Numerical modeling of the upper and lower major temporal arcade in fundus images using genetic algorithms

In this paper, a new numerical modeling methodology is presented for the thickest vein in the retina, the major temporal arcade, since previous studies have shown that modifications in its opening, tortuosity and even thickness are indicative that the patient suffers from a type of retinopathy, which if not treated promptly, can lead to irreversible blindness. A model for the arcade vein is analyzed by spline functions, where a genetic algorithm was applied to determine the control points. Subsequently, once the model was determined, the equations of the cubic tracers were used to estimate the opening angle of the arcade. The results obtained were compared using two measures, the mean distance to the closest point and the Hausdorff distance. Although the UMDA+SA method remains the fastest, the proposed method is only 0.39 seconds below it, however, its measurements are 27.81 and 68.39 (Mean Distance to the Closest Point and Hausdorff distance) pixels larger with respect to the new method. Different measurements for the opening angle were obtained for the set of images from the DRIVE database. The models of cubic splines and the opening angle have been obtained quickly and this type of functions are excellent since they are smooth functions and do not present abrupt oscillations in the fit.