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A novel diagnostic scheme to develop quantitative indexes of diabetes is introduced in this paper. The fractal dimension of the vascular distribution is estimated because we discovered that the fractal dimension of a severe diabetic patient's retinal vascular distribution appears greater than that of a normal human's. The issue of how to yield an accurate fractal dimension is to use high-quality images. To achieve a better image-processing result, an appropriate image-processing algorithm is adopted in this paper. Another important fractal feature introduced in this paper is the measure of lacunarity, which describes the characteristics of fractals that have the same fractal dimension but different appearances. For those vascular distributions in the same fractal dimension, further classification can be made using the degree of lacunarity. In addition to the image-processing technique, the resolution of original image is also discussed here. In this paper, the influence of the image resolution upon the fractal dimension is explored. We found that a low-resolution image cannot yield an accurate fractal dimension. Therefore, an approach for examining the lower bound of image resolution is also proposed in this paper. As for the classification of diagnosis results, four different approaches are compared to achieve higher accuracy. In this study, the fractal dimension and the measure of lacunarity have shown their significance in the classification of diabetes and are adequate for use as quantitative indexes.