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

An Investigation of Line and Dot Forms of the Muller-Lyer and Poggendorff Illusions

Both the Müller-Lyer and Poggendorff illusions were found to be reduced by about 70% when all-line figures were replaced by all-dot figures. These data are consistent with some other recent reports and they suggest that Coren's (1970) original finding of a 30% reduction represents an underestimation so that, in his terms, cognitive factors do not account for the larger proportion of these illusions. An additional experiment on mixed line and dot Poggendorff figures provided evidence for a similarity effect, so that larger effects occurred with all-line or all-dot figures than with mixed line-dot configurations. Also, mean effects with line-parallels exceeded those with dot-parallels. However, the interaction between these main effects was not significant. Thus, both figural structure (lines vs. dots) and figural homogeneity (all lines, all dots or mixed) may be independent determinants of the Poggendorff effect.

Testing the Tilt-Constancy Theory of Visual Illusions

Prinzmetal and Beck (2001) Journal of Experimental Psychology: Human Perception and Performance27 206–217) argued that a subset of visual illusions is caused by the same mechanisms that are responsible for the perception of vertical and horizontal—a theory they referred to as the tilt-constancy theory of visual illusions. They argued that these illusions should increase if the observer's head or head and body are tilted because extra reliance would then be placed on the illusion-inducing local visual context. Exactly that result had previously been reported in the case of the tilted-room and the rod-and-frame illusions. Prinzmetal and Beck reported similar increases in the tilt illusion (TI), as well as the Zöllner, Poggendorff, and Ponzo illusions. In two experiments, we re-examined the effect of head tilt on the TI. In experiment 1, we used more conventional TI stimuli, more standard experimental methods, and a more complete experimental design than Prinzmetal and Beck, and additionally extended the investigation to attraction as well as repulsion effects. Experiment 2 more closely replicated the Prinzmetal and Beck stimuli. Although we found that head tilt did increase TIs in both experiments, the increases were of the order of 1°–2°, more modest than the 7° reported by Prinzmetal and Beck. Significantly, the TI increase was larger when inducing tilts and head tilts were in the same direction than when they were in opposite directions, suggesting that the tilt-constancy theory may be oversimplified. In addition, because previous evidence renders unlikely the claim that the Poggendorff illusion can be explained simply in terms of misperceived orientation of the transversals, the question arises whether there might be some other explanation for the increase in the Zöllner, Poggendorff, and Ponzo illusions with body tilt that Prinzmetal and Beck reported.

Stochastic re-calibration: contextual effects on perceived tilt

The human visual system exaggerates the difference between the tilts of adjacent lines or grating patches. In addition to this tilt illusion, we found that oblique flanks reduced acuity for small changes of tilt in the centre of the visual field. However, no flanks--regardless of their tilts--decreased sensitivity to contrast. Thus, the foveal tilt illusion should not be attributed to orientation-selective lateral inhibition. Nor is it similar to conventional crowding, which typically does not impair letter recognition in the fovea. Our observers behaved as though the reference orientation (horizontal) had a small tilt in the direction of the flanks. We suggest that the extent of this re-calibration varies randomly over trials, and we demonstrate that this stochastic re-calibration can explain flank-induced acuity loss in the fovea.

Natural-scene geometry predicts the perception of angles and line orientation

Visual stimuli that entail the intersection of two or more straight lines elicit a variety of well known perceptual anomalies. Preeminent among these anomalies are the systematic overestimation of acute angles, the underestimation of obtuse angles, and the misperceptions of line orientation exemplified in the classical tilt, Zollner, and Hering illusions. Here we show that the probability distributions of the possible real-world sources of projected lines and angles derived from a range-image database of natural scenes accurately predict each of these perceptual peculiarities. These findings imply that the perception of angles and oriented lines is determined by the statistical relationship between geometrical stimuli and their physical sources in typical visual environments.

Why are angles misperceived?

Although it has long been apparent that observers tend to overestimate the magnitude of acute angles and underestimate obtuse ones, there is no consensus about why such distortions are seen. Geometrical modeling combined with psychophysical testing of human subjects indicates that these misperceptions are the result of an empirical strategy that resolves the inherent ambiguity of angular stimuli by generating percepts of the past significance of the stimulus rather than the geometry of its retinal projection.

Parsing surrounding space into regions

Surrounding space is not inherently organized, but we tend to treat it as though it consisted of regions (e.g., front, back, right, and left). The current studies show that these conceptual regions have characteristics that reflect our typical interactions with space. Three experiments examined the relative sizes and resolutions of front, back, left, and right around oneself. Front, argued to be the most important horizontal region, was found to be (a) largest, (b) recalled with the greatest precision, and (c) described with the greatest degree pf detao. Our findings suggest that some of the characteristics of the category model proposed by Huttenlocher, Hedges, and Duncan (1991) regarding memory for pictured circular displays may be generalized to space around oneself. More broadly, our results support and extend the spatial framework analysis of representation of surrounding space (Franklin & Tversky, 1990).

