Abstract
The Necker cube is a striking example for perceptual dominance of 3D over 2D. Object symmetry and obliqueness of angles are co-varying cues that may underlie the perceived slant of Necker cubes. To investigate the power of the oblique-angle cue, slants were judged of extremely simple symmetrical shapes. Slant computations based on an assumption of orthogonality were made for two abutting lines as a function of vertex angle and the slant of the screen. Computed slants were compared with slants judged by six subjects under binocular viewing conditions. Judged slant was highly correlated with slant specified by the oblique angles under an assumption of orthogonality. The contributions of screen cues, including binocular disparity, were negligible. The consistency of the judgments across subjects indicates the assumption of orthogonality as one of the principles underlying slant perception. Necker cubes illustrate that the visual system can disengage unambiguous cues in favor of ambiguous object-symmetry and oblique-angle cues, if the latter indicate very different slants. Selective disengagement of cues may be the mechanism that underlies the success of 2D images in ancient, as well as modern civilizations.
Highlights
Modern human beings watch pictures during many hours a day
Experimental studies have produced a variety of explanations for picture perception, ranging from being the result of competition between pictorial and other visual cues [11,14,16,17] via being derived from a cognitive process of rectification based on the recovery of the orientation of the screen [10,13,18], to claiming a non-Euclidean geometry for pictorial space perception [9,19,20]
Slant judgments of the symmetric angles show that an assumption of orthogonality must be the underlying principle, because these angles do not contain any other cue to slant
Summary
Modern human beings watch (moving) pictures during many hours a day. After having viewed pictures drawn on stone, paper and canvas, we devote much more time than ever before to viewing pictures, but displayed on light-emitting screens (i.e., televisions, laptops, tablets and smartphones). Saunders and Backus [27] reported evidence that the orthogonality assumption contributed to the slant of surfaces in certain conditions Their stimuli, contained skew symmetry, i.e., skewed surfaces in pictures that can be understood as projections of symmetric surfaces, oriented non-perpendicularly to the observer. Φ becomes more symmetric until, for vertices placed at the axis, φ is described by the symmetric relationship φ = ±√90 √|αd − 90| , with φ and αd expressed in degrees This relationship between an oblique angle and slant provides an objective test for the hypothesis that the perceived slant of obtuse angles is based on an assumption of orthogonality. Arranging slant judgments of subjects as functions of φ and σ and comparing these with the predictions shown in Figure 3b provides the possibility to estimate the contribution of the oblique-angle cue and screen cues to the slant perceived of obtuse angles. Raising the viewpoint defines an orthogonal line slanting away from the observer (this condition is not shown in the figure)
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