Numerical Modeling of the Major Temporal Arcade Using BUMDA and Jacobi Polynomials

Abstract

Within eye diseases, diabetic retinopathy and retinopathy of prematurity are considered one of the main causes of blindness in adults and children. In order to prevent the disease from reaching such an extreme, a timely diagnosis and effective treatment must be applied. Until now, the way to verify the state of the retina has been to make qualitative observations of fundus images, all carried out by an ophthalmological specialist; however, this is totally restricted to their experience, and some changes in the vascular structure of the retina could be omitted, in addition to the fact that very high resolution images would be needed to be able to detect significant changes. Accordingly, with the help of computational tools, this diagnostic/monitoring process can be improved. This paper presents a novel strategy for the modeling of the MTA by using an estimation of distribution algorithm (EDA) based on the probability density function in order to determine the coefficients and parameters (α,β) of a Jacobi polynomial series. A model using polynomials is the novel aspect of this work since in the literature there are no models of the MTA of this type, in addition to seeking to better cover the profile of the retinal vein. According to the experimental results, the proposed method presents the advantage to achieve superior performance in terms of the mean distance to the closest point (4.34 pixels), and the Hausdorff distance (14.43 pixels) with respect to different state-of-the-art methods of the numerical modeling of the retina, using the DRIVE database of retinal fundus images with a manual delineation of the MTA performed by an specialist.

Keywords

• Boltzmann univariate marginal distribution algorithm
• estimation of distribution algorithm
• jacobi polynomials
• major temporal arcade
• retinal fundus images