The retina can provide evidence of diseases originating in other parts of the body. Among the eye diseases that can be diagnosed through a retinal examination, age-related macular degeneration, glaucoma, and diabetic retinopathy are the most common, and they cause vision loss. Although these diseases can be diagnosed by examining blood vessels and the optic disk in retinal images, assessment of blood vessels on colored fundus images is a time-consuming and subjective process. Here, we present an automated blood vessel segmentation algorithm that facilitates the evaluation of diabetic retinopathy through assessment of blood vessel abnormalities. The blood vessels are extracted using a random forest classification model combined with wavelet features and local binary pattern texture information. Discriminant analysis is modified and used for feature selection to train the proposed classification model. The boundary of the optic disk is identified using low-pass filtering, fuzzy c-means clustering, and template matching so that it may be removed and not confound the segmentation analysis. Validation test results using three publicly available retinal image datasets demonstrated that our proposed method achieves as good or better blood vessel segmentation accuracy than the other supervised model approaches examined. Results show that the proposed scheme is able to segment the blood vessels and optic disk structures accurately (Accuracy Index) in 95.80%, 95.20%, and 97.10% of the testing Digital Retinal Images for Vessel Extraction (DRIVE), Structured Analysis of the Retina (STARE), and CHASE_DB1 image datasets respectively. The main advantage of our proposed model is that it provides robust and computationally efficient segmentation of blood vessels and the optic disk. The proposed model aims to provide supportive information for cases in which a diagnosis remains unclear following a clinical examination.