Factors affecting perceived orientation of the Poggendorff transversal

The Poggendorff figure was simplified by removing the right transversal segment. When Ss judged the distance between a dot located on the right parallel and the imagined point where the left transversal, if extended, would intersect the right parallel, the error was independent of dot location. This result is consistent with the idea that the Poggendorff figure is processed asymmetrically by (mis)projecting one of the transversals across to the opposite parallel. Systematically omitting line segments reduced (and sometimes reversed) illusory effects. The most critical Poggendorff feature was the obtuse angle formed between transversal and parallel. Ss vertically adjusted one of two dots to apparent collinearity with an implied transversal, the tip of an intervening vertical line and the other (stationary) dot. Which dot was stationary proved critical. This primitive Poggendorff display generated no illusion unless the implied transversal, defined by the stationary dot, was the one that formed an obtuse angle with the vertical line. This result also strongly supports asymmetric active processing ideas. Perceived orientation is a property of directed line segments.     

The effect of line-figure information on the magnitude of the dot forms of the Poggendorff and Müller-Lyer illusions

The magnitudes of the dot and line forms of the Poggendorff illusion and the Brentano version of the Müller-Lyer illusion were assessed in two groups of subjects: the informed group was given information about the implied figure configuration in the dot pattern, the uninformed group was not. The informed group produced a significantly greater dot illusion than the uninformed group, and there was no difference between the two groups in the magnitudes of the line illusions. The experiments are discussed in the context of Coren and Porac's proposal that illusion-inducing mechanisms can be divided into structural and cognitive components. The results suggest that about 64% of the magnitude of the Poggendorff illusion and about 54% of the Müller-Lyer illusion can be attributed to the involvement of cognitive factors.     

The Poggendorff illusion: Amputations,rotations, and other perturbations

Studies of the Poggendorff illusion (a transversal interrupted by parallel lines) showed that illusory effects increased linearly with increasing separation between the parallels, increased in inverse proportion to the tangent of the angle of intersection between transversal and parallels, decreased whenever line segments (other than a transversal segment) were omitted, decreasing to zero when the segment of a parallel forming the obtuse angle with the transversal was omitted, and varied systematically with the tilt of the whole display, approaching zero when the transversal was oriented in a horizontal or vertical position. Hypothesis: The Poggendorff illusion involves at least three kinds of effects on the perceived orientation of a segment: distortion by other segments (especially a segment intersecting at an obtuse angle), stability of vertical and Horizontal orientations, and assimilation towards vertical or horizontal.     

Slope and the Zöllner illusion

Informal observation suggests that the magnitude of the Z?llner illusion is reduced when the figure is viewed on a sloping plane. The hypothesis that this effect derives from the enlargement of the acute angle of intersection between the obliques and the verticals in the figure when it is viewed on a sloping plane is here investigated. The magnitude of the Z?llner illusion was measured with the use of a visual analogue scale. The results show that the change in the magnitude of the Z?llner effect as a function of the slope of the figure is different from that for corresponding figures, with enlarged angles of intersection between the obliques and the verticals, presented vertically. It is concluded that the enlargement of the angles of intersection can only partly account for the reduction of the Z?llner effect when the figure is viewed under slope, and that some other factor must be involved. An alternative hypothesis is evaluated whereby the effects result from the diminution in the contrast of the obliques when the figure is viewed under slope. Data are also presented to show that observers are able to perceive the enlarged or foreshortened angles of intersection veridically.     

Curved movement paths and the Hering illusion: Positions or directions?

When trying to move in a straight line to a target, participants produce movement paths that are slightly (but systematically) curved. Is this because perceived space is curved, or because the direction to the target is systematically misjudged? We used a simple model to investigate whether continuous use of an incorrect judgement of the direction to the target could explain the curvature. The model predicted the asymmetries that were found experimentally when moving across a background of radiating lines (the Hering illusion). The magnitude of the curvature in participants' movements was correlated with their sensitivity to the illusion when judging a moving dot's path, but not with their sensitivity when judging the straightness of a line. We conclude that a misjudgement of direction causes participants to perceive a straight path of a moving dot as curved and to produce curved movement paths.     

