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Glaucoma is one of the leading factors of vision loss, where the people tends to lose their vision quickly. The examination of cup-to-disc ratio is considered essential in diagnosing glaucoma. It is hence regarded that the segmentation of optic disc and cup is useful in finding the ratio. In this paper, we develop an extraction and segmentation of optic disc and cup from an input eye image using modified recurrent neural networks (mRNN). The mRNN use the combination of recurrent neural network (RNN) with fully convolutional network (FCN) that exploits the intra- and interslice contexts. The FCN extracts the contents from an input image by constructing a feature map for the intra- and interslice contexts. This is carried out to extract the relevant information, where RNN concentrates more on interslice context. The simulation is conducted to test the efficacy of the model that integrates the contextual information for optimal segmentation of optical cup and disc. The results of simulation show that the proposed method mRNN is efficient in improving the rate of segmentation than the other deep learning models like Drive, STARE, MESSIDOR, ORIGA, and DIARETDB. [ABSTRACT FROM AUTHOR]