Background Glaucoma is the leading cause of irreversible blindness worldwide. It is a heterogeneous group of conditions with a common optic neuropathy and associated loss of peripheral vision. Both over and under-diagnosis carry high costs in terms of healthcare spending and preventable blindness. The characteristic clinical feature of glaucoma is asymmetrical optic nerve rim narrowing, which is difficult for humans to quantify reliably. Strategies to improve and automate optic disc assessment are therefore needed to prevent sight loss. Methods We developed a novel glaucoma detection algorithm that segments and analyses colour photographs to quantify optic nerve rim consistency around the whole disc at 15-degree intervals. This provides a profile of the cup/disc ratio, in contrast to the vertical cup/disc ratio in common use. We introduce a spatial probabilistic model, to account for the optic nerve shape, we then use this model to derive a disc deformation index and a decision rule for glaucoma. We tested our algorithm on two separate image datasets (ORIGA and RIM-ONE). Results The spatial algorithm accurately distinguished glaucomatous and healthy discs on internal and external validation (AUROC 99.6% and 91.0% respectively). It achieves this using a dataset 100-times smaller than that required for deep learning algorithms, is flexible to the type of cup and disc segmentation (automated or semi-automated), utilises images with missing data, and is correlated with the disc size (p = 0.02) and the rim-to-disc at the narrowest rim (p<0.001, in external validation). Discussion The spatial probabilistic algorithm is highly accurate, highly data efficient and it extends to any imaging hardware in which the boundaries of cup and disc can be segmented, thus making the algorithm particularly applicable to research into disease mechanisms, and also glaucoma screening in low resource settings.