Posterior Segment Eye Diseases (PSED) namely Diabetic Retinopathy (DR), glaucoma and Age-related Macular Degeneration (AMD) are the prime causes of vision loss globally. Vision loss can be prevented, if these diseases are detected at an early stage. Structural abnormalities such as changes in cup-to-disc ratio, Hard Exudates (HE), drusen, Microaneurysms (MA), Cotton Wool Spots (CWS), Haemorrhages (HA), Geographic Atrophy (GA) and Choroidal Neovascularization (CNV) in PSED can be identified by manual examination of fundus images by clinicians. However, manual screening is labour-intensive, tiresome and time consuming. Hence, there is a need to automate the eye screening. In this work Bi-dimensional Empirical Mode Decomposition (BEMD) technique is used to decompose fundus images into 2D Intrinsic Mode Functions (IMFs) to capture variations in the pixels due to morphological changes. Further, various entropy namely Renyi, Fuzzy, Shannon, Vajda, Kapur and Yager and energy features are extracted from IMFs. These extracted features are ranked using Chernoff Bound and Bhattacharyya Distance (CBBD), Kullback–Leibler Divergence (KLD), Fuzzy-minimum Redundancy Maximum Relevance (FmRMR), Wilcoxon, Receiver Operating Characteristics Curve (ROC) and t-test methods. Further, these ranked features are fed to Support Vector Machine (SVM) classifier to classify normal and abnormal (DR, AMD and glaucoma) classes. The performance of the proposed eye screening system is evaluated using 800 (Normal=400 and Abnormal=400) digital fundus images and 10-fold cross validation method. Our proposed system automatically identifies normal and abnormal classes with an average accuracy of 88.63%, sensitivity of 86.25% and specificity of 91% using 17 optimal features ranked using CBBD and SVM-Radial Basis Function (RBF) classifier. Moreover, a novel Retinal Risk Index (RRI) is developed using two significant features to distinguish two classes using single number. Such a system helps to reduce eye screening time in polyclinics or community-based mass screening. They will refer the patients to main hospitals only if the diagnosis belong to the abnormal class. Hence, the main hospitals will not be unnecessarily crowded and doctors can devote their time for other urgent cases.