A method determines the position and/or radius of the limbus and/or the position and/or radius of the pupil of a patient eye. In the method, an image of the patient eye is obtained and a plurality of different ring-shaped comparison objects having respective radii and respective centers are provided. The image is correlated with the plurality of comparison objects to yield a local best match between the image and the comparison objects when there is a coincidence of one of the ring-shaped comparison objects and a ring-shaped jump in brightness in the image having the same radius and the same center. The comparison objects having a local best match with the image are determined. Thereafter, the position of the center of the comparison object having a local best match with the image is selected as the position of the center of the limbus and/or the position of the center of the pupil.