The Poggendorff illusion: Consider all the angles.

Abstract

In the Poggendorff display, which consists of parallel lines interrupting a transversal, one of the two transversal segments was replaced by a dot lying along the parallel. The angle between the remaining transversal segment and the parallels was varied in 15 degree increments, as was the orientation of the transversal with respect to the subject. Subjects set the dot to appear collinear with the transversal. Judgmental errors can be partitioned into additive components, one linearly related to the size of the obtuse angle between transversal and parallels and the other a sinusoidal function of transversal and parallels and the other a sinusoidal function of transversal orientation (collinearity settings err toward the horizontal or vertical, whichever is closer), plus a meridional effect, an interaction term that magnifies the errors of a given obtuse angle as the transversal approaches an oblique orientation.

Structure and strategy in encoding simplified graphs

“…Poulton (1985) observed a kind of acute-angle expansion when subjects read the values of points on multiple function lines in graphs; he interpreted this distortion as a variant of the classical Poggendorf illusion. The tendency to view complex displays, such as the Poggendorf and Zollner illusions, as structural variants of the simpler tilt-contrast illusion is common (e.g., Kobayashi, 1956;Wallace, 1975;Wallace & Crampin, 1969; see also Coren & Girgus, 1978) but not uncontroversial (e.g., Day & Dickinson, 1976;Hotopf, 1966Hotopf, , 1981Hotopf & Hibberd, 1989;Weintraub & Krantz, 1971;Weintraub, Krantz, & Olson, 1980) in the perceptual literature.…”

Spatial context affects the Poggendorff illusion

“…Thus, there are determinants of the Poggendorff illusion that are not counteracted by transversally aligned reference frames. Indeed, there are likely to be several factors that combine simultaneously to produce the illusion (Day & Kasperczyck, 1985;Weintraub et al, 1980), some of which are affected by reference frames and some of which are not.…”

“…The results have suggested that the effect is attributable to an increase in perceived size of the smaller angle and/or a decrease in perceived size of the larger angle (Helmholtz 1910(Helmholtz /1962Hotopf & Ollereamshaw, 1972;Imai, 1973), and/or to perceived rotation of the transversals toward perpendicular with respect to the parallels (Hotopf, Ollereamshaw, & Brown, 1974;Krantz & Weintraub, 1973;Weintraub & Krantz, 1971;Weintraub, Krantz, & Olson, 1980). However, the illusion still exists when presented with only dots instead of transversals (Coren, 1970;Day & Dickinson, 1976;Day & Kasperczyck, 1985;Predebon, 1983;Tong & Weintraub, 1974;Wenderoth, Beh, & White, 1978;Wenderoth & Wade, 1981), thus ruling out perceived angle size and rotation as comprehensive explanations.…”

Geometrical features underlying the perception of collinearity

“…The Method of Adjustment, which is probably the most widely used method in the field (e.g. Ninio & O'Regan, 1999;Weintraub et al, 1980;Predebon, 2006;Blakemore et al, 1980;Morgan, 1999) avoids this difficulty, but allows the observer some degree of experimentation with the figure, in conjunction with scanning eye movements, which may not be altogether desirable. In our 2AFC Method the observer never knew which of the two figures was in reality 'more aligned', and any perceptual bias would have no effect on the distribution of responses between the two categories 'left more collinear' or 'right more collinear'.…”