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.

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.

The "centroid" explanation of the Müller-Lyer and similar illusions of extent supposes the perceptual positional shifts of the stimulus terminators in direction of the centers-of-masses of adjacent contextual flanks. In the present study, the validity of the assumption was tested in psychophysical examination of illusory figures comprising the Müller-Lyer wings or arcs of a circle as the contextual objects. In experiments, the illusion magnitude changes evoked by the tilting of stimulus flanks have been measured. A good resemblance between the experimental data and theoretical predictions was obtained that strongly supports the idea of local positional shifts and serves in favor of "centroid" explanation of illusions investigated.