Fractal and multifractal new metrics for pathological characterization and quantification in diabetic retinopathy and glaucoma

Abstract

Fractal and multifractal analysis of retinal vasculature are considered as potential biomarkers to detect several vascular pathologies affecting the retina, by analysing fundus images. The use of these tools requires additional metrics that allow the quantification and characterization of the retinal image. In the present study, fractal and multifractal analysis were used to characterize images of pathological retinas classified as diabetic retinopathy and glaucoma. Using both tools, several quantitative metrics based on Kullback–Leibler divergence and Mahalanobis distance among others, were developed to quantify the severity of the pathology in each retina within the two groups. These metrics allow to give a value of the affectation of the retinal vasculature, identify all the points considered as anomalous and facilitate the classification of the retinas according to their degree of severity. The analysis allowed to distinguish between healthy and pathological retinas. In addition, with the developed metrics it has been possible to determine the affected areas of each pathological retina, determine the degree of affectation of these areas, and quantify the severity of the retina. The results were based on quantitative and qualitative measures obtained through fractal and multifractal analysis. The metrics used showed consistent agreement with the findings obtained in the study.