Determinants of filled/empty optical illusion: Search for the locus of maximal effect

A subdivided path in the visual field usually appears longer than an empty path of the same length. This phenomenon, known as the filled/empty or Oppel-Kundt illusion, depends on multiple properties of the visual stimulus, but the functional dependences have not been yet precisely characterized. We studied the illusory effect as a function of its two main determinants, the height of vertical strokes subdividing a spatial interval of a fixed length (visual angle 2.8 degree) and the number of the filling strokes, using the standard-variable distance matching paradigm. Non-monotonic dependence of the effect (over-reproduction of the spatial extension) on the varied parameters was observed in two experimental series. In the first series, the maximum effect was obtained for the fillers height roughly equal to the delimiters height (visual angle 0.25 degree); in the second series, the maximum effect was obtained for 11-13 equispaced fillers, and more accurately estimated to 15-16 as a result of a functional fit. Both data series were successfully modeled by curves generated by a single two-parametric system of form functions. Problems of determination of the maximum effect are discussed, and arguments for a genuinely multivariate approach are presented.