Glaucoma is a chronic eye disease that leads to vision loss. As it cannot be cured, detecting the disease in time is important. Current tests using intraocular pressure (IOP) are not sensitive enough for population based glaucoma screening. Optic nerve head assessment in retinal fundus images is both more promising and superior. This paper proposes optic disc and optic cup segmentation using superpixel classification for glaucoma screening. In optic disc segmentation, histograms, and center surround statistics are used to classify each superpixel as disc or non-disc. A self-assessment reliability score is computed to evaluate the quality of the automated optic disc segmentation. For optic cup segmentation, in addition to the histograms and center surround statistics, the location information is also included into the feature space to boost the performance. The proposed segmentation methods have been evaluated in a database of 650 images with optic disc and optic cup boundaries manually marked by trained professionals. Experimental results show an average overlapping error of 9.5% and 24.1% in optic disc and optic cup segmentation, respectively. The results also show an increase in overlapping error as the reliability score is reduced, which justifies the effectiveness of the self-assessment. The segmented optic disc and optic cup are then used to compute the cup to disc ratio for glaucoma screening. Our proposed method achieves areas under curve of 0.800 and 0.822 in two data sets, which is higher than other methods. The methods can be used for segmentation and glaucoma screening. The self-assessment will be used as an indicator of cases with large errors and enhance the clinical deployment of the automatic segmentation and screening.