equation (26) captures a key evaluation of classification performance on an unbalanced dataset. The F1-score is high only if both Precision and Recall are performing well together.

(26)

Whichever metric we use, these need to be interpreted in tandem with each other to be able to get a clear understanding of the classification ability possessed by the YOLOv8m model. As suggested in our earlier work, this allows for a comprehensive evaluation of the proposed approach to accurately categorize eggplant leaf diseases.

We determine the better model by benchmarking YOLOv8n, YOLOv8s, YOLOv8m, YOLOv8l, and YOLOv8x. Model selection occurs at this step based on evaluating metrics derived from the experiment, with focus given to the F1 score because it can balance precision and recall contributions represented in equation (27).

M* = arg max_M F1(M) (27)

Here, M is the set of candidate YOLOv8 models, and F1(M) denotes the F1 score on a specific model. This means that M* is the model that optimizes F1-score and is bounded by the rest of the variant configurations. To prioritize a model is to maximize the F1-score because it considers false positive and false negative predictions at the same time, compared to accuracy, which considers only the true value of predicted classes. This is especially crucial for multi-class disease classification tasks where maintaining consistent performance across every class is a must-have.

Experimental results show that the YOLOv8m model provides the optimal trade-off between classification accuracy and computational efficiency. Smaller variants, such as YOLOv8n, allow for faster inference speed with lower cost of computation but suffer in terms of classification performance. On the flip side, bigger models like YOLOv8l and YOLOv8x can obtain marginally better accuracy with a substantially larger amount of compute and training time. The YOLOv8m model can achieve stable convergence and high classification accuracy with efficient computational performance, thus allowing real-time Classification of eggplant leaf diseases. Therefore, YOLOv8m is selected as the model that will be deployed within an in-house programmed system.

Figure 2 conveys the training accuracy curves of the YOLOv8 versions after the same number of training rounds. The approximate comparison of curves in the graph demonstrates the speed of classification performance improvement for each version of YOLOv8 during training. Each YOLOv8 version continuously increases classification performance after each round of training, and each version of YOLOv8 demonstrates the successful learning of deep features in the eggplant leaf dataset. YOLOv8n, the lightweight version of YOLOv8, has a slow convergence speed and a low classification accuracy. Meanwhile, larger versions of YOLOv8, such as YOLOv8m, have a stable convergence speed and a capacity for good classification performance. While YOLOv8l and YOLOv8x demonstrate a slightly higher classification achievement than other YOLOv8 versions, this comes at the cost of greater computational complexity and a longer training time than YOLOv8m. However, YOLOv8m achieves a better balance between performance and efficiency, which makes it more applicable in real-time disease classification applications. In this regard, the figure proves that the YOLOv8 architecture is suitable for Eggplant leaf disease classification and recommends that YOLOv8m is appropriate for implementation in real-world agricultural systems.

In Figure 3, we show how the training loss varies for different YOLOv8 model variants, YOLOv8n, YOLOv8s, YOLOv8m, YOLOv8l, and YOLOv8x, over multiple epochs of training. The graph indicates how well each model minimizes the loss function for learning. All models have high loss in the initial epochs of training, and this reduces with each subsequent epoch. As a result, the decrease in loss suggests that both models are learning to reduce classification errors and improve their predictions over time. The last three YOLOv8m, YOLOv8l, and YOLOv8x models reach lower values of final loss compared to the original model, YOLOv8n, and remain faster in terms of loss reduction. The YOLOv8n model keeps relatively larger loss during training because it can not learn complex features from its lightweight architecture. Comparatively, larger models tend to have better optimization behavior because of their more powerful representational capabilities. YOLOv8m is the most efficient from the tradeoff perspective for convergence speed and computational cost, as the other large versions (YOLOv8l and YOLOv8x) are not, due to their very small differences in performance from YOLOv8m and their computational complexity. Overall, the training process is confirmed to perform the deep learning function of YOLOv8, which is to customize the training, and subsequently, the migration classification errors are minimized. Given the training results, YOLOv8m is the most effective model for the classification of eggplant leaf diseases.

