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.

Sharpness of vision depends on the resolution of details conveyed by individual neurons in the visual pathway. In the dorsal lateral geniculate nucleus (LGN), the neurons have receptive fields with center-surround organization, and spatial resolution may be measured as the inverse of center size. We studied dynamics of receptive field center size of single LGN neurons during the response to briefly (400-500 ms) presented static light or dark spots. Center size was estimated from a series of spatial summation curves made for successive 5-ms intervals during the stimulation period. The center was wide at the start of the response, but shrank rapidly over 50-100 ms after stimulus onset, whereupon it widened slightly. Thereby, the spatial resolution changed from coarse-to-fine with average peak resolution occurring approximately 70 ms after stimulus onset. The changes in spatial resolution did not follow changes of firing rate; peak firing appeared earlier than the maximal spatial resolution. We suggest that the response initially conveys a strong but spatially coarse message that might have a detection and tune-in function, followed by transient transmission of spatially precise information about the stimulus. Experiments with spots presented inside the maximum but outside the minimum center width suggested a dynamic reduction in number of responding neurons during the stimulation; from many responding neurons initially when the field centers are large to fewer responding neurons as the centers shrink. Thereby, there is a change from coarse-to-fine also in the recruitment of responding neurons during brief static stimulation.

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 filled-space (or Oppel-Kundt) illusion, the filled part of the stimulus for most observers appears longer in comparison with the empty one. In the first two experimental series of the present study, we investigated the illusory effect as a function of continuous filling (by a shaft-line segment) of the reference spatial interval of the three-dot stimulus. It was demonstrated that for the fixed length of the reference interval, the magnitude of the illusion increases non-linearly with the shaft length. For the fixed length of the shaft, the illusion magnitude gradually decreases with the lengthening of the reference interval. In the third series, psychophysical examination of the conventional Oppel-Kundt stimulus with different number of equally spaced elements (dots) subdividing its filled part was performed. Based on the analysis of the functional dependencies established, we have proposed a simple computational model that was successfully applied to fit the experimental data obtained in the present study.

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.