Vessel segmentation in photographies of the retina is needed in a set of computer-supported medical applications related to diagnosis and surgery planning. Considering each pixel in an image as a point in a feature space, segmentation is a binary classification problem where pixels need to be assigned to one of two classes: object and background. We describe a paradigm of hysteresis-classifier design that we apply to the problem of vessel segmentation. Before classification, a multidimensional feature vector is computed for each pixel, such that in the corresponding feature space, vessels and background are more separable than in the original image space. Several classifiers that stem from the hysteresis-classifier design paradigm are tested with this feature space on publicly available databases. These classifiers are very fast and achieve results that are comparable or even superior to known dedicated methods. Hysteresis-based classifiers represent a fast and accurate solution for the retinal-vessel segmentation problem.