Differentiation Filtered Feature Selection Method for Diabetic Retinopathy Detection from Fundus Images

Diabetic retinopathy is the leading cause of vision loss worldwide, caused by diabetes-related damage to retinal blood vessels. Fundus imaging is a non-invasive approach for capturing detailed images of the retina, which allows for the detection of microaneurysms, hemorrhages, and other disease-related abnormalities [1, 2]. Recent advances in imaging technology, such as ultra-widefield and handheld fundus cameras, have improved the ability to detect central and peripheral retinal lesions. Such devices enable thorough retinal evaluations, facilitating early diagnosis and intervention [3, 4]. High-resolution imaging has enhanced the clarity and precision of detecting small retinal changes. The use of fundus imaging in routine screenings allows for better disease progression tracking and treatment efficacy evaluation [5]. Early diagnosis using fundus inputs reduces the chance of blindness through precautionary medications. The availability of portable fundus cameras has increased screening capacity, especially in remote and underserved areas, hence improving overall healthcare outcomes for diabetic patients [4, 6].

Machine learning (ML) methods have become essential for automating diabetic retinopathy identification using fundus pictures. Such algorithms, particularly convolutional neural networks, are highly effective at detecting microaneurysms, exudates, and neovascularization [7, 8]. Advanced models combine standard image processing with deep learning, which increases detection accuracy while decreasing computational complexity [9]. Transfer learning techniques increase efficiency by adapting pre-trained models to specific datasets and reducing the requirement for substantial training data. Automated systems allow uniform and objective grading of retinal anomalies, which overcomes the limitations of manual examinations [10, 11]. ML is useful for large-scale screening programs because it can process data in real time. The algorithms improve diagnostic precision while decreasing false positives, which leads to dependable and scalable solutions for early detection. ML in diabetic retinopathy screening promotes effective healthcare delivery, especially for resource-constrained areas, and aids in preventing vision loss through timely interventions [8, 12]. The contributions of the article are:

• Proposal and description of the novel Differentiation-Responsive Feature Selection (DRFS) method for improving the accuracy of the diabetic retinopathy detection process using fundus images.

• The implication and discussion of the graph neural network for responsive feature identification by analyzing the linear and non-linear pixel distributions is presented.

• The presentation of the performance assessment using experimental results and comparative metrics to evaluate and validate the proposed method’s performance.

The article is organized as follows: The related works are discussed in Section 2, with the problem identified, and in Section 3, the proposed method is described with mathematical equations, diagrammatic illustrations, and explanations. In Section 4, the experimental and comparative performance assessments are described, followed by the conclusion, limitations, and future inclusions in Section 5.

Early detection and diagnosis of Diabetic Retinopathy (DR) are important to prevent severe infection complications. Fundus imaging, which acts as a non-invasive diagnostic tool, helps to detect retinal abnormalities. In this paper, refined image processing and feature selection techniques accurately identify DR-related infection. The incorporation of the DRFS method enhances DR detection precision by combining a graph neural network with a differentiation function. This filters non-linear pixel distributions to identify critical features based on flexible pixel detection to ensure high accuracy, which is adaptable to various input image sizes. The proposed DRFS is presented in Figure 1.

Figure 1. Proposed DRFS method

The responsive feature selection is performed using a non-linear pixel distribution from the extracted ones. The differentiation output is reliable for detecting pixel distribution based on intensity, wherein the responsiveness is accounted based on mapping. In the mapping process, the invariant feature that distinguishes the pixels is identified for detecting infected regions. The responsiveness of a feature is identified from its mapping and intensity verification using a similarity measure. This turns out to be the novelty of the proposed method that clearly differentiates various features that coexist with multiple features in normal or overlapping regions. From the fundus image, the feature extraction for Diabetic Retinopathy includes vascular changes, which are denoted as $ves$ for $k$ number of regions, and $cb$ epresents the color-based features that identify abnormalities. The texture of the image is termed as $tx$, which helps to differentiate the infected and non-infected regions. The size of the area is denoted as $sz$, ich indicates the varying stages of DR. The term size refers to the pixel regions that represent the infected part. This is represented by the $(x, y)$ regions of the input image; the segmenting region resembles these specific pixels through different representations. In the extraction process, the size is unknown and it represents the size of the entire image whereas the segmentation shrinks the actual representation to maximize the infected region detection without false positives. The direction is represented as $dr$, which helps to detect the boundaries of the image. The following equation $f t_{e x t}$ extracts feature from the fundus image at $(x, y)$ pixel coordinates.

