Neovascularization is the primary manifestation of proliferative diabetic retinopathy (PDR) that can lead to acquired blindness. This paper presents a novel method that classifies neovascularizations in the 1-optic disc (OD) diameter region (NVD) and elsewhere (NVE) separately to achieve low false positive rates of neovascularization classification. First, the OD region and blood vessels are extracted. Next, the major blood vessel segments in the 1-OD diameter region are classified for NVD, and minor blood vessel segments elsewhere are classified for NVE. For NVD and NVE classifications, optimal region-based feature sets of 10 and 6 features, respectively, are used. The proposed method achieves classification sensitivity, specificity and accuracy for NVD and NVE of 74%, 98.2%, 87.6%, and 61%, 97.5%, 92.1%, respectively. Also, the proposed method achieves 86.4% sensitivity and 76% specificity for screening images with PDR from public and local data sets. Thus, the proposed NVD and NVE detection methods can play a key role in automated screening and prioritization of patients with diabetic retinopathy.