This study is a theoretical exercise dealing with discrimination between images and mirror-images. It focuses on the way codes of shapes represent their handedness. We compare two code systems with different reference frames. These frames determine the specific sensitivity of each system. One system uses an asymmetric reference frame. It is called the H-system and was inspired by an idea of Corballis (1988 Psychological Review 95 115-123). The other system, being our proposal, uses a symmetric reference frame and we have named it the M-system. We demonstrate the following. A code of the H-system provides a cue for the handedness of a shape, but not for rotation, i.e. no cue for the appropriate kind of code rotation which should be tested in case images and mirror-images are discerned by mental rotation. The M-system is the converse in both respects. A code of this system does not provide a handedness cue but, instead, a rotation cue. Thus, for handedness discrimination, the H-system neither needs nor guides mental rotation, whereas the M-system does both. This M-system generates object-centred structural codes enriched with viewpoint information. Various visual experiments reported in the literature favour the M-system over the H-system, implying that perception does not make use of an asymmetric but of a symmetric reference frame.