$\begin{gathered}f t_{e x t}=\sum_{j=1}^k\left[{ves}_j(x, y) \times c b_j(x, y) \times t x_j(x, y)\right] +s z_j(x, y)+d r_j(x, y)\end{gathered}$          (1)

Here, the identified features help to reduce the impact of the relevant infected region, which leads to difficulty in the diagnosis of Diabetic Retinopathy. It enables the system to adapt to various fundus images that improve the accuracy of detection. This enhances the DRFS method to detect Diabetic Retinopathy with high precision. The feature direction relies on the pixel position from (1, 1) to $(x, y)$; the extraction from definite pixel position is alone considered to identify the direction. In particular, the direction factor refers to the pixel traversal identified until maximum pixel is reached. Such traversal is referred to maximize the feature extraction, region detection, and to improve segmentation accuracy. Besides, the feature extraction texture and intensity factors are considered to identify the pixels and regions. Depending on the different image sizes, the direction traversal time varies. In a conventional feature extraction method, the available features are extracted and processed. This method also follows the same with pre-computed extraction. The pre-computation for high intensity and low texture (patterns) is the constraint in handling features based on the regions. From this feature extraction, the following $n l_{{transform }}$ and $n l_{{inter }}$ equations evaluate the non-linear transformation and interaction.

$\begin{aligned} n l_{ {transform }}(x, y)= & {\left[\left(s z_{j-1} \times s z_j(x, y)\right)\right.}  \left.+\left(d r_{j-1} \times d r_j(x, y)\right)+f t_{ {ext }}\right]\end{aligned}$          (2)

$\begin{aligned} n l_{{inter }}=\left(\frac{1}{\left(f t_{ {ext }-1}-f t_{ {ext }-2}\right)}\right)  & \times\left(1+\left(n l_{{transform }}(x, y) \times c b_j(x, y)\right)\right)\end{aligned}$          (3)

Eq. (2) focuses on transforming pixels that highlight the important features of the retina. The previous regions of size and directions are measured as $s z_{j-1}$ and $d r_{j-1}$ which helps to understand the distribution of infected regions from previous regions. This normalizes the variations that are prioritized and improves the identification of changes in the retina. In Eq. (3), the term $\left(\frac{1}{\left(f t_{e x t-1}-f t_{e x t-2}\right)}\right)$ estimates the difference between extracted features $f t_{e x t-1}$ to $f t_{e x t-2}$. It helps to identify the relationship between various features that often categorize complex and simple variations in the region. The chances for $\left(f t_{e x t-1}-f t_{e x t-2}\right)=0$ (least) is less as the pixels exhibit multiple features and the resultant is either greater than 0 or less than 0. Therefore, the chances of denominator less than the numerator are not possible until the pixels exhibit one feature and a one-to-one mapping is made. Therefore, the interaction in positive side identifies new edges between the features whereas a negative interaction reduces a replicated edge. This interaction between the retinal images provides an accurate classification of detection. This enhances the accuracy of the DR detection.

