We present a framework for robust optic disc segmentation using convolutional neural networks. Optic disc is an important anatomical landmark in the fundus image used for the diagnosis of ophthalmological pathologies. Our objective is to develop a system for unsupervised, early and robust detection of diseases such as glaucoma. We introduce the Fine-Net, which generates a high-resolution optic disc segmentation map (1024 × 1024) from retinal fundus images. The network is trained on three publicly available datasets, MESSI-DOR, DRIONS-DB, and DRISHTI-GS. The proposed framework generalizes well as it performs reliably even on test images that have a significant variability. For experimental evaluation, we perform a five-fold cross-validation and achieve accurate optic disc localization in 99.4% of cases. Moreover, for optic disc segmentation we achieve an average Dice coefficient and Jaccard coefficient of 0.958 and 0.921, respectively.