Current research in automated disease detection focuses on making algorithms “slimmer” reducing the need for large training datasets and accelerating recalibration for new data while achieving high accuracy. The development of slimmer models has become a hot research topic in medical imaging. In this work, we develop a two-phase model for glaucoma detection, identifying and exploiting a redundancy in fundus image data relating particularly to the geometry. We propose a novel algorithm for the cup and disc segmentation “EffUnet” with an efficient convolution block and combine this with an extended spatial generative approach for geometry modelling and classification, termed “SpaGen” We demonstrate the high accuracy achievable by EffUnet in detecting the optic disc and cup boundaries and show how our algorithm can be quickly trained with new data by recalibrating the EffUnet layer only. Our resulting glaucoma detection algorithm, “EffUnet-SpaGen”, is optimized to significantly reduce the computational burden while at the same time surpassing the current state-of-art in glaucoma detection algorithms with AUROC 0.997 and 0.969 in the benchmark online datasets ORIGA and DRISHTI, respectively. Our algorithm also allows deformed areas of the optic rim to be displayed and investigated, providing explainability, which is crucial to successful adoption and implementation in clinical settings. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.