In DR detection, GNN analyzes complex relationships and interactions between various features extracted from fundus images by processing these features through a message-passing mechanism. The complex relationships refer to the representation of appropriate features and their regions with different shared pixels. Therefore, mapping one-to-one pixels and regions is tedious, as a single pixel exhibits different features and therefore one-to-many mapping is inferred. Besides, the neighbor region also shares the common features from different pixels such that the feature filtering relies on specific mapping made. Thus, the complexity in identifying false rates is high such that the one-to-many representation is to be simplified explicitly. In this, each region aggregates information from its neighboring region to update its feature representation. This captures higher-order interactions and correlations between blood vessels and exudates, which are indicative of DR. The layers continuously pass messages to improve the model's ability to detect infected regions. It filters out irrelevant features and concentrates on the most distinguishing ones to reduce false positives. The GNN's ability to process non-linear relationships between features enhances the detection of subtle retinal abnormalities. The differentiation part is responsible for filtering features that result in less distribution detection, which is expressed as $f t_{{diff }}(x, y)$ in the equation below:

$\begin{aligned} f t_{\ {filter }}=\left[f t_{ {ext }}\right. & \left(n l_{ {inter }}-\widehat{n l}_{ {inter }}\right) \left.\times\left(1-n l_{{transform }}(x, y)\right)\right]\end{aligned}$          (4)

$\begin{aligned} f t_{{diff }}(x, y)=\| & f t_{ {ext }-2}-f t_{{ext }-1} \| +\exp \left(-\mid d i s_{f t}(x+j, y+j)\right.  \left.-f t_{ {filter }}(x, y) \mid\right)\end{aligned}$          (5)

The obtained features were filtered as $f t_{ {filter }}$ based on the feature extraction that combines non-linear parts. Here, the term $\left(n l_{ {inter }}-\widehat{n l}_{{inter }}\right)$ identifies the difference between actual non-linear interaction and the change in non-linear interaction, and is denoted $\widehat{n l}_{{inter }}$. The term $\left(1-n l_{{transform }}(x, y)\right)$ analyzes the impact of non-linear transformation. Together, this process helps to filter features that cause significant changes. The term $\left\|f t_{e x t-2}-f t_{e x t-1}\right\|$ evaluates the difference between two different extracted features for accurate anomaly detection. Feature filtering and differentiation referred in equations above are used to define the uniform and non-uniform mapping between the features.

This is performed to reduce the number of transform outputs influencing the true rate of the region. Besides, the computation identifies differentiable outputs through separating erroneous and positive features that illustrates the pixels (independent and shared). Therefore, these equations are distinct to identify independent features and their corresponding differences, if any. The feature filtering process is illustrated in Figure 2.

Figure 2. Feature filtering process

The $f t_{ {filter }}$ the process is diagrammatically presented in the above Figure 2. The features extracted are used to identify $t x \in s z$. First, $d i s_{f t}$ is computed for $c b$ under distinguishable differentiation and linear (assumption) distributions. However, if $\left[\frac{1}{\left(f_{ {text }-1}-f_{{text }-2}\right)}\right]>0$, then the normalization process is pursued. If the normalization does not fit the $n l_{{transform }}$, then the linearity is disturbed for which $f t_{ {diff }}(x, y)$ estimation is required. Depending on the major difference between $(x+j, y+j)$, the $\hat{n} l_{{inter }}$ is detected and therefore $p x_{ {flex }}(x, y)$ is only applicable for those $f t_{{ext }}$. Therefore, the number of $k \in c b$ and $d r$ region detection is eased through filtering. These features are required to concatenate pixel distributions based on intensity. Such grouping is useful in identifying invariant features even after normalization. The pixel variation between specific regions was computed based on dissimilarities in features and is expressed as ${dis}_{f t}(x+j, y+j)$. It helps to identify regions with high variations based on pixel coordinates, which is crucial for identifying DR features. In DR detection, the differentiation process filters out features that have low variance, which contributes less to detecting DR infection. This enhances both the accuracy and efficiency of the detection process. The following equation $p x_{ {flex }}(x, y)$ computes how the detection is flexible for pixel distributions with high false rates.

