Glaucoma poses a significant threat to global vision health, often striking at advanced stages when symptoms become evident, complicating early detection efforts. The current screening process, reliant on subjective assessments and limited eye specialists, presents substantial challenges. To mitigate this, we propose a two-stage automatic glaucoma screening system aimed at easing the burden on ophthalmologists. In the first stage, our system utilizes a modified DeepLabv3+ architecture, segmenting the optic disc region exactly by using numerous deep convolution neural networks within the framework of the encoder module. We explored three classification methods: transfer learning, feature descriptor learning with support vector machines, and a combined ensemble approach. Analysis of 2787 retinal images across five datasets indicated that a merger of MobileNet and DeepLabv3+ enabled optimum optic disc segmentation. Moreover, our ensemble method surpassed traditional techniques in glaucoma classification. Particularly noteworthy are the outstanding accuracies achieved on ORIGA, DRISHTI-GS1, RIM-ONE, and ACRIMA datasets, reaching 90.00%, 86.84%, 97.37%, and 99.53%, respectively, with corresponding AUC (Area Under Curve) scores of 92.06%, 91.67%, 100%, and 99.98%. Notably, with an accuracy of 95.60% and an AUC of 95.11%, our system's performance on the REFUGE dataset was in proximity with that of CUHKMED, the top team in the REFUGE challenge.