The phenomena of geometrical illusions of extent suggest that the metric of a perceived field is different from the metric of a physical stimulus. The present study investigated the Müller-Lyer and Oppel-Kundt illusions as functions of spatial parameters of the figures, and constructed a neurophysiological model. The main idea of the modelling is based on the uncertainty principle, according to which distortions of size relations of certain parts of the stimulus, so-called geometrical illusions, are determined by processes of spatial filtering in the visual system. Qualitative and quantitative agreement was obtained between psychophysical measurement of the strength value of the illusions and the predictions of our model.
A combined influence of stimulus orientation and structure on the judgment of length was tested in psychophysiological experiments. The subjects adjusted the test part of a stimulus to be equal in length to the reference part. The orientation of the parts of the stimulus varied in the experiments. The stimuli (three dots or the Oppel-Kundt figure, which had ten dots within the filled part) were generated on the monitor. In the Oppel-Kundt figure, the filled part was considered as a reference and the empty part as a test. In sessions of the experiments, values of errors were measured as functions of the size and orientation of the stimulus. The reference part length varied within 14-150 min are range, and the orientation was fixed in 0 degree, 90 degrees, 180 degrees or 270 degrees positions. The orientation of the test part varied from 0 degree to 360 degrees in 7 degrees steps. We assume, that the experiments with the three-dot stimuli yielded pure characteristics of visual field anisotropy, while those with the Oppel-Kundt figure showed the combined effect of both the components (anisotropy and spatial filtering). The data demonstrated independence of the two factors from each other in a simultaneous manifestation. The characteristics of a pure Oppel-Kundt illusion have been found to be in close correspondence with the predictions of the model of spatial filtering.
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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