In this work a computational approach for detecting and quantifying diabetic retinopathy is proposed. Particular attention has been paid to the study of Foveal Avascular Zone (FAZ). In fact, retinal capillary occlusion produces a FAZ enlargement. Moreover, the FAZ is characterized by qualitative changes showing an irregular contour with notchings and indentations. Our study is mainly focused on the analysis of the FAZ and on the extraction of a proper set of features to quantify FAZ alterations in diabetic patients. We tried to extract features which can capture not only the size of the object, but also its shape and spatial orientation. The theory of moments provides an interesting and useful way for representing the shape of objects. We used a set of region and boundary moments to obtain a FAZ description which is complete enough for diagnostic purposes and in order to assess the effectiveness of moment descriptors we performed several classification experiments to discriminate diabetic from non-diabetic subjects. The theory of moments provided us with an interesting and useful tool for representing the shape characteristics. In this way we were able to transform the qualitative description of the FAZ used by ophthalmologists into quantitative measurements.