$p x_{f l e x}(x, y)=\sum_{j=1}^k\left(d r_j(x, y) \times f t_{e x t}\right)+\left[d i s_{f t}-\frac{1}{\left(p x_{i n t e n}-f t_{d i f f}(x, y)\right)}\right]$          (6)

The direction of boundaries with extracted features was combined to monitor the changes that depend on the reliability of the pixel. The term $\left[{dis}_{f t}-\frac{1}{\left(p x_{{inten }}-f t_{{diff }}(x, y)\right)}\right]$ incorporates pixel intensity, which is denoted as $p x_{{inten }}$ helps to analyze how quickly the variations occur based on the intensity of pixels. It determines how the features of pixels $(x, y)$ contribute to the overall detections. This identifies whether the pixels are reliable or unreliable in the particular region that contains high false positive rates. It helps to filter the regions that cause high false rates during the detection. The system can adjust the regions of feature extraction based on the characteristics of pixel distribution that highlight high variability and change in the pattern. It improves the detection of DR even in the presence of highly varying feature regions. The pixel distribution is stable based on the pixel intensity that is expressed as $f\left(p x_{{flex }}\right)$ in the following.

$\begin{aligned} & f\left(p x_{{flex }}\right) =\left\{\begin{array}{c}\left(d r_j(x, y)+d i s_{f t}\right) \forall p x_{{inten }} \geq x_{\max } \\ \left(d r_j(x, y)+d i s_{f t}-f t_{ {filter }}\right) \forall p x_{ {inten }}<x_{\min }\end{array}\right.\end{aligned}$          (7)

The pixel distribution is considered reliable for DR detection during $p x_{i n t e n} \geq x_{\max }$ based on $\left(d r_j(x, y)+d i s_{f t}\right)$ that indicates the features are similar to DR. A high variation in pixel intensity provides a significant change in pixel distribution, which helps to indicate the abnormalities in the fundus image. An unreliable feature was identified based on $p x_{{inten }}<x_{\min }$ with $\left(d r_j(x, y)+d i s_{f t}-f t_{f i l t e r}\right)$ which indicates false positive regions with uniform pixel distribution. This unreliable region was filtered out from the DR detection. The reliable and unreliable regions were analyzed based on the maximum and minimum threshold values, which are termed as $x_{\max }$ and $x_{\min }$. This helps to minimize the irrelevant features and regions that do not contain any DR infections. The GNN trains the features at the layer $l$ based on the pixel data, which is computed in the equation below.

$\begin{aligned} f t_{l+1}(x, y)=f & t_l(x, y) +\sum_{k \in(x, y)}\left(f t_{f i l t e r}+f t_{d i f f}\right) \times\left(p x_{f l e x}(x, y)-d i s_{f t}\right)\end{aligned}$          (8)

The extracted feature information from layer $l$ is trained using pixels in each region. The new layer is updated from the previous information and is denoted as $f t_{l+1}(x, y)$. he continuous iteration of GNN updates each layer based on its existing feature with the neighboring feature values. It allows the system to capture the relationship between features of different regions, which is important for the accurate detection of DR-related abnormalities in the retina. The following equation $E_{ {decision }}(x, y)$ analyzes how the feature for detecting DR through the comparative decision is increased by identifying sufficient distributions.

$\begin{aligned} & E_{{decision }}(x, y) =\left\{\begin{array}{l}=\left(f t_{{diff }}+f t_l(x, y)\right) \times\left|\begin{array}{c}n l_{{inter }} \\ -n l_{ {transform }}\end{array}\right|+f t_{ {filter }} \\ =f t_{{ext }}\left(p x_{{flex }}(x, y)+{ dis }_{f t}\right) \forall(x, y) \in(1,2, \ldots, k)\end{array}\right.\end{aligned}$          (9)

The above equation compares the distribution of various extracted features in the fundus image with their pixels. The feature is considered sufficient with $E_{ {decision }}=1 \forall(x, y) \in(1,2, \ldots, k)$ and ensures it is reliable in detecting DR-related abnormalities. It prioritizes the features based on their importance, which is learned during the training. This enables the system to adjust based on the features that meet the requirement. It enhances the performance of the system when sufficient discriminative features increase. This decision helps to classify DR and on-DR regions from various features. The decision model represented in Eq. (9) considers the filtering and distribution flexibility across various pixels. The one-to-one and one-to-many mapping using the GNN requires the precise classification of differentiated features and extracted features through pixel to region detection. For an overlapping pixel, the region differentiation is mandatory whereas for an independent feature, one-to-one mapping is alone required. These differences are highlighted in this equation that is required to train the learning model. From the above decision, the invariant features were evaluated as ${inv}_{f t}(x, y)$ in the below equation.

