Visual detection of 3D mirror-symmetry and 3D rotational-symmetry
Detecting 3D symmetry is important for the human visual system because many objects in our everyday life are 3D symmetrical. Many are 3D mirror-symmetrical and others are 3D rotational-symmetrical. But note that their retinal images are 2D symmetrical only in degenerate views. It has been suggested that a human observer can detect 3D mirror-symmetry even from a 2D retinal image of a 3D mirror-symmetrical pair of contours. There are model-based invariants of the 3D mirror-symmetrical pair of contours in the retinal image and there are additional invariant features when the contours are individually planar. There are also model-based invariants of a 3D rotational-symmetrical pair of contours. These invariant features of 3D mirror-symmetry and rotational-symmetry are analogous to one another but the features of 3D rotational-symmetry are computationally more difficult than the features of 3D mirror-symmetry. Experiment 1 showed that only 3D mirror-symmetry could be detected reliably while the detection of 3D rotational-symmetry was close to chance-level. Experiment 2 showed that the detection of 3D mirror-symmetry is partly based on the model-based invariants of 3D mirror-symmetry and the planarity of the contours. These results show that the visual system has evolved to favour the perception of 3D mirror-symmetry.