A field theory of visual illusions

An attentional approach to geometrical illusions

It is known for a long time that some drawings composed of points, lines, and areas are systematically misperceived. The origin of these geometrical illusions is still unknown. Here we outline how a recent progress in attentional research contributes to a better understanding of such perceptual distortions. The basic idea behind this approach is that crucial elements of a drawing are differently attended. These changes in the allocation of spatial attention go along with systematic changes in low-level spatial coding. As a result, changes in the perception of spatial extent, angles, positions, and shapes can arise. How this approach can be applied to individual illusions is discussed.

Oppel – Kundt Illusion in Three-Dimensional Space

A three-dimensional form of the Oppel – Kundt illusion was examined. Subjects viewed arrays consisting of two parallel rows of lights. For one group the rows consisted of equal numbers of lights (2, 3, or 4), while for a second group the row nearest the subject always had the greater number of lights. Subjects viewed these arrays from two vantage points, one directly in front of the array and the other displaced laterally. For each array subjects adjusted the extent of the far array until they felt the two rows were the same length. Both the nature of the array and the viewpoint had a significant influence on the perceived length of the far row. The size of the near row was overestimated significantly more when the array was viewed from the central position and also when the number of lights in the near row exceeded that of the far row. These results confirm that a lateral viewing position decreases the perspective effect and indicate that the Oppel – Kundt illusion can occur with three-dimensional stimuli.

Defining filled and empty space: reassessing the filled space illusion for active touch and vision

In the filled space illusion, an extent filled with gratings is estimated as longer than an equivalent extent that is apparently empty. However, researchers do not seem to have carefully considered the terms filled and empty when describing this illusion. Specifically, for active touch, smooth, solid surfaces have typically been used to represent empty space. Thus, it is not known whether comparing gratings to truly empty space (air) during active exploration by touch elicits the same illusionary effect. In Experiments 1 and 2, gratings were estimated as longer if they were compared to smooth, solid surfaces rather than being compared to truly empty space. Consistent with this, Experiment 3 showed that empty space was perceived as longer than solid surfaces when the two were compared directly. Together these results are consistent with the hypothesis that, for touch, the standard filled space illusion only occurs if gratings are compared to smooth, solid surfaces and that it may reverse if gratings are compared to empty space. Finally, Experiment 4 showed that gratings were estimated as longer than both solid and empty extents in vision, so the direction of the filled space illusion in vision was not affected by the nature of the comparator. These results are discussed in relation to the dual nature of active touch.

Size and Direction of Distortion in Geometric-Optical Illusions: Conciliation between the Müller-Lyer and Titchener Configurations

Over the past few decades, different theories have been advanced to explain geometric-optical illusions based on various perceptual processes such as assimilation and/or contrast. Consistent with the contradictory effects of assimilation and contrast, Pressey's assimilation theory provided an explanation for the Müller-Lyer illusion, but failed to account for the Titchener (Ebbinghaus) illusion. A model that explains both Müller-Lyer and Titchener illusions according to a common underlying process may outline a unified explanation for a variety of geometric-optical illusions. In order to develop such a model, the concept of empty space is introduced as an area of the illusory figure that is not filled by line drawings. It was predicted that the magnitude of illusion would increase with the area of the empty space around the illusory figures. The effect of empty space on the magnitude of perceptual distortion was measured in Müller-Lyer figures, with outward arrowheads of different length. The results indicated an overestimation of the target stimulus in all of the figures. Nevertheless, consistent with the prediction of the present model, the horizontal line in the Müller-Lyer figure with the longest arrowheads appeared shorter than that with the shortest arrowheads, although the size contrast of these figures was the same. According to the analysis proposed in the present study, the area of empty space not only affects the magnitude of illusion but also serves as a contextual cue for the perceptual system to determine the direction of illusion (orientation). The functional relationships between the size contrast and empty space provide a common explanation for the Müller-Lyer, Titchener, and a variety of other geometric-optical illusions.

Image features selected by neurons of the cat primary visual cortex

The sensitivity of neurons in field 17 of the visual cortex in cats to cross-shaped, Y-shaped, and star-shaped figures flashing in the receptive field was studied. About 40% of the neurons studied (114 of 289) were found to generate large responses (with an average response factor of 3.06 +/- 0.32) to one of the figures flashing in the center of the receptive field, as compared with the responses produced to a single bar in the optimal orientation. Most of these neurons (72%) were selectively sensitive to the shape and orientation of figures; the remainder demonstrated some degree of tuning invariance to these properties. The latent periods of responses to figures were usually shorter than those of responses to bars. Tuning parameters for bars and figures were generally related: neurons with acute orientational tuning to a bar were usually highly selective to both the configuration and the orientation people figures. Separate or combined stimulation with crosses in the center and near periphery of the receptive fields demonstrated summation, antagonism, or the lack of any interaction between these zones in producing sensitivity to crosses. Local blockade of intracortical GABAergic inhibition by microiontophoretic application of bicuculline showed that in one third of the neurons studied, sensitivity to figures was generated or enhanced by inhibition in normal conditions, while one third of cells showed suppression by inhibition, and sensitivity in the remainder was independent of inhibition. These data show that reconsideration of existing concepts of the role of field 17 in selecting only first-order shape features of images (i.e., the orientations of single lines) is needed, since almost half the neurons in the cat primary visual cortex can efficiently detect second-order features (angles and line intersections).

