Objects, raised lines, and the haptic horizontal-vertical illusion

Experiments were conducted to determine whether the haptic horizontal-vertical illusion occurs with solid, three-dimensional objects as well as with tangible lines. The objects consisted of round or square bases, with dowel rods projecting above them at heights equal to the widths of the horizontal bases. A negative illusion, with overestimation of horizontals, was found with free haptic exploration, but not with tracing with the fingertip. The negative illusion occurred when subjects felt wooden Ls and inverted Ts with a grasping, pincers motion of the index finger and thumb. The presence or absence of illusory misperception was dependent upon exploration strategy, since the negative illusion vanished with finger tracing. A negative illusion was also found when subjects adjusted a vertical dowel so that it was judged to be equal in extent to a round or square base. A general overestimation of judged size derived from the pincers response measure, but was not found with the use of a tangible ruler. Comparable illusory results are most likely when drawings and objects promote similar haptic scanning methods. The results were consistent with the idea that the orientation of an edge or line is more important than whether one explores a tangible line or a three-dimensional object.     

The tactual horizontal-vertical illusion depends on radial motion of the entire arm

Wesought to clarify the causes of the tactual horizontal-vertical illusion, where vertical lines are overestimated as compared with horizontals in Land inverted-T figures. Experiment 1 did not use L or inverted-T figures, but examined continuous or bisected horizontal and vertical lines. It was expected that bisected lines would be perceived as shorter than continuous lines, as in the inverted-T figure in the horizontal-vertical illusion. Experiment 1 showed that the illusion could not be explained solely by bisection, since illusory effects were similar for continuous and bisected vertical and horizontal lines. Experiments 2 and 3 showed that the illusory effects were dependent upon stimulus size and scanning strategy. Overestimation of the vertical was minimal or absent for the smallest patterns, where it was proposed that stimuli were explored by finger movement, with flexion at the wrist. Larger stimuli induce whole-arm motions, and illusory effects were found in conditions requiring radial arm motion. The illusion was weakened or eliminated in Experiment 4 when subjects were forced to examine stimuli with finger-and-hand motion alone, that is, their elbows were kept down on the table surface, and they were prevented from making radial arm motions. Whole-arm motion damaged performance and induced perceptual error. The experiments support the hypothesis that overestimation of the vertical in the tactual horizontal-vertical illusion derives from radial scanning by the entire arm.     

A new illusion of height and width: taller people are perceived as thinner

It is commonly said that tall people look thinner. Here, we asked whether an illusion exists such that the taller of two equally wide stimuli looks thinner, and conversely whether the thinner of two equally tall stimuli looks taller. In five experiments, participants judged the horizontal or vertical extents of two identical bodies, rectangles, or cylinders that differed only in their vertical or horizontal extents. Our results confirmed the folk wisdom that being tall makes you look thinner. We similarly found that being thin makes you look taller, although this effect was less pronounced. The same illusion was present for filled rectangles and cylinders, but it was consistently stronger for both photographs and silhouettes of the human body, raising the question of why the human form should be more prone to this illusion.     

Visual and haptic perception of the horizontal-vertical illusion

The horizontal-vertical illusion consists of two lines of the same length (one horizontal and the other vertical) at a 90 degree angle from one another forming either an inverted-T or an L-shape. The illusion occurs when the length of a vertical line is perceived as longer than the horizontal line even though they are the same physical length. The illusion has been shown both visually and haptically. The present purpose was to assess differences between the visual or haptic perception of the illusions and also whether differences occur between the inverted-T and the L-shape illusions. The current study showed a greater effect in the haptic perception of the horizontal-vertical illusion than in visual perception. There is also greater illusory susceptibility of the inverted-T than the L-shape.     

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.     

The tilted Hermann grid illusion: 'illusory spots' versus 'phantom bands'

The Hermann grid illusion became a cause célèbre, when it was reported that small figural changes from straight to curved bars abolish the dark illusory spots. We demonstrate that this is not an all-or-none effect; rather, the visual system tolerates some tilt/curviness. We transformed straight and curved Hermann grids to rhombic Motokawa grids by gradually tilting the horizontal bars. Initially, we observed only dark illusory spots, then dark spots combined with phantom bands traversing the rhomb along the minor axis, and finally dark phantom bands only. This shows that two kinds of illusions can coexist in the same grid pattern.     

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.     

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.     

Illusory three-dimensional rotation of horizontal lines: a new motion-depth illusion.

A new motion--depth illusion is reported. When a curved aperture translates vertically and stationary horizontal lines can be seen through it, the line lengths on the retina change continuously because of the occlusion. Instead of seeing the aperture translate, subjects sometimes see the lines rotate in depth around a vertical axis. This is a rare kind of illusion: an ambiguous motion which can be seen as either stationary in two dimensions or rotating in three dimensions. Three-dimensional rotation was more often observed when the luminance difference between the horizontal lines and the background was larger than that between the aperture and the background. This illusion demonstrates that motion detection and the structure-from-motion process correlate with figure--ground segregation, depth stratification, and figural-completion processes based on luminance contrast.     

