Glaucoma leads to irreversible blindness and its diagnosis relies heavily on cup to disc ratio. This ratio can be calculated by segmenting the optic disc (OD) and optic cup (OC) from the fundus image. However, the segmentation of OD and OC is a complex process and should be carried out with utmost accuracy to screen the risk of glaucoma. In order to circumvent this complexity, this study presents two novel algorithms to segment the OD and OC boundaries, respectively by creating an automated region of interest (ROI). The first algorithm uses the inverse polar transform to segment OD where the horizontal coefficients of sixth level decomposition Daubechies stationary wavelet transform of ROI is processed. The second algorithm uses maximum vessel pixel sum to extract the complete OC region by extending the partial cup edges to the nasal side of the cup boundary. This approach covers the region under central retinal blood vessels also which were missing in earlier research. The proposed algorithms achieved an accuracy rate up to 99.70% for OD and 99.47% for OC segmentation, respectively even under severe retinal pathological conditions.