A theoretical and experimental study concerning shape processing by human visual system

The shape, as a synthetic feature resulting from the particular contour of a figure, may be considered to specify certain spatial relations between the figure domain and surrounding domain. For the study of these relations the figure and the background were considered to belong to a single plane. A characteristic feature of figure-ground relations depending on the figure as a whole was introduced, the "degree of isolation" of the figure from the surrounding ground, with its opposite feature, the "degree of dispersion" into the surrounding ground. A model was elaborated in which the parts radiating from the nucleus of the figure are considered to contribute to the whole figure in inverse proportion to their distance from the nucleus. The corresponding mathematical approach was the convolution between the characteristic function of the figure and a function depending in inverse proportion on the distance from the convolution center (f=1/2 pi r). The maximum value of this convolution integral divided by the radius of the circle having the same area as the figure was introduced as a measure of the degree of isolation of the figure from the surrounding domain. Using symmetrical figures varying in their shape it was found that normal individuals are able to distinguish small differences in this shape parameter and that their evaluations are in good agreement with those predicted by the theoretical model.