We propose a machine learning framework based on sliding windows for glaucoma diagnosis. In digital fundus photographs, our method automatically localizes the optic cup, which is the primary structural image cue for clinically identifying glaucoma. This localization uses a bundle of sliding windows of different sizes to obtain cup candidates in each disc image, then extracts from each sliding window a new histogram based feature that is learned using a group sparsity constraint. An epsilon-SVR (support vector regression) model based on non-linear radial basis function (RBF) kernels is used to rank each candidate, and final decisions are made with a non-maximal suppression (NMS) method. Tested on the large ORIGA(-light) clinical dataset, the proposed method achieves a 73.2% overlap ratio with manually-labeled ground-truth and a 0.091 absolute cup-to-disc ratio (CDR) error, a simple yet widely used diagnostic measure. The high accuracy of this framework on images from low-cost and widespread digital fundus cameras indicates much promise for developing practical automated/assisted glaucoma diagnosis systems.