Differential effects of stimulus context on perceived length: Implications for the horizontal-vertical illusion

Six experiments examined orientation-specific effects of stimulus context on the visual perception of horizontal and vertical lengths: Using a paired-comparison method, Experiments 1–5 showed that the probability of judging a given vertical line to be longer than a given horizontal line was relatively great when the stimulus set comprised relatively long horizontals and short verticals, and relatively small when the stimulus set comprised short horizontals with long verticals. To the extent that stimulus context exerts orientation-specific effects on perceived length, it thereby modulates the degree to which verticals appear longer than physically equivalent horizontals: the horizontal—vertical illusion (HVI). Under various contextual conditions, the HVI was as small as 3% (horizontals had to be 3% greater than verticals to be perceived as equally long) and as great as 15%, equaling about 12% in a “neutral” context. In Experiment 6, subjects judged the absolute physical length of each stimulus, and the results indicated that stimulus context acted largely by decreasing perceived lengths. The results are consistent with the hypothesis that differential effects of context reflect a process of stimulus-specific perceptual attenuation.     

Displacement effects caused by converging lines and dots

Changes induced in orientation were examined under conditions of a dot or full-line version of a stimulus consisting of a test and inducing line. 44 subjects visually extended the test line to the surrounding circle on 11 trials and indicated their response by a mark on the circle. Magnitude of illusion was reduced by 54% for the dot version compared with the full-line form, but both produced an illusion significantly greater than zero. A significant practice effect was obtained with full lines but not with the dot form. Results are discussed in terms of lateral inhibition theory and related research.     

The Fraser illusion: complex figures

The cause of the Fraser illusion, which occurs when a line made up of tilted segments itself appears tilted, is examined further. In this series of experiments, we used figures that resembled the original Fraser illusion; they were more complex than those reported on in our previous paper (Stuart & Day, 1988). The figures were used to explore two theories of the Fraser illusion further: that it is the result of interactions between orientation selective units, and that it is a consequence of the local, distributed processing of orientation. The presence of background elements like those used in the original illusion led to an increase in the strength of the illusion, but the shape of these elements had no differential effect on illusion strength. There was a differential effect of the background on the assimilative and contrast illusions, owing respectively to small and large tilts of the inducing elements. The illusion was markedly reduced at small visual angles when the background was absent, but it was only slightly affected when the background was present. All these findings are difficult to explain in terms of interactions between single units, either at the same or at different scales in the image. The effects of luminance contrast and isoluminance on the illusion were not consistent with either theory, but they indicated that researchers need to consider the role of figure-ground organization in this illusion.     

Similar processing of real- and subjective-contour Poggendorff figures by men and women

Measures of illusion magnitude for a real-contour and two subjective-contour Poggendorff figures were obtained from 42 men and 42 women. Although magnitudes of illusion differed as a function of figure type, male-female differences in magnitude of illusion did not vary across figures or judgment orders. Also, correlations among the illusions observed for three types of figures did not differ for men and women. These data are consistent with the view that real- and subjective-contour Poggendorff figures evoke similar processing strategies and that sex differences, when observed, are probably the result of differences in cognitive-judgmental strategy rather than differences in the optical and neural properties of the visual system.     

Reduction of the Zöllner illusion with motion of inducing figure

The magnitude of the Zöllner illusion was measured when the inducing lines moved rightward or leftward and were tracked by subjects. Motion of the inducing lines significantly reduced the magnitude of illusion, as in the Poggendorff illusion. Increasing velocity markedly increased the reduction, and, again, this effect was not significantly different from that obtained with the Poggendorff illusion. The current evidence seems to support the suggestion outlined earlier in relation to the Poggendorff illusion, that is, moving and stationary figures are processed by separate channels and, therefore, the interaction between them is reduced.     

Framing effects and the reversed Müller-Lyer illusion.

The enclosure hypothesis of the reversed Müller-Lyer illusion was examined in three experiments. In Experiment 1, the ingoing- and outgoing-wings forms of the illusion were measured separately, as a function of the size of the gap between the ends of the shaft and the apices of the wings. In Experiments 2 and 3, the effects of a square frame and of complete and amputated versions of a rectangle on the perceived length of an enclosed horizontal line were examined. For all non-Müller-Lyer illusion figures, an inverted U-shaped function describes the relationship between illusion magnitude and the length of the test line. The peak overestimation of the test line's length was obtained when the ratio of total figure length to test line length was about 3:2. Taken together, the results of the three experiments suggest that the reversed Müller-Lyer illusion can be explained within current theoretical frameworks, such as assimilation theory, without recourse to a special factor of enclosure.     