A test of the gravity lens theory

Naito and Cole [1994, in Contributions to Mathematical Psychology: Psychometrics and Methodology Eds G H Fischer and D Laming (New York: Springer)] provide a configuration which they describe as the Gravity Lens illusion. In this configuration, four small dots are presented in proximity to four large disks, and one is asked to compare the slope of an imaginary line which connects one pair of dots with the slope of a line which connects the other pair. In fact the slopes are the same, i.e. their axes are parallel, but because of the positioning of the large disks they appear to be at different orientations. Naito and Cole propose that the perceptual bias is analogous to the effects of gravity on the metrics of physical space, such that mental projections in the vicinity of a disk (or an open circle) are distorted just as the path of light is bent as it passes a massive body such as a star. Here we provide a simple test of this concept by having subjects judge alignments of dots which lie near tangents to a circle. Subjects were asked to project straight lines through pairs of stimulus dots, selecting and marking points in open space which were collinear with each pair. As would be predicted by the Gravity Lens theory, the locations selected by subjects were displaced from straight lines. However, the error magnitudes were substantially larger for judgments of dot pairs which had an oblique alignment, as compared with dot pairs which were aligned with a cardinal axis. This differential of effect as a function of stimulus orientation is not predicted by the gravity concept.

Sensitivity to cross-like figures in the cat striate neurons

The responses and orientation tuning in 48 out of 62 (77.4%) neurons of the cat striate cortex (area 17) significantly, but with different sign, changed at stimulation by specific cross-like figure flashing in receptive field as compared with single light bar of preferred orientation. Neurons of the first group (19 units from 62, 30.6%) were found to increase the responses by 3.3 times if stimulated by a certain cross-like figure, specific for each cell configuration and orientation. Under the same conditions, neurons of the second group (29 or 46.8% revealed a three-fold decrease of responses and all tuning characteristics worsened. Among them 8% of total number of cells showed bimodal or double orientation tuning when stimulated by some configurations of crosses due to an angle specific inhibition. Dependence of the revealed effects on excitatory convergence from neurons with different orientation tuning, on inhibitory influences from end-stop and side-zones of receptive field, as well as possible functional implication of the first group neurons for an angle and line-crossing detection are discussed.

Double orientation tuning in the cat visual cortex units

Orientation tuning of 271 neurons of the cat visual cortex (area 17) was studied with a light bar flashing in the receptive field. Under different conditions, 27-57% of units were found to have double-orientation tuning: they demonstrated the main preferred orientation and an additional preferred orientation. The statistical reliability and reproducibility of additional preferred orientation were shown. The quality of orientation tuning in the second maximum did not differ statistically from the first one. The angle between preferred orientation and additional preferred orientation was either 90 degrees (29% of cases) or an acute one (60.1 +/- 3.1 degrees, 71% of cases). The ratio of discharge frequency in responses to additional preferred orientation and preferred orientation was equal to 0.74 +/- 0.05. Neurons with double-orientation tuning clearly preferred 67 degrees and 157 degrees, while monomodal units preferred 0 degrees and 90 degrees. Probability of the double-tuning increased under bar lengths of near 3 degrees and near 10 degrees and with increase of stimulus/background contrast. At the same time some neurons displayed double-orientation tuning only with relatively low stimulus/background contrast. The proportion of units with double-orientation tuning was lowered by about 1.5-times under general Nembutal narcotization as compared with local anesthesia of the animal. In about one-third of units simultaneous stimulation by two flashing lines crossing in the receptive field center under an angle specific for the cell, evoked a response from 1.5 to four times larger than to the preferred orientation.(ABSTRACT TRUNCATED AT 250 WORDS)

Modifications of the Poggendorff effect as a function of random dot textures between the verticals

In the present research, we investigated the modification of the strength of the Poggendorff illusion as a function of different densities of random dot textures filling the space between the verticals. The results of Experiment 1 show that the illusory effect is a nonlinear function of the texture parameter r, the ratio of black pixels to white and black pixels, with a minimum for r = 0.5, approximately, and a maximum for r = 0 and r = 1. The results may be interpreted by an analytical model of perceptual space dynamics, in which the effect depends on the amount of interaction between points of different light intensity. A computer simulation performed by applying the analytical model to different values of r shows a good agreement between the predictions and the experimental data. To test the hypothesis underlying the model, a second experiment was carried out to measure the magnitude of the expansion of the space between the verticals as a function of the parameter r. The results are consistent with the hypothesis of the model. The overall data are discussed in terms of their implications on various theories proposed for the Poggendorff illusion.

