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Glaucoma is a leading cause of permanent blindness. However, disease progression can be limited if detected early. The optic cup-to-disc ratio (CDR) is one of the main clinical indicators of glaucoma, and is currently determined manually, limiting its potential in mass screening. In this paper, we propose an automatic CDR determination method using a variational level-set approach to segment the optic disc and cup from retinal fundus images. The method is a core component of ARGALI, a system for automated glaucoma risk assessment. Threshold analysis is used in pre-processing to estimate the initial contour. Due to the presence of retinal vasculature traversing the disc and cup boundaries which can cause inaccuracies in the detected contours, an ellipse-fitting post-processing step is also introduced. The method was tested on 104 images from the Singapore Malay Eye Study, and it was found the results produced a clinically acceptable variation of up to 0.2 CDR units from the manually graded samples, with potential use in mass screening.