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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.
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.
In the present study, the predictions of the computational model of centroid extraction were verified in psychophysical examination of the length illusion induced by stimuli comprising the conventional or asymmetric Müller-Lyer wings as the contextual distractors. In experiments, the illusion magnitude changes evoked by rotation of distractors with different spatial parameters were quantitatively determined. It was demonstrated that the model calculations adequately account for the illusion magnitude variations shown by all the subjects for all modifications of stimuli. A good correspondence between the experimental and theoretical data supports the suggestion that local positional biases caused by the neural processes of automatic centroid extraction can be one of the main reasons of emergence of illusions of the Müller-Lyer type.
In the present communication, a possible role of perceptual displacements of stimulus elements in the occurrence of visual illusions of extent has been considered. In psychophysical experiments with a single set of Muller-Lyer wings, subjects were asked to place an imaginary reference rectangle into a position that made the apex of the wings appear to be at the rectangle center. Three different stimulus parameters (the length, internal angle, or tilt angle of the wings) were used as independent variables in different series of experiments. It was demonstrated that the magnitude of perceptual displacements of stimulus terminator is commensurate with that of illusions of extent obtained in our previous studies of full versions of illusory figures. Good correspondence between the experimental data and the predictions of our computational model of automatic centroid extraction strongly supported the suggestion that the effects of centroid extraction are powerful enough to be considered as one of the main causes of illusions of extent of the Muller-Lyer type.
In the present study, we tested the ability of our computational model of the filled-space illusion to account for data collected in experiments with stimuli comprising single-dot distractors. In three sets of experiments, we investigated this illusory effect as a function of distance between the distractor and lateral terminator of the reference spatial interval of the three-dot stimulus. We found that the model calculations properly predicted all of the observed changes in magnitude of the illusion for stimuli with a single distracting dot placed both within and outside the interval, as well as, for stimuli with two distractors arranged symmetrically relative to the lateral terminator. To additionally test the model, in a fourth set of experiments we performed psychophysical examination of the conventional Oppel-Kundt stimulus with a different number of equally spaced dots subdividing the filled part. Adequate correspondence between the computational and experimental data supports our assumptions concerning the origin of the filled-space illusion.
In the present study, a computational model of the automatic centroid extraction based on the processes of local integration of excitatory profiles in the visual pathways has been developed. The model predictions have been compared with the results of our psychophysical examination of the perceptual distortions of the spatial extent. In experiments, the subjects matched two spatial intervals flanked by one of the three types of the contextual objects: either the Müller-Lyer wings, or vertical stripes, or spot pairs. A good resemblance between the theoretical functions and dependencies of the illusions’ magnitudes on various spatial parameters of the stimuli has provided evidence that the effects caused by indirect positional coding via centroids are powerful enough to explain the phenomena of the geometric illusions investigated.
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