Abstract
Perspective projection distorts the retinal silhouette of a planar object as a function of the object's shape, size and position, yet observers often perceive veridical shapes. The automatic corrections applied by the visual system can involve assumptions about regular shapes (Ames 1951), right angles (Griffiths & Zaidi 2000), and axes of symmetry that are imaged as skew symmetries (Kanade & Kender, 1983; Saunders & Knill, 2001).
We analyze an interesting case where a peanut-shaped tabletop (8′ long, 4′ at the widest two points and 3′ wide at the neck) appears to be an S-shaped object when viewed binocularly at a distance of 4′, at an angle of 45° from the long axis, and at a viewing height 3′ above its surface. The visual system appears to correct for the distortion due to foreshortening, but the irregular shape of the projected image, which contains no symmetries, is corrected to a percept containing a rotational symmetry, but not the two orthogonal axes of reflective symmetry in the object.
We have studied this illusion using smaller planar figures, based on symmetric pairs of regular shapes joined at a point (e.g. squares & diamonds), along an edge (e.g. octagons), as well as two circular disks joined by necks containing concave and convex contours. We found that while the peanut shape yields the strongest effect, the illusion persists for shapes based on straight lines and vertices, nor do painted axes of symmetry have an effect on the final percept. Two squares joined at their corners appear as an S-shape formed by an offset pair of identical rectangles. The common component among the shapes that best produce the illusion are necks formed by a pair of concavities opposite one another, which enable the shapes to be partitioned (Hoffman & Richards, 1985). In conclusion, perceptual priors that enable observers to correct for perspective distortions of globally convex shapes are not sufficient for regular symmetric shapes that can be visually partitioned.