Bisection and dissection of horizontal lines: The long and the short of the Oppel-Kundt illusion

Mamassian & Montalembert (2010) have proposed that there are two components to the vertical- horizontal illusion; the bisection of the horizontal line by the vertical contributing 16% and the anisotropy only 6%, making the horizontal appear shorter by 22%. In contrast, in the Oppel-Kundt illusion a horizontal line divided by a regular series of vertical ‘tick’ marks appears longer than an unbroken line of the same length. Therefore, the aim of this study was to determine the conditions under which the size of a horizontal line is underestimated or overestimated depending on the presence of one or more vertical lines. We used the method of constant stimuli to generate psychometric functions from which PSEs were determined. We varied the size of the horizontal comparison line between 5.2–7.0 degrees and manipulated the number (0, 1, 5, and 9), the size (6.1/0.61 degrees) and the position (crossing/touching) of vertical lines on a horizontal line in a series of experiments. We also compared illusory percept when the divided and undivided segments were presented as a single stimulus to a condition where the two were presented separately. Results generated showed that the perceived length of a bisected horizontal line with a single central vertical tick is only decreased by 5–10% depending on the position and the size of the tick, whereas additional ticks increase the perceived size of the horizontal line by 5–6%. Additionally, we observed no illusory percept when the size of the vertical segment was equal to the size of the horizontal. Finally, we investigated the effects of asymmetrical bisection and monocular viewing on the vertical-horizontal and Oppel-Kundt illusions.