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Open Access Publications from the University of California

Factors that determine depth perception of trapezoids, windsurfers, runways

  • Author(s): Tseng, CH
  • Gobell, JL
  • Sperling, G
  • et al.

© 2015 Tseng, Gobell and Sperling. We report here a windsurfer illusion, a naturally occurring trapezoidal illusion in which the small end of the sail viewed at a distance appears to be pointed away from the observer even when it is closer. This naturally occurring illusion is so compelling that observers are unaware of their gross perceptual misinterpretation of the scene. Four laboratory experiment of this kind of trapezoidal illusion investigated the joint effects of retinal orientation, head position, relative motion, and the relative direction of gravity on automatic depth perception. Observers viewed two adjacent white trapezoids outlined on a black background rotating back and forth ± 20° on a vertical axis much like the sails of two adjacent windsurfers. Observers reported which side of the trapezoids (long or short) appeared to be closer to them (i.e., in front). The longer edge of the trapezoid was reported in front 76 ± 2% of trials (“windsurfer effect”) whether it was on the left or on the right. When the display was rotated 90° to produce a runway configuration, there was a striking asymmetry: the long edge was perceived to be in front 97% when it was on the bottom but only 43% when it was on top (“runway effect”). The runway effect persisted when the head was tilted 90° or when displays on the ceiling were viewed from the floor. Ninety-five percent of the variance of the variance in the strikingly different 3D perceptions produced by the same 2D trapezoid image was quantitatively explained by a model that assumes there are just three additive bias factors that account for perceiving an edge as closer: Implicit linear perspective, lower position on the retina (based on an automatic assumption of viewing from above), and being lower in world coordinates.

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