We present a method to detect vessels in images of the retina. Instead of relying on pixel classification, as many detection algorithms do, we propose a more natural representation for elongated structures, such as vessels. This new representation consists of primitives called affine convex sets. On these convex sets we apply the classification step. The reason for choosing this approach is two-fold: (1) By using a dedicated representation of image structures, one can exploit prior knowledge. (2) A method based on pixel classification is often computationally unattractive. The method can also be applied to other image structures, if an appropriate representation for the structures is chosen. The method was tested on fundus reflection images. We obtained an accuracy of 0.897, a sensitivity of 0.700 and a specificity of 0.923.