Quantifying Diabetic Retinopathy Variation Through Fractal Dimension: A Statistical Approach

Fractal analysis of fundus imaging data of the human retinal vasculature could reveal vascular abnormalities caused by diabetic retinopathy. Instead of using an existing technique from earlier research to determine the fractal dimension value of the complete vessels of the retina to distinguish between the three types of diabetic retinopathy (DR), a novel approach is used in this research to determine the fractal dimension values of the vessels, arteries and veins in the retina separately. Box-counting technique is used to calculate the fractal dimension values. Additionally, the three stages of diabetic retinopathy (DR1, DR2, and DR3) are compared to the fractal dimension (FD) of the retina which is normal. For each category, retinal images were obtained from the Kaggle dataset. The FD of retinal vasculature, retinal artery structure, and retinal vein structure of each retinal image are then computed using box-counting technique. A calculated p-value from t-test are used to compare the mean fractal dimension values of each pair's artery, vein, and overall vasculature in order to determine whether there is a dissimilarity between each pair (DR1 vs. DR2, DR2 vs. DR3, DR3 vs. DR1, Normal vs. DR1, Normal vs. DR2, Normal vs. DR3). When the entire vascular structure is considered, there is no dissimilarity between the mean fractal dimension values of each pair, as shown by the calculated p-values of 0.34, 0.60, and 0.62 for pairs DR1 versus DR2, DR2 versus DR3, and DR1 versus DR3, respectively however, when the artery and vein structures are considered independently, the significance is seen because all computed p-values are below the significance level. The fractal dimension value of the retinal image can differentiate between a normal retina and one that has experienced diabetic retinopathy when applied to the full vascular anatomy.