Figure 4 provides the confusion matrices for YOLOv8n, YOLOv8s, YOLOv8m, YOLOv8l, and YOLOv8x models for classifying eggplant leaf disease. A confusion matrix summarizes the results of a classification process by matching true class labels with predicted class labels. The statistics of the classification results for each confusion matrix are shown on the diagonal, and the statistics for the confusion cases among the disease classes are shown in the non-diagonal elements. Larger figures on the diagonal indicative of better classification performance and higher reliability or confidence in model predictions. The results indicate that all YOLOv8 variants perform well in terms of classification for most disease classes. Nevertheless, lightweight architectures such as YOLOv8n misclassify these diseases at a relatively higher rate than others, especially in a visually similar range of disease categories. This means low classification errors as the model complexity increases, good feature representation, and discrimination capability. Among the models evaluated, YOLOv8m shows highly consistent classification performance, and the misclassified samples in all disease categories are also much fewer compared to other models. From the confusion matrix of YOLOv8m, it is apparent that there is a dominant diagonal, suggesting that the healthy leaves were predicted correctly, and multiple disease conditions. While the YOLOv8l and YOLOv8x also perform competitively for classification, they require more computation than YOLOv8m. It also shows that diseases with distinct visual symptoms, such as Wilt Disease and White Mold Disease, are better classified in all models. In classes that appear similar, Leaf Spot Disease and Mosaic Virus Disease, for example, there is minor confusion. Figure 4 verifies the effectiveness of the proposed YOLOv8-based classification framework and shows that both accuracy and stability are in harmony between classifying methods, with high classification efficiency to achieve real-time eggplant leaf disease identification, where YOLOv8m is a satisfactory one.

Figure 5 lays out the Receiver Operating Characteristic (ROC) curves for YOLOv8n, YOLOv8s, YOLOv8m, YOLOv8l, and YOLOv8x versions for classifying eggplant leaf disease. The ROC curve observes the classification of the models by balancing the positive prediction rate with the false positive rate. All versions place the ROC curves for the disease models in the upper-left area, reflecting their deep understanding of the disease categories. All YOLOv8 models tested performed beyond a random guess classification. YOLOv8 models showed good predictions for separating different disease classes and good predictions relative to other classification models for this dataset. All variants of the YOLO v8 classification models showed the predicted class “leaf disease” trending toward the upper area of the curve. YOLOv8n models’ prediction class “leaf disease” trended toward being good, while YOLOv8m models’ curve, in addition to being good, showed a cutting prediction loss for class “leaf disease” in a leftward direction. YOLOv8m models showed the most class-stable ROC results for the evaluated class models, with the least computational implementation among the other evaluated models, YOLOv8l and YOLOv8x, respectively. All class disease prediction models remained with a good prediction, a class-stable and reliable model beyond a random prediction. The ROC analysis also highlights the parameter-set-built YOLOv8-based framework for the overall categorization capability of multiple eggplant leaf diseases. The results provide evidence that YOLOv8m is a practical candidate, balancing computational power demands and providing decent classification accuracy.

The Precision-Recall (PR) curves of eggplant leaf disease classification for YOLOv8n, YOLOv8s, YOLOv8m, YOLOv8l, and YOLOv8x are illustrated in Figure 6. The PR curve quantifies the balance between precision and recall, thus providing a better assessment metric for classification reliability for each disease. The curves cluster in the upper right quadrant, indicating they are the best models for predicting a class and for discriminating between classes. The larger the curve area, the better the precision and recall. This means the models are classifying disease categories, and they are minimizing the model outputs that are classified as positive when they are negative in reality, thus improving the quality of the disease recognition. The weaker PR characteristics of several classes in the YOLOv8n model could be attributed to the model not learning predictive features. This is in contrast to YOLOv8m, which exhibits precision-recall curves that are smooth and more stable on the boundaries, indicative of better variance in model prediction learning and classification. YOLOv8m curves are close to the optimal region, implying classification for healthy leaf samples remained stable, as did disease leaf classification. The high values of the area of the curves under the disease categories show that the classification model has a reliable Classification of the disease and recognition capability of the related patterns. On the other hand, the classes with the most visually similar symptoms exhibit less variance. The implementation of the YOLOv8-based system for multi-class eggplant leaf disease classification shows positive results. Both single and combined usage have shown results indicative of the system’s capacity for practical real-time deployment, with YOLOv8m demonstrating more than adequate performance.