Straightness as the main factor of the hErmann grid illusion

The generally accepted explanation of the Hermann grid illusion is Baumgartner's hypothesis that the illusory effect is generated by the response of retinal ganglion cells with concentric ON-OFF or OFF-ON receptive fields. To challenge this explanation, we have introduced some simple distortions to the grid lines which make the illusion disappear totally, while all preconditions of Baumgartner's hypothesis remain unchanged. To analyse the behaviour of the new versions of the grid, we carried out psychophysical experiments, in which we measured the distortion tolerance: the level of distortion at which the illusion disappears at a given type of distortion for a given subject. Statistical analysis has shown that the distortion tolerance is independent of grid-line width within a wide range, and of the type of distortion, except when one side of each line remains straight. We conclude that the main cause of the Hermann grid illusion is the straightness of the edges of the grid lines, and we propose a theory which explains why the illusory spots occur in the original Hermann grid and why they disappear in curved grids.     

How configurations of binocular disparity determine whether stereoscopic slant or stereoscopic occlusion is seen

A partially occluded contour and a slanted contour may generate identical binocular horizontal disparities. We investigated conditions promoting an occlusion resolution indicated by an illusory contour in depth along the aligned ends of horizontally disparate line sets. For a set of identical oblique lines with a constant width added to one eye's view, strength, depth, and stability of the illusory contour were poor, whereas for oblique lines of alternating orientations the illusory contours were strong, indicating a reliance on vertical size disparities rather than vertical positional disparities in generating perceived occlusion. For horizontal lines, occlusion was seen when the lines were of different lengths and absolute width disparity was invariant across the set. In all line configurations, when the additional length was on the wrong eye to be attributed to differential occlusion, lines appeared slanted consistent with their individual horizontal disparities. This rules out monocular illusory contours as the determining factor.     

Perception of the standard and the reversed Müller-Lyer figures in pigeons (Columba livia) and humans (Homo sapiens)

The authors compared perception of the standard and reversed Müller-Lyer figures between pigeons (Columbia livia) and humans (Homo sapiens). In Experiment 1, pigeons learned to classify 6 lengths of target lines into "long" and "short" categories by pecking 2 keys on the monitor, ignoring the 2 brackets so placed that they would not induce an illusion. In the test that followed, all 3 birds chose the "long" key more frequently for the standard Müller-Lyer figures with inward-pointing brackets (><) than for the figures with outward-pointing brackets (<>). The subjects' responses were accountable by neither overall lengths of the figures nor horizontal gaps between the 2 brackets. For the reversed figures, effects of the brackets were absent. These results suggested that the pigeons perceived the standard Müller-Lyer illusion but not the reversed one. Experiment 2 confirmed that humans perceived both types of the illusion. Pigeons and humans may perceive the same illusory figures in different ways.     

Straight lines, 'uncurved lines', and Helmholtz's 'great circles on the celestial sphere'

Helmholtz's famous pincushioned chessboard figure has been used to make the point that straight lines in the world are not always perceived as straight and, conversely, that curved lines in the world can sometimes be seen as straight. However, there is little agreement as to the cause of these perceptual errors. Some authors have attributed the errors to the shape of the retina, or the amount of cortex devoted to the processing of images falling on different parts of the retina, while others have taken the effects to indicate that visual space itself is curved. Helmholtz himself claimed that the 'uncurved lines on the visual globe' corresponded to 'direction circles' defined as those arcs described by the line of fixation when the eye moves according to Listing's law. Careful re-reading of Helmholtz together with some additional observations lead us to the conclusion that two other factors are also involved in the effect: (i) a lack of information about the distance of peripherally viewed objects and (ii) the preference of the visual system for seeing the pincushion squares as similar in size.     

Connectedness underlies the underestimation of the horizontal vertical illusion in L-shaped configurations

L-shaped configuration is a commonly used stimulus configuration in studying horizontal vertical illusion. Here, we report that the horizontal vertical illusion is substantially underestimated when the L-shaped configuration is used for evaluating the illusion. Experiment 1 found that, in a length perception task, the perceived length of a vertical bar was about 10% longer than that of a horizontal bar with the same physical size. Similar amount of HVI was found in a length comparison task, in which the length of a horizontal bar was compared to that of a vertical bar and the two bars were presented separately in space or in time. In contrast, when the length comparison task was conducted with the two bars being arranged in a connected L-shape, the illusion was halved in strength. Experiment 2 and 3 studied what might be the cause of this L-shape induced HVI-underestimation. Two factors were investigated: the connectedness of the two lines, and the 45° absolute orientation or the 45° inner angle information embedded in the upright isosceles L-shape. The results showed that the HVI strength was not much affected when the 45° absolute orientation and the 45° angle information was made useless for the length comparison task. In contrast, the illusion was significantly reduced in strength whenever the two lines were separated as compared to when they were connected. These results suggested that the connectedness of the two lines must underlie the underestimation of the horizontal vertical illusion in the L-shaped configurations.     

