Locating the optic disc center and the fovea in digital fundus images is surprisingly difficult due to the variation range in color and contrast and the possible presence of pathologies creating bright spots or changing the appearance of retinal landmarks. These reasons make it difficult to find good templates of optic disc and fovea shape and color for pattern matching. In this paper we propose radial symmetry as the principal cue to locate both optic disc and macula centers. Centers of bright and dark circularly symmetrical regions with arbitrary radii, can be found robustly against changes in brightness and contrast by using the Fast Radial Symmetry transform. Detectors based on this transform coupled with a weak hypothesis on vessel density (optic disc intersects large vessels while the fovea lies in an avascular region), can provide a fast location of both OD and macula with accuracy similar or better than state-of-the-art methods. The approach has been chosen as the default technique for fast localization of the two landmarks in the VAMPIRE software suite.