The advanced development of mobile phone and lens technology has made retinal imaging more convenient than ever before. In the digital health era, mobile phone fundus photography has evolved into a low-cost alternative to the standard ophthalmoscope. Existing image processing algorithms have a problem with handling the narrow field of view and poor quality of retinal images from a mobile phone. This paper enhances the accuracy of our previously proposed scheme, ADI-GVF snakes, to improve the segmentation of the optic disk (OD) and the optic cup (OC) for glaucoma pre-screening [1] from retinal images obtained from a mobile phone. This work integrated a better OD localization method, namely, the exclusion method (EM) with ADI-GVF segmentation for the OD and the OC. The improved algorithm can segment the regions of the OD and OC more accurately, resulting in a more precise value of the cup-to-disk area ratio (CDAR). The proposed method yields as high as 93.33% for true positive rate (TPR) and 93.87% for true negative rate (TNR) and as low as 6.12% and 6.66% for false omission rate (FOR), and false discovery rate (FDR). It also improves TPR, TNR, FOR, and FDR of the previous scheme [1] by 4.45%, 4.08%, 4.08%, and 4.44% respectively.