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 Poggendortf illusion as a function of different densities ofrandom dot textures failing the space between the verticals. The results ofExperiment 1 show that the illusory effect is a nonlinear function ofthe texture parameterr, the ratio of black pixels to white and black pixels, with a minimum forr=0.5, approximately, and a maximum forr=0 andr=1. The results may be interpreted by an analytical model of perceptual space dynamics, in which the effect dependson the amount of interaction between points of different light intensity. A computer simulation performed by applying the analytical model to different values ofr 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 ofthe space between the verticals as a function of the parameterr. 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 Poggeadorff illusion.     

Framing effects and the reversed Müller-Lyer illusion

The enclosure hypothesis of the reversed Müller-Lyer illusion was examined in three experiments. In Experiment 1, the ingoing- and outgoing-wings forms of the illusion were measured separately, as a function of the size of the gap between the ends of the shaft and the apices of the wings. In Experiments 2 and 3, the effects of a square frame and of complete and amputated versions of a rectangle on the perceived length of an enclosed horizontal line were examined, For all non-Müller-Lyer illusion figures, an inverted U-shaped function describes the relationship between illusion magnitude and the length of the test line. The peak overestimation of the test line’s length was obtained when the ratio of total figure length to test line length was about 3:2. Taken together, the results of the three experiments suggest that the reversed Müller-Lyer illusion can be explained within current theoretical frameworks, such as assimilation theory, without recourse to a special factor of enclosure.     

The poggendorff illusion with subjective contours

Gregory (1972) has claimed that the Poggendorff misalignment effect occurs when the collinear obliques are separated by subjective rather than real contours. He used two figures to demonstrate this variant of the illusion. Two experiments to test the claim are reported. The first showed that apparent misalignment in one of the two original figures is no greater than that with two obliques alone (the oblique line effect), but misalignment in the other is greater than with two oblique lines and than with a control without subjective contours. The second experiment showed that apparent misalignment in the second figure was less than in two control figures without subjective contours. Since this reduced effect was probably due to the nature of the intersection between the oblique and a semi-circular element, the role of subjective contours remains unsettled.     

The horizontal-vertical illusion and knowledge of results

The Horizontal-Vertical (HV) Illusion was examined in two studies in which subjects adjusted the vertical line in L-shaped and inverted-T figures or produced lines in the vertical and horizontal planes. On the adjustment tasks, vertical lines were made significantly shorter than horizontal comparison lines, especially for the inverted-T figure. On the production tasks, lines drawn in the vertical plane were significantly shorter than lines drawn in the horizontal plane. The adjusted and created lines of subjects receiving intertrial feedback on illusion magnitude were significantly more accurate and less variable than the estimations of control subjects. Performance on either task or figure type did not differ as a function of sex of subject. The present results show that the HV illusion exists in the absence of line bisection or a comparison line and results from the overestimation of vertical lines. These findings further clarify the relative contributions of the structural and strategy mechanisms in the formation of the Horizontal-Vertical Illusion.     

Ponzo错觉解释的合理性：倾斜恒常性理论的局限

倾斜恒常性理论是一种新的解释Ponzo错觉的理论,但是似乎存在一些局限。本研究采用调节法通过两个实验考察了四种Ponzo错觉版本在各种条件(视角和水平线段间距)下的错觉量情况,以此来检验倾斜恒常性理论。实验一中,对称Ponzo错觉变异版本在50mm时的错觉量情况和Prinzmetal(2001)的结果相似,但是在85mm和120mm时得到了较多的错觉量,这和倾斜恒常性理论的理论预期不符。实验二对不对称Ponzo错觉的考察得到了和实验一类似的结果,只有50mm时的情形符合倾斜恒常性理论预期。通过以上实验得到水平线间距和视角因素都是产生Ponzo错觉的重要因素,而倾斜恒常性理论过分强调了背景线的倾斜诱导效应,忽略了其他结构因素对Ponzo错觉的影响,所以倾斜恒常性理论具有一定的局限性,不能有效地解释Ponzo错觉的产生机制。     

