Globally, glaucoma has been recognized as the secondmost common reason for blindness. This affects the anatomy of the eyes, including blood vessels (BVs) and optic disc (OD). State-of-the-art literature has revealed that this disease is the root cause of degeneration in the OD, with some effects on the morphology of the BVs in the retina. These can result in total blindness if left untreated. Previous studies have shown that to effectively diagnose a disease, it is necessary to automatically detect the OD and the BVs with high accuracy in the fundus image. Segmentation of OD and BVs has, however, been challenging, due to the complex and poor segmentation performances. Such performances arise from the intricacies of vascular network width variation, illumination of images, and the structure of retinal images. Examples are retinal image boundaries on ODs and retinal lesions, due to disease. Hence the need for an investigation of the appropriate image feature(s) that will facilitate improvements to OD and BV segmentation performances. Texture is an important indicator used in image analysis for object segmentation. This work proposed the use of image-correlation texture information computational approaches for the segmentation of BVs, using variant window sizes; and OD using grayscale and green channel in the retinal images. This study revealed that the segmentation of BVs using variant window sizes (15x15) and (17x17) achieved high accuracy values of 95.11 per cent and 94.93 per cent; with accuracy values of 94.21 per cent and 93.98 per cent revealed in the DRIVE and STARE databases, respectively. Usually, sensitivity values of 74.84 per cent and 75.94 per cent, with average sensitivity values of 74.58 percent and 78.48 per cent, are achieved BV segmentation on the window sizes (15x15) and (17x17), indicated in DRIVE and STARE databases, respectively. Also, an average specificity value of 97.08 per cent and 96.77 per cent with average specificity values of 95.77 per cent and 95.18 per cent are achieved for BV segmentation on the window sizes (15x15) and (17x17), on DRIVE and STARE databases, respectively. Further, the segmentation of OD using grayscale achieved a slightly greater accuracy rate (98.59%) compared to the accuracy rate (98.36%) realized on green channel. This study also showed that the proposed approaches for BV and OD segmentation in this research achieved better results compared with several existing methods in the literature.