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.
Highlights
The human visual system is sensitive to a number of 2D configurations that are composed of local image features in a retinal image [1,2,3,4,5,6,7,8]
This study examined how, from a theoretical point of view, 3D centro-symmetry can be used to organize a 2D image of an object and to recover its 3D shape from the 2D image
Centro-symmetrical shape is always 2D rotation-symmetrical, (ii) a 3D centro-symmetrical shape can be recovered from its single 2D perspective projection but not from its 2D orthographic projection, (iii) any pair of 2D curves is consistent with a 3D centro-symmetrical interpretation under a perspective projection, and (iv) additional model-based invariants of 3D rotational symmetry can be introduced under a perspective projection if the 3D centro-symmetrical set of curves are planar, individually
Summary
The human visual system is sensitive to a number of 2D configurations that are composed of local image features in a retinal image [1,2,3,4,5,6,7,8]. A 2D retinal image of a 3D mirror-symmetrical object is 2D mirror-symmetrical on a spherical retina only if the symmetry plane of the object passes the center of projection of the eye under a perspective projection Such a view of this kind of a mirror-symmetrical object is degenerate. A centro-symmetrical shape can be segmented into two symmetrical halves by a plane with an arbitrary orientation that passes the symmetry point. The relation between these two halves can be represented by a combination of reflection about the plane and rotation for 180◦. The geometrical properties of 3D centro-symmetry and its 2D orthographic and perspective projections were studied to make it possible to discuss (i) the potential sensitivity of the human visual system to 3D centro-symmetry and (ii) whether this kind of sensitivity can aid the perception of 3D
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