Classical geometric illusion effects with nonclassical stimuli: angular induction from decomposing lines into point arrays

Angular induction is the process by which one line segment can bias judgment of orientation and/or collinearity of another segment, and it has been established that the magnitude of error is a determinate function of the relative angle between the two. We examined how these known relationships are affected by decomposing the induction segment into an array of scattered points. The bias that was produced by such arrays was found to be consistent with a formal model of angular induction, with the strength of the effect decreasing as the scatter among the points was increased. This decline in strength was almost linear with a logarithmic transform of the dimensions of the stimulus array. We also evaluated the hypothesis that the induction stimulus is detected by one or more channels--for example, neurons--for which the sensitivity profiles are modeled as Gabor wavelets. The change in induction strength with increasing point scatter was not predicted by a single width of channel. However, the combined activity of an ensemble of channels that differed in width did match the perceptual effects if one also stipulated that each channel would respond maximally to a fine-line stimulus.

Line intensity affects perceived shape

A method for measuring the variation of one stimulus parameter with respect to another is applied to show how line intensity affects the perceived tilt of lines, internal angle of chevrons, and curvature of circular arcs. Perceived curvature increased with increasing line intensity, but analogous effects were found only for obtuse chevrons, not for acute ones, suggesting a limit to the range of orientations which contribute to the processing of curvature. The absence of a clear trend for tilted lines and acute angles highlights the specificity of the curvature findings. Explanations based on a computer model and other psychophysical and single-unit studies are examined.

Angular induction is modulated by the orientation of the test segment but not its length

Angular induction is the basic process by which the orientation of line segments can affect the perceived orientation of other segments as well as their alignment. In this laboratory, we have found that the effect on alignment follows approximately linear rules, with the inducing segment having its greatest influence when its orientation is near to that of the segment being judged. Other laboratories, however, have reported peak effects when the relative angle between the two is at 45 degrees, and with the inducing segment being aligned with one of the cardinal axes of the observer. It has been said that the length of the test segment being judged is a critical factor, but the first experiment of the present study shows a similar linear decline of induction strength irrespective of test segment length. The second experiment indicates that the orientation of the test segment relative to the observer modulates the induction to determine the location of peak effects. A two-factor linear model predicts the observed pattern of results.

Strategic and perceptual factors producing tilt contrast in dot localization

Encoding spatial location in a frame of reference is often biased by both perceptual and strategic factors. For example, tilt contrast occurs when a line presented in the frame of horizontal and vertical axes appears to be repulsed from the nearest axis, including the diagonal axis of symmetry, due to symmetry perception mechanisms. Research has demonstrated, however, that people can adopt particular viewing strategies that eliminate this effect. In Experiment 1, a similar tilt contrast effect was observed when subjects reproduced from memory the position of a single dot in this reference frame. It was hypothesized that this effect resulted from a combination of strategic and perceptual factors. Specifically, people employ an origin strategy, coding the location of the dot relative to the origin of the horizontal and vertical axes, thereby establishing a virtual line that appears tilted away from the axes due to the same perceptual processes affecting physically present lines. Two additional experiments support this hypothesis. In Experiment 2, no clear tilt contrast effect was observed in a perception condition, indicating that the tilt effect for dots cannot be accounted for by purely perceptual processes. In Experiment 3, the tilt contrast effect was found to be contingent upon the use of the origin strategy as opposed to a different strategy. The results demonstrate the importance of a viewer's strategy in determining the pattern of distortion observed in spatial encoding.

Obliquity integration: variations on a theme of Delboeuf

An optical-geometrical illusion, described by Delboeuf and not familiar to specialists, is investigated. The results of two experiments show that the divergence between a bar filled with parallel slanting lines and a line drawn above it is clearly related to this angle of the lines which fill the bar. The illusion is already present when this angle is 10 degrees, reaches its maximum at 20 degrees, decreases at 30 degrees, and almost disappears at 40 degrees. These results are similar to those found for the tilt illusion, are slightly different from those found for the rod-and-frame illusion, and differ greatly from those found for the Zöllner illusion. The other variables considered-the distance between the slanting lines filling up the bar, the distance between the upper line and the bar, and the width of the bar--do not influence the illusion as much. Since either the line appears as diverging from the bar, or the bar seems inclined in relation to the line, the illusion should be considered a complex one. The small oblique lines inside the bar induce obliquity in the opposite sense in the display, but which of the elements is seen as diverging from the other depends on which of the two is established as the frame of reference.

Structure and strategy in encoding simplified graphs

Tversky and Schiano (1989) found a systematic bias toward the 45 degrees line in memory for the slopes of identical lines when embedded in graphs, but not in maps, suggesting the use of a cognitive reference frame specifically for encoding meaningful graphs. The present experiments explore this issue further using the linear configurations alone as stimuli. Experiments 1 and 2 demonstrate that perception and immediate memory for the slope of a test line within orthogonal "axes" are predictable from purely structural considerations. In Experiments 3 and 4, subjects were instructed to use a diagonal-reference strategy in viewing the stimuli, which were described as "graphs" only in Experiment 3. Results for both studies showed the diagonal bias previously found only for graphs. This pattern provides converging evidence for the diagonal as a cognitive reference frame in encoding linear graphs, and demonstrates that even in highly simplified displays, strategic factors can produce encoding biases not predictable solely from stimulus structure alone.

