Fractal and bifurcation theory analysis of retinal images: Advancing diabetic retinopathy diagnosis using the MESSIDOR database

Diabetic retinopathy (DR) is the main cause of blindness in working-age adults, and early detection is essential for effective treatment. The quality of retinal images is a key factor in the accuracy of automated diagnostic systems. Based on retinopathy images from the MESSIDOR database, this paper explores the application of fractal analysis to evaluate the quality and classification of diabetic retinal images. The results show that the fractal dimension (FD) can be used as an index to quantify image quality. The relationship between image parameters (mean, standard deviation, and skewness) and FD is analyzed to quantitatively assess image quality and the effect of vessel extraction. The average FDs decrease from grade 0 to grade 1, remain nearly unchanged between grades 1 and 2, and increase from grades 2 to 3. The simulation of the fractal tree-like branching network indicates that symmetry has a minor effect on FDs. As DR progresses, blood flow transitions from laminar to turbulent, the vessel radius decreases and blood pressure increases. The findings of this paper have significant implications for diagnostic decision-making, the development of personalized treatment plans, and the long-term monitoring of retinopathy progression.