$\begin{aligned} {inv}_{f t}(x, y)=p x_{{flex }}(x, y)  +\left(\frac{p x_{ {inten }}}{f t_{ {diff }}- { dis }_{f t}}\right) \times\left(f t_{ {ext }-2}-f t_{\ {ext }-1}\right) \forall E_{{decision }}=0\end{aligned}$          (10)

$\begin{aligned} D R_{{infection }}(x, y) & =f t_{ {ext }}  +\left(n l_{{inter }}+p x_{ {flex }}(x, y)\right)  \times E_{{decision }}+i n v_{f t}(x, y)\end{aligned}$          (11)

Eq. (10) focuses on patterns that indicate the DR regions rather than the irrelevant regions. It combines features that are consistent and reliable, even in varying input image conditions. The GNN model for invariable feature detection is presented in Figure 3.

In Figure 3, $inV_{f t}$ detection process is described using $(x, y, j)$ variants. The $p x_{{inten }}$ using $(x, y)$ is the first assumed intensity for categorizing $x_{\min }$ and $x_{\max }$. This categorization is required to perform $E_{ {decision }}(x, y)$ under multiple $d i s_{f t}$ identified. The first mapping using $k \forall\left(f t_{{diff }}\right.$, $\left.d i s_{f t}\right)$ is useful in identifying $x_{\max }$ based on $\left(f t_{{ext-1 }}-f t_{{ext-2 }}\right)$ provided the $f\left(p x_{{flex }}\right)$ is defined as either high/low. These output cases are matched with $i$ and $j$ until $(x+j)=(y+j)$ is true, and therefore the mapping is repeated without $\left(d i s_{f t}>0\right)$. Therefore the $(i=j)$ cases are used to update the $p x_{{inten }}$ for $x_{\min }$ or $x_{\max }$ classification. Using the consecutive mapping, the graph neural network layers for $i n V_{f t}$ are defined. Features with small variations were considered stable, and large variations may lower the value for an invariable feature that leads to instability. In a graph representation, the features, pixels, and $x_{\min}$  constitutes the structure. These elements form the nodes and the mapping (one-to-one or one-to-many) forms the edges based on different regions occupied. Besides, the final edges are formulated based on similarity index. The similarity index represents the intensity and invariable detection identified between the nodes. It enhances the system’s ability to detect DR based on stable features. Eq. (11) identifies the infected regions by integrating the previous factors. A high value of $D R_{{infection }}(x, y)$ indicate the region as an infected region, and a lower value ensures a healthy and non-infected region.

The confusion matrix for differences in feature detection monitors the performance of the features considered. In the proposed method, how it classifies pixels or regions in fundus images as infected or non-infected is described. The proposed DRFS ensures that only discriminative features are utilized to achieve higher True positives and True negatives. It minimizes the false positives and false negatives. The existing methods often rely on linear distributions, whereas the proposed method reduces false negatives by accurately identifying subtle abnormalities in early detection (Figure 4).

Figure 3. GNN model for invariable feature detection

Figure 4. Confusion matrix for difference detection

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Figure 5. ROC for invariable feature detection

The ROC identifies the true positive rate against the false positive rate based on the evaluation of the specificity of invariable feature detection. The ROC indicates high performance by the proposed method in distinguishing DR-infected regions from healthy areas. The invariable features were extracted through differentiation ${inv}_{f t}(x, y) \forall E_{{decision }} \in(1,2, \ldots, k)$ that allowed the proposed method to maintain a consistent True positive rate even at low false positive rates. The existing methods often suffer from a high false rate due to their inability to adapt to non-linear distributions, leading to an inconsistent ROC curve. The proposed approach shows significant improvements in detecting invariable features across varied image conditions when compared to the existing methods (Figure 5).