The basis of the Bourdon illusion

Day (1990) and Day, Mitchell, and Stecher (1990) recently reported new data on the Bourdon illusion, showing that the effect occurs in novel variations of the classic figure--for example, with orthogonal and parallel test edges--and also that it occurs in the haptic modality. Day (1990) criticized theories of the Bourdon effect proposed by Wenderoth, Criss, and van der Zwan (1990), Wenderoth and O'Connor (1987a, 1987b), and Wenderoth, O'Connor, and Johnson (1986), and proposed his own "perceptual compromise" hypothesis. It is argued that Day has inaccurately portrayed the Wenderoth et al. theory, and that his own hypothesis lacks predictive power because it lacks any reference to neural mechanisms. Day's theory is thus unable to account for extant data, including his own. It is demonstrated how Day's novel experiments provide insights into the mechanisms of the Bourdon effect, and also how the Wenderoth et al. theory can account for the new data of Day (1990) and Day et al. (1990).

What is the appropriate control for the tilt illusion?

Recently it has been suggested that when tilt illusions are measured by parallel matching to the test arm of an acute angle, the usual control condition involving a match to the test arm in the absence of the inducing arm is inappropriate. According to Hotopf et al this is so because the pretest contains a second, depth-based illusory effect which is not contained in the test conditions. Whereas Hotopf et al gave indirect evidence for this claim, direct evidence is presented here for their assertion. The results suggest that there is no single stimulus configuration which could serve as a pretest control for all tilt illusion stimuli. Rather, the condition in which the test and inducing lines intersect at 90 degrees probably is the appropriate control for all other inducing-test-line angle displays.

Acute angle enlargement and the Zoellner illusion

The direction rather than the magnitude of the Zoellner illusion was assessed for intersect angles greater than 40 degrees. Data support the illusion's description as an instance of the principle of acute angle enlargement.

Illusion of extent in simple angular figures

With the exception of very small angles (less than 15 degrees) Heywood and Chessell found systematic misestimations of the baseline distances of angles. Here three experiments are reported two of which indicate that the baseline distances of a wide range of acute angles (less than 75 degrees) are overestimated while the third confirms Heywood and Chessell 's pattern of errors. The results are discussed with reference to a possible confounding present in the method used in the third experiment and, therefore, in the original Heywood and Chessell experiments.

Position in the visual field and spatial expansion

Measurements of the tilt illusion by parallelism matches have taken as their baseline data estimates of parallelism between two lines. This is because Carpenter and Blakemore and others found in this situation that parallel lines appeared to diverge at their upper ends. It was hypothesised that this effect was due to inappropriate constancy scaling-the parallel lines being interpreted as being located in a receding plane-and that consequently it was inappropriate to take this effect into account in assessing the degree of the tilt illusion. To test the theory, a horizontal line was compared with other horizontal and vertical lines lower down in the visual field. A tendency to underestimate the length of lines lower down in the visual field was found but this varied inversely with distance from the standard. The findings were accounted for on the assumption that the occurrence of inappropriate constancy scaling depended upon prior organization by contiguity which determined whether the two lines were taken as a group or not.

Fine's frame and perceived tilt

In 1980 Fine asserted that in all rod-and-frame studies, frame tilt has been experimenter-defined. This claim is unwarranted. Attempts to manipulate rod-and-frame illusions by setting observers to see identical frames as squares or diamonds are discussed, as are the difficulties of interpreting the obtained data.

The role of the second oblique in the Poggendorff illusion

It has been observed previously in the classic Poggendorff illusion figure that the end of the oblique line which abuts onto the vertical parallel appears more misaligned than its free end. Various theories suggest that angular distortions are largest at the point of abutment. Two experiments are reported which, however, suggest that, compared to displays in which a single dot is aligned with an oblique line, the introduction of a second, parallel oblique segment does not increase errors more at the abutting tip than at the free end, but, rather, reduces them more at the free end. These results not only cast doubt on the relative importance of angular effects alone in the classic Poggendorff display, but also emphasise the complexity of that figure as a tool in the investigation of visual processing.

Size-analysis of retinal images by orientation detectors

A model for the determination of retinal-image size is presented. The size-analysis is based upon the range of orientation detectors activated by a stimulus. The model is applied to size aftereffects and is also used to predict changes in perceived size in configurations which may be expected to affect the range of orientation detectors activated. The relevance of the model to illusions of direction and the perceived length of lines forming angles is also discussed.

Inhibition of--but not between--orientation detectors: a theoretical note on illusions of direction

In accounting for illusions of direction, many current models assume lateral inhibition among orientation detectors; however, that assumption is unnecessary. Rather, the illusions can be predicted by a model based on the pattern of inhibition and excitation across orientation detectors as caused by a single stimulus line. From the collective effects of multiple stimulus lines, a pattern of excitation and inhibition results which is perceived as an illusion of direction. This collective effect is predicted by convoluting a function representing physical orientation of stimulus lines with a function representing the pattern of inhibition and excitation elicited by a single line. Both perceived angle-expansion (repulsion) and perceived angle-contraction (attraction) are generated by the model.