<p>Glaucoma is a leading contributor to global blindness and visual impairment. Preventing glaucoma-related blindness requires early detection and treatment. Accurate delineation of the optic disc and optic cup is critical for effective glaucoma screening. Hence, achieving reliable and automated segmentation of these structures from retinal fundus images remains a key objective. While current deep learning-based segmentation frameworks utilize local and global contextual information for pixel-wise classification, they often exhibit limited accuracy in delineating object boundaries. To address this shortcoming, A hybrid segmentation framework is introduced that combines deep learning and parametric active contour modeling to achieve anatomically precise extraction of the optic disc and optic cup from retinal fundus images. The approach uses U-Net, a convolutional neural network designed for biomedical image segmentation, for initial region detection, HED for multi-scale edge extraction, and a shape-aware contour model to refine boundaries. Unlike conventional pixel-wise approaches, our framework embeds geometry-sensitive evolution driven by probabilistic edge maps, ensuring accurate boundary adherence. The proposed approach method is utilized separately for optic disc and optic cup segmentation tasks. The REFUGE, DRISHTI-GS, and DRION-DB public datasets are used for method’s evaluation. Even at low input resolutions, the proposed method achieves performance comparable to existing optic disc and optic cup segmentation approaches, as measured by Dice and IoU metrics. it provides a modular, explainable, and clinically valuable solution for retinal structure segmentation, offering potential applications in automated glaucoma screening and ophthalmic decision support.</p>