• Persistent Homology and Fractal Dimension-Based Classification of Retinal Fundus Images

Diabetic Retinopathy (DR) is a progressive microvascular complication of diabetes and remains one of the leading causes of preventable blindness worldwide. Early and reliable detection is essential for reducing vision loss. Conventional image-based methods primarily rely on intensity and texture features. These features often fail to capture the complex geometric organization and subtle structural alterations of retinal vasculature seen in disease progression. In this study, we propose a mathematically driven framework that combines Topological Data Analysis (TDA) with nonlinear dynamics to improve DR classification. Persistent homology was applied to the dataset to extract multiscale topological descriptors, such as connected components and loops, by filtration. The results from persistent homology were encoded as persistence diagrams and then converted into quantitative feature vectors for input to a machine learning model. In parallel, we computed the fractal dimension to quantify vascular complexity and spatial irregularities, reflecting pathological changes. The combined topological and fractal features were used to train a Support Vector Machine (SVM) classifier to grade DR severity. The proposed hybrid approach achieved an overall classification accuracy of 94%. It showed strong discriminative performance across disease stages and improved sensitivity to early structural abnormalities while maintaining high specificity. By capturing intrinsic geometric and dynamical characteristics of retinal images, this integrated TDA–nonlinear dynamics framework offers a robust, interpretable, and clinically relevant methodology for automated diabetic retinopathy screening.