Influence of 3D Centro-Symmetry on a 2D Retinal Image

Abstract

An object is 3D centro-symmetrical if the object can be segmented into two halves and the relationship between them can be represented by a combination of reflection about a plane and a rotation through 180° about an axis that is normal to the plane. A 2D orthographic image of the 3D centro-symmetrical object is always 2D rotation-symmetrical. Note that the human visual system is known to be sensitive to 2D rotational symmetry. This human sensitivity to 2D rotational symmetry might also be used to detect 3D centro-symmetry. If it is, can this detection of 3D centro-symmetry be helpful for the perception of 3D? In this study, the geometrical properties of 3D centro-symmetry and its 2D orthographic and perspective projections were examined to find out whether 3D centro-symmetry plays any role in the perception of 3D. I found that, from a theoretical point-of-view, it is unlikely that 3D centro-symmetry can be used by the human visual system to organize a 2D image of an object in a way that makes it possible to recover the 3D shape of an object from its 2D image.