Collinearity judgment as a function of induction angle

The misalignment which is seen in the Poggendorff illusion can be studied with better control by using a configuration which has only two line segments. Two experiments were conducted in which subjects judged collinearity of a test segment, this judgment being subjected to a biasing influence from a second (induction) segment. Exp. 1 held the test segment at one of three orientations relative to the observer (30 degrees, 45 degrees, and 60 degrees) and systematically varied the orientation of the induction segment in 15 degrees increments through the range of possible positions. The orientation of the page relative to the observer was varied as well. Exp. 2 varied the test segment through a greater range of angles and sampled more levels of induction segment orientation. Analysis indicated that projection errors follow orderly rules similar in kind to but different in magnitude from those observed for the Tilt Illusion, most notably, (a) misprojection is greatest when the orientation of the interfering line is similar to that of the line segment being projected and (b) the strength of this influence decreases as the relative angle becomes orthogonal. Also, the orientation of the segment being projected relative to the observer serves to modulate the strength of the basic induction effect. These perceptual interactions are discussed in relation to neural models for orientation selectivity.

The orientation of a parallel-line texture between the verticals can modify the strength of the Poggendorff illusion

In the present experiments, we attempted to evaluate the modification of the strength of the Poggendorff illusion as a function of the different orientation of a parallel-line texture filling the space between the vertical lines. In Experiment 1, the standard version of the Poggendorff configuration was tested against four different parallel-line textures oriented at 0 degrees, 45 degrees, 90 degrees, and 135 degrees with respect to the obliques. The results showed that the illusory effect was a linear function of the progressive discrepancy between the angle of the lines of the texture and that of the obliques. In Experiment 2, we tested the same textures used in Experiment 1 after the elimination of the two vertical lines. The data obtained approximated a linear function, as in the previous experiment, but the alignment errors were consistently lower. The statistical analysis performed on the data of all eight experimental conditions shows that both factors--texture and presence/absence of verticals--were significant, but most of the effect was due to the texture factor. The results may be interpreted through the "perceptual compromise hypothesis," originally proposed for the bisection forms of the Poggendorff illusion, but with important modifications. The data are also discussed in terms of their implications for other theories proposed for the Poggendorff illusion.

The corner Poggendorff

With the classic Poggendorff illusion a set of parallel 'induction lines' will cause a set of oblique line segments to look misaligned even though they are collinear. A different kind of misalignment can be produced by placing the induction lines so that they form a corner. Under these conditions the obliques will appear to be angled slightly, one relative to the other. The effects are small, but can be seen and reliably reported by a group of naive subjects. The influence of the induction lines drops sharply as their relative position is moved from parallel to orthogonal, but there is a small residual influence which may be called the corner Poggendorff effect.

The relative contribution of contact and target lines in the magnitude of the Poggendorff effect

It is well known that a set of parallel lines can cause misperception of the projected path of an oblique. Most studies of this effect have emphasized either the proximal or the distal stimulus components--the line with which the oblique makes contact, or the line that serves as the target of the projection. An experiment is reported in which the relative contribution of the contact and target lines was examined. The results indicate that rotation of either line can determine the magnitude of the projection error.

Another optical-geometrical illusion

A new optical-geometrical illusion is described. The parallelism of short rows of dots is affected by some unknown factor, so that the rows appear as pivoting on their middle point. Some explanations of the illusion are considered, but with no success.

The components of the standard and reverse Müller-Lyer illusions

The absolute contribution of each type of oblique figure in the standard and reverse Müller-Lyer illusions is determined by placing one oblique figure at different distances from the end of a test line (either horizontal or vertical) and measuring shift in the line's apparent midpoint as a function of proximity of the oblique figure. The absolute effect of both types of figure, apex-in > < or apex-out < > is one of contraction, and superimposed on this, again for both types of figure, is a smaller expansion effect which is phasic and varies with proximity of the figure to the line. The major factor in the reverse illusion appears to be the apex-in > < and not the apex-out < > figure as previously supposed. For both standard and reverse illusions, and again for both types of figures, there is a visual field effect, since contraction is greater when the obliques lie in the right or in the lower hemifield. The fundamental similarities in mode of action of each type of oblique are further demonstrated by showing that geometrical figures in general, regardless of shape or orientation, give rise to similar patterns of absolute contraction with a phasic expansion component superimposed. The Müller-Lyer oblique figures therefore operate as two of many possible examples of a single underlying mechanism, and recent arguments that the Müller-Lyer is really two separate constituent illusions are not supported.