Obliquity Integration: Variations on a Theme of Delbœuf

Abstract

An optical—geometrical illusion, described by Delbœuf and not familiar to specialists, is investigated. The results of two experiments show that the divergence between a bar filled with parallel slanting lines and a line drawn above it is clearly related to this angle of the lines which fill the bar. The illusion is already present when this angle is 10°, reaches its maximum at 20°, decreases at 30°, and almost disappears at 40°. These results are similar to those found for the tilt illusion, are slightly different from those found for the rod-and-frame illusion, and differ greatly from those found for the Zöllner illusion. The other variables considered—the distance between the slanting lines filling up the bar, the distance between the upper line and the bar, and the width of the bar—do not influence the illusion as much. Since either the line appears as diverging from the bar, or the bar seems inclined in relation to the line, the illusion should be considered a complex one. The small oblique lines inside the bar induce obliquity in the opposite sense in the display, but which of the elements is seen as diverging from the other depends on which of the two is established as the frame of reference.