Various ophthalmic procedures critically depend on high-quality images. For instance, efficiency of teleophthalmology, a framework to bring advanced eye care to remote regions, is determined by the capability of assessing diagnostic quality of ocular fundus photographs (FPs), and rejecting poor-quality ones at the source. In this context, we study algorithmic methods of classifying high-and low-quality FPs. Crucially, diagnostic quality (DQ) -determined by clinically, but not necessarily perceptually, significant structures -is not synonymous with perceptual appeal. Yet, traditional methods handpick features individually (or in small subsets) to meet certain ad hoc perceptual requirements. In contrast, we investigate the efficacy of a comprehensive set of structure-preserving features, systematically generated by a deep scattering network (ScatNet). Specifically, we consider three advanced machine learning classifiers, train each using ScatNet as well as traditional features separately, and demonstrate that the former ensure significantly superior performance for each classifier under multiple criteria including classification accuracy. © 2019 IEEE.