In this work, we present a novel method for blood vessel segmentation in fundus images based on a discriminatively trained, fully connected conditional random field model. Retinal image analysis is greatly aided by blood vessel segmentation as the vessel structure may be considered both a key source of signal, e.g. in the diagnosis of diabetic retinopathy, or a nuisance, e.g. in the analysis of pigment epithelium or choroid related abnormalities. Blood vessel segmentation in fundus images has been considered extensively in the literature, but remains a challenge largely due to the desired structures being thin and elongated, a setting that performs particularly poorly using standard segmentation priors such as a Potts model or total variation. In this work, we overcome this difficulty using a discriminatively trained conditional random field model with more expressive potentials. In particular, we employ recent results enabling extremely fast inference in a fully connected model. We find that this rich but computationally efficient model family, combined with principled discriminative training based on a structured output support vector machine yields a fully automated system that achieves results statistically indistinguishable from an expert human annotator. Implementation details are available at http://pages.saclay.inria.fr/ matthew.blaschko/projects/retina/.