Determinants of the Bourdon effect

The Bourdon illusion is the apparent inward bending of straight, collinear edges in a solid figure consisting of two elongated triangles meeting at their apexes. This effect was investigated in five experiments. In the first and third experiments, it was shown that the apparent bending is greatest when the apical angles are about 12 deg and the axis of the figure is oriented at about 22 deg from the vertical. The second experiment was a control involving visual acuity for angular departures of two lines from collinearity and served as a basis of selection for subjects in Experiments 3, 4, and 5. Experiments 4 and 5 showed that the illusion occurs strongly in a solid (“filled in”) figure but is notably smaller in outline figures of the same size and shape. It tends to be negative in outline figures with boundaries formed by continuous and broken lines. The relationship between the Bourdon illusion and the “negative” Zöllner illusion is considered.     

Haptically straight lines

In this research, we set out to investigate haptically perceived space. Large deviations with respect to physical space have already been shown to exist. Here, research on haptic space is continued by investigating straight lines constructed by touch. In four experiments, subjects were asked to produce straight lines between two reference markers that were in the horizontal plane at a fixed distance from each other. Each experiment corresponded to a different task: two different interpolation tasks, an intersection task, and a pointing task. Straight lines had an orientation that was approximately frontoparallel. Subjects used both hands; manipulation was unrestricted. Although we found considerable differences between observers, the overall pattern of results showed that haptically straight lines were generally curved away from the observer. However, in one of the interpolation tasks they corresponded to physically straight lines. In addition, the pointing task generally produced larger deviations than the other three tasks. Taken together, the results show that there is no unique definition of the straight line, a conclusion that questions the viability of the concept of haptic space.     

Perception of self-tilt in a true and illusory vertical plane

A tilted furnished room can induce strong visual reorientation illusions in stationary subjects. Supine subjects may perceive themselves upright when the room is tilted 90 degrees so that the visual polarity axis is kept aligned with the subject. This 'upright illusion' was used to induce roll tilt in a truly horizontal, but perceptually vertical, plane. A semistatic tilt profile was applied, in which the tilt angle gradually changed from 0 degrees to 90 degrees, and vice versa. This method produced larger illusory self-tilt than usually found with static tilt of a visual scene. Ten subjects indicated self-tilt by setting a tactile rod to perceived vertical. Six of them experienced the upright illusion and indicated illusory self-tilt with an average gain of about 0.5. This value is smaller than with true self-tilt (0.8), but comparable to the gain of visually induced self-tilt in erect subjects. Apparently, the contribution of nonvisual cues to gravity was independent of the subject's orientation to gravity itself. It therefore seems that the gain of visually induced self-tilt is smaller because of lacking, rather than conflicting, nonvisual cues. A vector analysis is used to discuss the results in terms of relative sensory weightings.     

Bantams (Gallus gallus domesticus) also perceive a reversed Zöllner illusion

Although pigeons have been shown to be susceptible to several size and length illusions, other avian species have not been tested intensively for illusory perception. Here we report how bantams perceive the Zöllner figure, in which parallel lines look nonparallel due to short crosshatches superimposed on the lines. Watanabe et al. (Cognition 119:137–141, 2011) showed that pigeons, like humans, perceived parallel lines as nonparallel but that the orientation of subjective convergence was opposite to that of humans. We trained three bantams to peck at the narrower (or wider) of the two gaps at the end of a pair of nonparallel lines. After adapting them to target lines with randomly oriented crosshatches (which result in no apparent illusion to humans), we tested the bantams’ responses on randomly inserted probe trials, in which crosshatches that should induce the standard Zöllner-like illusion for humans replaced the randomly oriented ones. The results suggested bantams, like pigeons, perceive a reversed Zöllner illusion.     

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.     

An illusion of movement complementary to the horizontal-vertical illusion

Blindfolded subjects moved a stylus held in the hand over a standard distance of 4.5 ins. in a given direction. They then attempted to move the same distance in a direction at right angles to the first. Eight combinations of movements were investigated. The results reveal an illusion such that the extent of movements to left or right across the body is underestimated, while the extent of movements towards or away from the body in the mid-line is overestimated. The illusion applies to speed as well as extent of movement. Movement up or down in a vertical plane is equivalent to movement towards or away from the body in a horizontal plane.

The interaction of this illusion with the well-known horizontal-vertical illusion of visual perception explains a failure to find any net illusory effect where lines visually displayed in different orientations were matched for length by unseen movements in similar orientations.

Whether the visual and movement illusions simply co-exist or whether they are functionally related is not yet clear.