Effect Of Shape On The Magnitude Of The Delboeuf Illusion

The Delboeuf illusion is a visual phenomenon invented by the Belgian philosopher Franz Joseph Delboeuf. In this illusion, two circles(test patterns) of equal radius are presented next to each other and surrounded by concentric circles(inducing stimulus)of different radii; the central circle surrounded by a slightly larger concentric circle appears larger than the one surrounded by a circle that is much larger. This illusion has been extensively studied among humans and results have shown that viewers’ size perception is strongly influenced by the luminance and color of the background and stimulus. However, existing research has largely ignored the role of shape in the Delboeuf illusion, though the shape of the test circle or inducing stimulus may exert an important effect. The Counter Attraction theory illustrates that the magnitude of the Delboeuf illusion maximizes when the shape of the inducing figure is close to circular. Under assimilation, more magnitude of illusion is usually expected when the spacing between the inducing figure and the testing figure decreases. Based on this hypothesis, we further explored how the magnitude of the quasi-Delboeuf illusion was affected by the shape of the figures under polygonal background. Does it arise from the shape of the inducing figure or the testing figure? When the inducing figure goes to round but maintains the same area with a constant testing figure does the spacing between the inducing figure and the testing figure still affect the magnitude of the illusion?Thirty undergraduates participated our investigation, containing thirteen male students and seventeen female students. Five shapes of figure were chosen,including circle, regular octagon, regular hexagon, regular quadrilateral, and regular triangle. The Geometer’s Sketchpad program with adjustment method was employed to provide students necessary material and operation. A completed pattern was displayed as a reference on the left side while the right side was left as blank.Students were asked to draw a testing figure and adjust it on this right blank area based on the left reference in order to make the newly created figure look as similar as possible to the left reference. The radii of these drawn testing figures were collected.In experiment 1a, the shape of the inducing figure and the testing figure changes synchronously. In experiment 1b, the testing figure maintains round as the shape of the inducing figure varies with a dissimilar area. In experiment 2, the testing figure keeps circular while the shape of the inducing figure alters but retains the same area.In Experiment 1a, the shape of the test pattern and the inducing stimulus changed synchronously. In Experiment 1b, the test pattern remained a circle while the inducing stimulus changed shape. Experiment 2 was similar to Experiment 1b except that the areas of the test pattern and inducing stimulus were kept the same. The present study examined the quasi-Delboeuf illusion and obtained several important findings in the case of polygons. First, the illusion is more strongly influenced by the shape of the inducing stimulus than that of the test pattern. When the inducing stimulus is a polygon, the closer the resemblance of the stimulus to a circle, the greater the magnitude of the illusion. Second, under assimilation, when the shape of the inducing stimulus is constant, the shorter the distance between the inducing stimulus and test pattern, and the greater the magnitude of the illusion. However, this phenomenon does not occur when the shape of the inducing stimulus changes.