In the present communication, we have developed a computational model related to the conception of positional coding via centers-of-masses (centroids) of the objects' luminance distributions. The model predictions have been tested by the results of our psychophysical study of geometrical illusion of extent evoked by a modified Brentano figure consisting of three separate spots clusters. In experiments, the centroids of the clusters were manipulated by varying the positions of additional non-target spots flanking the stimulus terminators. A good correspondence between the model predictions and the illusion magnitude changes provided convincing evidences in favor of "centroid" explanation of origin of the illusion investigated.

The Oppel-Kundt illusion was examined in the psychophysical experiments with the classical two-part stimuli and modified three-part figures. The modified versions comprised either one filled medial interval and two empty flanking intervals or one empty space situated in between two fillings. The illusion was measured as a function of the number of filling elements in the referential parts of the figures. The curves obtained by two modified figures and by the original two-part stimulus were quite similar in shape, but the magnitudes of the illusions differed significantly. The figure with two filled intervals yielded about twice-stronger illusory effect than the contrasting figure with a single filled and two empty intervals. The two-part stimulus showed the illusion magnitudes in the midst. Our assumption suggests the illusory effect being related particularly to overestimations of the filled interval when compared with the empty interval displayed side-to-side. The unfilled interval might not contribute to the illusion.

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Shape thresholds of geometrical figures have been found equal in cases when both the shortest and the longest linear dimensions of different stimuli were the same (Gutauskas et al, 1994 Perception23 Supplement, 43). The regularity depended neither on colour, nor on size, nor on spatial orientation of the stimuli. In the present study we have checked this result with five different stimuli, which had a central symmetry. Circles, squares, equilateral triangles, pentagons, and hexagons were taken for the psychophysical measurements of the increment shape thresholds. The stimuli, as bright filled objects, were shown on the dark screen of the optical stimulator. Monochromatic light (wavelength 552 nm) was used for the stimuli. As the area of the stimuli increased [from 8 to 1157 (min arc)2], the threshold decreased gradually. Five curves, running in parallel, were obtained in a certain order: squares, hexagons, circles, pentagons, and triangles, if seen from top to bottom. The data obtained demonstrate that the thresholds for identification of shape are different if various figures are of equal area, and they are the same if the figures are of equal height. This supports the idea that certain spatial frequencies of the two-dimensional spectra of the stimuli and the shape thresholds may be interrelated variables.