[A class of information integration models for the Oppel-Kundt illusion].

Oppel (1860/1861) first described the phenomenon that an equidistantly divided line usually looks longer than an undivided line of equal length (Oppel-Kundt illusion, OKI). The present paper begins with a discussion of the Hering-Kundt hypothesis (HKH) of the OKI. The HKH comprises two assumptions: (1) An assumption concerning the perceptual integration of the length of a single part of the divided line and the number of such parts; (2) an assumption about the psychophysical function of line length. There is no doubt that the HKH is empirically not tenable. However, nothing is known about the validity of the perceptual integration assumption when considered in isolation. It is shown that the HKH can be conceived as a special case of a more general information-integration model. According to this model, the subjective total length of a divided line is equal to the subjective length of one part of the line multiplied by the subjective number of parts. Two experiments with a total of 15 subjects are reported. The model is shown to be valid without any exception. On the background of these results published data on the OKI are re-analyzed, looking at whether they contain information about the psychophysical function for line length. It is shown that certain qualitative aspects of these data are inconsistent with a power function hypothesis while, at the same time, being compatible with a logarithmic (Fechner-) function.