In the illusion of interrupted spatial extent (also known as the filled-space or Oppel-Kundt illusion), the stimulus spatial interval filled with some visual elements (distractors) appears larger than the unfilled interval of the same size. Despite a long history of research, there is still no consensus on the origin of this visual phenomenon. It was recently shown (Bulatov, Bulatova, Surkys, & Mickienė, Acta Neurobiologiae Experimentalis, 77, 157-167, 2017) that the illusion emergence can be associated mainly with the integration of distractor-evoked effects in regions surrounding the endpoints (terminators) of the stimulus intervals. In the present study, we investigated the two-dimensional weighting profiles of these regions of distractors' influence on the magnitude of length misjudgments. We performed psychophysical experiments with three-dot stimuli that contain distracting line segments, the position of which varied either along or perpendicular to the main stimulus axis, thus scanning the profile in two orthogonal directions. It was demonstrated that for distractors shifted along the stimulus axis, the magnitude of the illusion increases to a certain maximum value with the increase of distractors displacement and smoothly decreases to zero thereafter. For distractors shifted orthogonally to the stimulus axis, the illusion magnitude monotonically decreases with the increase of distractors displacement. In the case of the distractor rotation, the greatest illusion magnitude refers to orientations of the distracting line segment along the stimulus axis and decreases to the minimum value for the orthogonal orientation. Based on the analysis of established functional dependencies, we proposed a simple quantitative interpretation of the obtained experimental data.

For most observers, the part of the stimulus that is filled with some visual elements (e.g., distractors) appears larger than the unfilled part of the same size. This illusion of interrupted spatial extent is also known as the 'filled-space' or 'Oppel-Kundt' illusion. Although the continuously filled-space illusion has been systematically studied for over a century, there is still no generally accepted explanation of its origin. The present study aimed to further develop our computational model of the continuously filled-space illusion and to examine whether the model predictions successfully account for illusory effects caused by distracting line-segments of various lengths that are attached to different endpoints (i.e., terminators) of the reference spatial interval of the three-dot stimulus. Our experiments confirm that the illusion manifests itself along a distracting segment located both inside and outside of the reference interval. In the case of two distractors arranged symmetrically with respect to the lateral terminator, we found that the magnitude of the illusion is approximately equal to the sum of the relevant values obtained with separate distractors. The results of experiments using vertical shifts of distractors supported the model's assumption regarding the two-dimensional Gaussian profile of hypothetical areas of weighted spatial summation of neural activity. A good correspondence between the experimental and theoretical results supports the suggestion that perceptual positional biases associated with the context-evoked increase in neural excitation may be one of the main causes of the continuously filled-space illusion.

The present study investigated whether the asymmetry in magnitude between the wings-in and wings-out versions of the Müller-Lyer illusion can be explained by the manifestation of accompanying effects of the filled-space illusion. In psychophysical experiments, the three-dot stimuli were used, and in different series, a single set of the Müller-Lyer wings was attached to the left or to right terminating dot. To check whether the summation of illusory effects occurs, experiments with two sets of the wings forming the Judd figure were performed. To evaluate the standalone manifestation of the filled-space illusion, we conducted experiments with distracting cross (two sets of coinciding and oppositely oriented wings) centered on the lateral terminator of the stimulus. To interpret the experimental data, we used computational procedures of previously developed quantitative models of hypothetical visual mechanisms underlying the emergence of the Müller-Lyer illusion and the filled-space illusion. It was demonstrated that theoretical calculations adequately account for the illusion magnitude variations for all modifications of stimuli, which convincingly supports the suggestion that the concomitant manifestation of the filled-space illusion is powerful enough to be considered as one of the main reasons for the asymmetric properties of illusions of extent of the Müller-Lyer type.

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