Performance metrics, including accuracy, precision, recall, and F1-score of the various YOLOv8-based architectures in the context of the classification of eggplant leaf diseases, are documented in Figure 7. The classification performance of the various designs has been summarized. YOLOv8n scored the lowest in performance compared to all architectures. From the comparative analysis of YOLOv8n, it can be inferred that its lightweight architecture was not able to learn disease-rich features. YOLOv8s, being of a larger design and compared to its predecessor, showed improved performance in classification. However, the performance compared to other larger variants was still scored lower because of YOLOv8s's comparatively weaker capacity in feature representation. YOLOv8l and YOLOv8x showed higher feature representation. In summary, these models have a higher potential to learn disease characteristics. However, each requires a substantial amount of RAM, inference time, and computational resources. Therefore, these models are less appropriate for real-time agriculture and other potential implementations that take place in resource-constrained circumstances. YOLOv8m scored the highest performance across all assessed architectures with an accuracy of 96.84%, a precision of 96.85%, a recall of 96.84%, and an F1-score of 96.84%. The result indicates that YOLOv8m can learn features of different diseases with the least variance in classification prediction. It also showed the least computational cost among larger models. In order to achieve real-time illness diagnosis in the field while also integrating the tracking system for targeted disease diagnosis, a precise agriculture system is essential. The YOLOv8m exhibits excellent performance in the real-time classification of eggplant leaf diseases.

The proposed YOLOv8m Framework for Eggplant Leaf Disease Classification shows visual results for interpreting the framework using Grad-CAM, Grad-CAM++, and EigenCAM, as shown in Figure 8. Since YOLOv8m is based on the architecture of the YOLO (You Only Look Once) framework, the results show how the trained model identifies parts of the image and is likely to focus and concentrate on classification. The first row is the original input images, which are classified as healthy leaf, white mold disease, leaf spot disease, wilt disease, mosaic virus disease, and insect pest disease, in that order. The following rows show various interpretations using the trained model, which determines model classification. The white mold and mosaic virus disease samples show regions of the image that are possibly infected and discolored, and are likely to focus on disease symptoms. The Grad-CAM and Grad-CAM++ techniques focus strictly on disease symptoms, and EigenCAM tends to represent a larger area in the image. The examples show consistency in identifying disease features in the provided dataset. The visual attention analysis shows the YOLOv8m architecture's ability to highlight the ease and flexibility of the approach in locating disease symptoms. This enhances the thoroughness of the deep learning process and builds a consistent classification model appropriate for real-world applications in farming. The YOLOv8m-based framework can capture specific visual disease patterns and provide a fully understandable decision-making process for the classification of eggplant leaf disease.

Figure 9 depicts a tree-based CV in a real-time eggplant leaf disease classification application using a YOLOv8m-based web application. Leaf images were uploaded, and responses were provided in real-time regarding disease prediction using the interactive interface. This app performed a multi-class classification on various disease classes: Healthy Leaf, White Mold Disease, Leaf Spot Disease, Wilt Disease, Mosaic Virus Disease, and Insect Disease. Each of the uploaded images was provided with a classification and confidence score, affirming the reliable prediction of various disease conditions. The interface employed Grad-CAM, Grad-CAM++, and EigenCAM visualization methods for interpretability. These heatmap visualizations highlight the most influential image regions for the classification. This shows the symptoms of the disease spread over the classification leaf. Introducing the used activation maps, we can conclude that our model focuses on almost all lesion areas, patches of discoloration, infected textures, and the structure of damaged leaves for different diseases. This visualization plays an important role in validating the learning behavior of the proposed framework, as well as enabling a clear insight into the prediction analysis. The deployment results confirm real-time leaf processing from previously unseen instances of the high-resolution image sets classified with stable performance using the YOLOv8m model. Streamlit’s interface, being light and easy to use, further enhances the experience of using it practically in the field for agricultural monitoring applications. The applications of this framework include automated eggplant leaf disease Classification and a real-time precision agriculture support system.