Reduction of the Poggendorff effect by the motion of oblique lines

The magnitude of the Poggendorff illusion was measured when the test lines were moved up or down and tracked by subjects. The difference between test lines and inducing lines caused by motion of the test lines significantly reduced the magnitude of illusion (60%). Supplementary experiments seemed to indicate that location of test lines, perceptual shrinkage of space in the vertical dimension, and effective display time were not the main factors contributing to the reduction in illusion magnitude. Instead, it seems that some reduction in interaction between test and inducing lines was the main cause of the reduction. The rising curve of the reduction was very steep with velocity, and the reduction magnitude was almost constant over most of the range of velocities studied. The current evidence seems to suggest that moving and stationary figures are processed by separate channels and that, therefore, the interaction between them is reduced.     

A comparison of visual tilt illusions measured by the techniques of verticle setting, parallel matching, and dot alignment.

The tilt illusion (TI) was investigated by using both short (19 min) and long (2 deg 6 min) test lines, at three angles of test line-inducing line separation (15 degrees, 45 degrees, and 75 degrees). Three groups of ten observers each provided data under one of three task conditions: vertical judgment, parallel matching, and dot alignment on a common visual display. The main result was that both the vertical judgment and the parallel matching task provided similar, classic TI angular functions with the means ordered 15 degrees greater than 45 degrees greater than 75 degrees and with small attraction effects at 75 degrees in three of the four relevant functions. The third task, dot alignment, yielded results different from the average of the other two: no attraction effects occurred and, with the short test line, the obtained mean illusion at 45 degrees exceeded those at the other intersect angles. These results are consistent with alignment data reported by others. One explanation is that the inducing line produces an apparent bowing of the test line which would be reflected in dot alignments but not in vertical setting or in parallel matching. However, direct evidence does not support this hypothesis. An alternate hypothesis, for which independent evidence exists, is that alignment errors reflect perceptual mistracking but that the origin of these errors is not the tip of the test line but within it. Although this does not explain dot alignment errors, it highlights their complexity and the need to interpret them with caution.     

The reversed Müller-Lyer illusion in conventional and in wing-amputated Müller-Lyer figures

Summary When the wings of the conventional or four-wing Müller-Lyer figures are displaced away from the shaft, the apparent elongation of the wings-out figure decreases and the apparent contraction of the wings-in figure changes to apparent elongation. Worrall and Firth (1974) reported a different pattern of illusion change for two-wing Müller-Lyer figures containing wings at only one end of the shaft. Whereas moving the wings away from the shaft decreased the magnitude of the wings-in illusion, it changed the wings-out illusion from apparent elongation to apparent contraction. The effect of wing displacement upon the Müller-Lyer illusion was measured in three experiments. Illusion magnitude was assessed by obtaining judgments of either the length (Experiment 1) or the apparent midpoint (Experiments 2 and 3) of the shaft of four-wing (Experiment 1), two-wing (Experiments 1–3), and one-wing (Experiments 1 and 2) Müller-Lyer figures. Both measures of the illusion showed that displacement of the wings away from the shaft had similar effects on the four and two-wing Müller-Lyer figures. The results are discussed in the context of assimilation theories of the Müller-Lyer illusion, and a possible reason for the apparent inconsistency between Worrall and Firth's conclusions and the present findings is outlined.     

Connectedness affects dot numerosity judgment: Implications for configural processing

Participants judged the number of dots in visual displays with brief presentations (200 msec), such that the numerosity judgment was based on an instantaneous impression without counting. In some displays, pairs of adjacent dots were connected by line segments, whereas, in others, line segments were freely hanging without touching the dots. In Experiments 1, 2A, and 2B, connecting pairs of dots by line segments led to underestimation of dot numbers in those patterns. In Experiment 3, we controlled for the number of freely hanging line segments, whereas Experiment 4 showed that line segments that were merely attached to dots without actually connecting them did not produce a considerable underestimation effect. Experiment 5 showed that a connectedness effect existed when stimulus duration was reduced (50 msec) or extended (1,000 msec). We conclude that connectivity affects dot numerosity judgments, consistent with earlier findings of a configural effect in numerosity processing. Implications of the role of connectedness in object representation are discussed.