An auditory time perception illusion analogous to the visual Müller-Lyer illusion.

According to the centroid hypothesis, the visual Müller-Lyer-type illusions in which subjects misperceive lines or gaps as longer or shorter depending on surrounding distracters result from the pooling of positioning neural signals such that the perceived object is shifted towards these distracters. However, it is uncertain if this type of pooling is a more general principal that influences perceptions in other sensory modalities, including time perception based on auditory signals. In this study, I show that by applying the principles of the centroid hypothesis, an audial time duration illusion can be constructed. The perception of two sequential time intervals, which were defined by three short tone signals, was distorted by placing distracting white noise sounds near each signal. Misperception magnitude, which peaked at 31%, changed with the time interval between the tone signals and distracters; the relationship between the target-distracter distance and the illusion strength closely paralleled with that of a Müller-Lyer-type illusion, whereby the visual objects were analogically arranged in space rather than time. These results demonstrate that even if signals and distracters are distinguishable, the neural mechanisms for estimating time duration utilize coarser sampling to preserve processing resources at the expense of high accuracy. I hypothesize that systems that are dedicated to visual length and time duration estimations are based on similar perceptual magnitude evaluation algorithms. Moreover, this signal pooling principle may be applicable to other perceptual modalities across different species.

Oppel-Kundt illusion balance.

Perceptual estimates of spatial dimensions of visual objects depend on their shape and surface attributes. The present psychophysical study emphasizes two main contributors to the Oppel­Kundt illusion: the outline of the filled space and the mode of filling. In past experiments, both factors have been considered significant. Our experiments were performed by using combined stimuli of the Oppel­Kundt figures and supplementary objects situated within the empty intervals of the figures. Line segments, empty and filled rectangles, blurred contours, and grey and color images were used for the supplementary stimuli role. The experimental data demonstrated an innate property of the objects to balance the illusion of distance if they were placed within the Oppel­Kundt figure and to create an illusion of extent when compared with an empty space interval. Both the balance magnitude and the induced illusion strength varied depending on the objects' spatial structure. The supplementary objects showed a tendency to differ from each other by their functional capacity and were ranked from lowest to highest: a line segment, a solid bar with a blurred outline, a contour of a rectangle, a solid fill rectangle, greyscale patterns, and color pictures. The experimental findings provided support for an explanation of the Oppel­Kundt illusion in terms of the spatial­temporal summation of excitations representing the object outline and surface attributes at the lower cortical levels of the visual system. Along with the facts already established in current literature, the experimental data gave rise to the assumption that any visual object could appear larger than its occupied area, and that the Oppel­Kundt illusion could become a separate case in the common sensory phenomenon of object size illusion.

Summation of two illusions of extent.

In the present visual psychophysical study, the Oppel­Kundt and and Müller­Lyer illusion magnitudes were measured separately (by single figures) and in combination (by two patterns superposed spatially). Data for 30 subjects revealed extensive variability both for the separate and combined illusion strength. Nevertheless, the effect of addition of the perceived length distortions was established. The combined illusions were significantly stronger than the separate ones. Dynamics of the misperceptions summation was studied by varying length of the Müller­Lyer wings in the superposed stimuli. According to the experimental data obtained, the two misperceptions in length occurred and combined into sensory response varying in dependence on the spatial parameters of the superposed stimuli and on the individual experimental accomplishment. The data supported an explanation for the origin of the filled/unfilled illusion: overestimate of a filled interval length developed due to the spatiotemporal integration along a continuous excitation path elicited by the real or imaginary contours of the filling.

An effect of continuous contextual filling in the filled-space illusion.

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.

A quantitative analysis of illusion magnitude changes induced by rotation of contextual distractor.

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.

Illusion of extent evoked by closed two-dimensional shapes.

In the present study, we have tested the applicability of the computational model of centroid extraction to account for the data collected in experiments with stimuli comprising of closed two-dimensional shapes. The outlined or uniformly filled pie-shaped circular sectors (contextual distractors) were arranged according to the Brentano pattern, and three different stimulus parameters (either the radius or the central angle or the tilt angle of the sectors) were used as independent variables in different series of experiments. It was demonstrated that the model calculations adequately predict the variations of illusion magnitude shown by all the subjects for all independent variables and that there is no significant difference between the data obtained for stimuli with the outlined and uniformly filled distractors. A good correspondence between the computational and experimental data provides convincing evidence in support of the "centroid" explanation of illusions of extent of the Müller-Lyer type.

