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Accurate segmentation of the cup region from retinal images is needed to derive relevant measurements for glaucoma assessment. A novel, depth discontinuity (in the retinal surface)-based approach to estimate the cup boundary is proposed in this paper. The proposed approach shifts focus from the cup region used by existing approaches to cup boundary. The given set of images, acquired sequentially, are related via a relative motion model and the depth discontinuity at the cup boundary is determined from cues such as motion boundary and partial occlusion. The information encoded by these cues is used to approximate the cup boundary with a set of best-fitting circles. The final boundary is found by considering points on these circles at different sectors using a confidence measure. Four different kinds of data sets ranging from synthetic to real image pairs, covering different multiview scenarios, have been used to evaluate the proposed method. The proposed method was found to yield an error reduction of 16% for cup-to-disk vertical diameter ratio (CDR) and 13% for cup-to-disk area ratio (CAR) estimation, over an existing monocular image-based cup segmentation method. The error reduction increased to 33% in CDR and 18% in CAR with the addition of a third view (image) which indicates the potential of the proposed approach.