Plato's Cave: Kanizsa psychophysics

Psychophysical Studies of the Kanizsa Figure

A number of parametric studies have been conducted to examine the perceptual salience of the illusory boundary in response to various factors. These studies have shown that the salience of the illusory contour is a function of the length of the inducing edges relative to the separation between them, [Banton & Levi, 1992] the contrast of the inducers relative to the background, [Banton & Levi, 1992] and the spatial alignment of the inducing edges [Kellman & Shipley, 1991].

Psychophysical experiments by Kellman and Shipley have revealed a distinction between a bending mis-alignment and shearing mis-alignment as shown below. While both forms of mis-alignment reduce the salience of the illusory contour, the contour can survive a considerable bending mis-alignment, but is far more sensitive to a shearing mis-alignment.

Kellman and Shipley formalized these findings in a mathematical model based on the linear extensions of the visible inducing edges. They propose that edges whose extensions intersect at an obtuse angle are relatable, i.e. capable of forming an illusory contour, while edges whose extensions either fail to intersect, or do so at an acute angle are non-relatable, as shown above. Note that for the purposes of this definition, the linear extension is only defined beyond the inducing edge, not within it.

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