Academic journal article Attention, Perception and Psychophysics

The New Moon Illusion and the Role of Perspective in the Perception of Straight and Parallel Lines

Academic journal article Attention, Perception and Psychophysics

The New Moon Illusion and the Role of Perspective in the Perception of Straight and Parallel Lines

Article excerpt

Published online: 20 September 2014

© The Psychonomic Society, Inc. 2014

Abstract In the new moon illusion, the sun does not appear to be in a direction perpendicular to the boundary between the lit and dark sides of the moon, and aircraftjet trails appear to follow curved paths across the sky. In both cases, lines that are physically straight and parallel to the horizon appear to be curved. These observations prompted us to investigate the neglected question of how we are able to judge the straightness and parallelism of extended lines. To do this, we asked observers to judge the 2-D alignment of three artificial "stars" projected onto the dome of the Saint Petersburg Planetarium that varied in both their elevation and their separation in horizontal azimuth. The results showed that observers make substantial, systematic errors, biasing their judgments away from the veridical great-circle locations and toward equalelevation settings. These findings further demonstrate that whenever information about the distance of extended lines or isolated points is insufficient, observers tend to assume equidistance, and as a consequence, their straightness judgments are biased toward the angular separation of straight and parallel lines.

Keywords 3-D perception . Space perception . Visual perception . Scene perception

It is often assumed that the judgment of straight and parallel lines is a straightforward perceptual task. Straight lines in the world remain straight in projection to both camera sensors and other planar surfaces, and parallel lines show linear convergence. However, because the retinal surface is approximately spherical, itmay be more appropriate to consider what happens to straight and parallel lines when they are projected onto Helmholtz's (1909/1962) "celestial sphere"1 (Fig. 1), Gibson's (1979) optic array, or Johansson and Börjesson's (1989) visual sphere. In Helmholtz's celestial sphere,2 straight lines in the world project to great circles,3 and parallel lines project to great circles that have identical poles. Note that the angular separation between the projections of parallel lines is not constant, but increases from one pole to reach a maximum before decreasing toward the other pole.

Given that the retinal surface is approximately spherical (although the lens is not at the center of the eye), it follows that straight and parallel lines project to particular arcs on the retina, not unlike the great circles on Helmholtz's "celestial sphere." Hence, if elongated receptive fields extended along those particular retinal loci, it ought to be straightforward for perceivers to judge whether an individual line is straight and whether a pair of lines are parallel. In practice, it turns out that this is not the case.

The experimental study of straightness and parallelism can be traced back to Helmholtz4 (1909/1962), who noticed that extended straight lines can appear curved and, conversely, that curved lines can appear straight, on the basis of observations using his famous chessboard pattern (Fig. 2). Viewed from a close distance, so that the lines between the chessboard squares extend over several tens of degrees, the curved lines appear to be straight. From his observations, Helmholtz concluded that the lines that appear straight are those that align with "direction circles" on the retinal surface. He defined "direction circles" as "the circular arcs which are described by the line of fixation in turning around a fixed axis according to Listing's law."5

More recent experiments by Rogers and Rogers (2009) and Oomes, Koenderink, van Doorn, and de Ridder (2009) have shown that observers' judgments do not always fit with this proposal, but there is a more fundamental problem with Helmholtz's suggestion. Though it is true that straight and parallel lines in the world project to great circles on his "celestial sphere," it is not true (geometrically) that the stimulation of great circles is always a consequence of straight and parallel lines in the world (Rogers& Rogers, 2009). …

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