On the basis of a predetermined three-dimensional vehicle environment model and of a second image, acquired at that time, of an image sequence, a corrected display image is determined. The vehicle environment model is determined based on at least a first image of the image sequence and includes an object detected in the first image that has a predetermined resultant absolute position and/or a predetermined resultant position with reference to the vehicle. The second image is acquired a predetermined period of time after the first image and includes the detected object. The corrected display image includes at least one graphic element which represents the detected object and is determined such that it is suitable for being projected onto a display area of the head-up display so as to be perceived by a viewer of the display area from a predetermined viewing position with direct reference to the actual environment of the vehicle.