Temporal dynamics of the Oppel-Kundt Illusion compared to the Müller-Lyer Illusion.

In psychophysical experiments, subjects reported whether the filled part of the Oppel-Kundt stimulus was longer than the empty one at different durations of the stimuli presentations. The experimental data yielded a smooth function indicating a gradual augmentation of the illusion strength within a relatively wide 100-1000 ms interval of the exposure durations. On the contrary, the experiments with the Müller-Lyer stimuli showed a gradual decrease of the illusion magnitude within the same interval of expositions. In the supplementary experiments, the stimuli with uniformly filled or outlined rectangles of fixed duration were used; various combinations of the rectangles with the regular sequences of filling stripes were also taken. It was demonstrated that the superposition of the stimuli did not change the illusion strength noticeably. The results obtained in the study support the suggestion that the filled interval overestimation in the Oppel-Kundt stimulus may be related to spatiotemporal integration along a continuous path of neural excitation evoked by the real and illusory contours of the filling.

Perpendicularity misjudgments caused by contextual stimulus elements.

It has been demonstrated in previous studies that the illusions of extent of the Brentano type can be explained by the perceptual positional shifts of the stimulus terminators in direction of the centers-of-masses (centroids) of adjacent contextual flanks [Bulatov, A. et al. (2011). Contextual flanks' tilting and magnitude of illusion of extent. Vision Research, 51(1), 58-64]. In the present study, the applicability of the centroid approach to explain the right-angle misjudgments was tested psychophysically using stimuli composed of three small disks (dots) forming an imaginary rectangular triangle. Stimuli comprised the Müller-Lyer wings or line segments (bars) as the contextual distracters rotated around the vertices of the triangle, and changes in the magnitude of the illusion of perpendicularity were measured in a set of experiments. A good resemblance between the experimental data and theoretical predictions obtained strongly supports the suggestion regarding the common "centroid" origin of the illusions of extent of the Brentano type and misperception of the perpendicularity investigated.

Contextual flanks' tilting and magnitude of illusion of extent.

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.

Three-part Oppel-Kundt illusory figure.

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 over estimations of the filled interval when compared with the empty interval displayed side-to-side. The unfilled interval might not contribute to the illusion.

Delboeuf illusion study.

In psychophysical experiments, the Delboeuf illusion was measured as a function of spatial parameters of the stimulus pattern. During the experiments, the stimulus shape, size, luminance, and the dimensions of inducing surround varied. Subjects were asked to change the size of the test part of the stimulus by adjusting its diameter to value that made the test part appear equal to the perceived size of the referent part. The difference in diameters between the test and referent parts of the stimulus, determined after the perceived equality was achieved, was considered to be the value of the illusion magnitude. The magnitude of the Delboeuf illusion was dependent on the type of the stimuli and their contrast: the filled circles with the luminance contrast yielded stronger illusion than the open circles and the stimuli with isoluminant colors. The magnitude of the illusion did not change noticeably with variations of the luminance of the stimulus, but diminished when the luminance of the stimulus approached the level of isoluminance with the background. The neurophysiological spatial filtering model, applied to the Delboeuf stimuli patterns, has provided computational results similar to the present experimental findings.

[Müller-Lyer illusion and colour contrast]. / Müller-Lyer iliuzija ryskio bei spalvos kontrasto salygomis.

In psychophysical experiments, subjects adjusted the test part of the Müller-Lyer figure to make it appear equal in length to the reference part of the figure in the absence and presence of luminance contrast. The illusion was measured as function of the length and internal angle of wings varying from 7 to 35 min of arc and from 40 degrees to 180 degrees, respectively. Müller-Lyer figures, 130 min of arc long with no shaft line, were generated by Cambrige Research Systems VSG2/3 and presented as stimuli on an EIZO T562 monitor with gamma correction. The CRT primary colors provided chromatic contrast between the stimulus and the background area. Prior to the experiments, the method of two-color gratings was used to detect isoluminance for each color pair. The experimental curves showed a significant increase of the illusion strength up to 1.5-2 times at isoluminance irrespective of the colors combined. The data obtained are interpreted in terms of spatial-frequency filtering and low-pass chromatic filters.