Glaucoma is one of the major causes of blindness. Researchers keep looking for better ways to detect glaucoma in its early stage before it gets worse and cannot be cured. Among existing methods, the vertical cup to disc ratio (CDR) has been found to be effective for glaucoma measurement, which is calculated from the diameters of the optic cup and disc regions. Therefore, in order to achieve a more accurate CDR, a good segmentation of the optic disc and cup regions is quite important. Noting that the shape of the disc and cup regions can be assumed to be an ellipse, in this work we propose to find the minimal bounding boxes for the two regions based on the recent advances of deep learning. Also, considering blood vessels, passing through the disc area in a fundus image, can affect the detection of the bounding boxes, we further propose to remove the blood vessels beforehand in order to further boost the overall performance. Comprehensive experiments show that our proposed method achieves state-of-the-art performance on ORIGA-650 for optic disc and cup segmentation.