Anisotropic perception of visual angle: implications for the horizontal-vertical illusion, overconstancy of size, and the moon illusion.

Three experiments investigated anisotropic perception of visual angle outdoors. In Experiment 1, scales for vertical and horizontal visual angles ranging from 20 degrees to 80 degrees were constructed with the method of angle production (in which the subject reproduced a visual angle with a protractor) and the method of distance production (in which the subject produced a visual angle by adjusting viewing distance). In Experiment 2, scales for vertical and horizontal visual angles of 5 degrees-30 degrees were constructed with the method of angle production and were compared with scales for orientation in the frontal plane. In Experiment 3, vertical and horizontal visual angles of 3 degrees-80 degrees were judged with the method of verbal estimation. The main results of the experiments were as follows: (1) The obtained angles for visual angle are described by a quadratic equation, theta' = a + b theta + c theta 2 (where theta is the visual angle; theta', the obtained angle; a, b, and c, constants). (2) The linear coefficient b is larger than unity and is steeper for vertical direction than for horizontal direction. (3) The quadratic coefficient c is generally smaller than zero and is negatively larger for vertical direction than for horizontal direction. And (4) the obtained angle for visual angle is larger than that for orientation. From these results, it was possible to predict the horizontal-vertical illusion, over-constancy of size, and the moon illusion.     

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.     

Vertical-horizontal illusion: One eye is better than two

The vertical-horizontal illusion is the tendency for observers to overestimate the length of a vertical line relative to a horizontal line that has the same length. One explanation of this illusion is that the visual field is elongated in the horizontal direction, and that the vertical-horizontal illusion is a kind of framing effect (Künnapas, 1957a, 1957b, 1957c). Since the monocular visual field is less asymmetric than the combined visual field, this theory predicts that the illusion should be reduced with monocular presentation. This prediction was tested in five experiments, in which the vertical-horizontal illusion was examined in a variety of situations—including observers seated upright versus reclined 90°, monocular presentation with the dominant versus the nondominant eye, viewing in the dark versus in the light, and viewing with asymmetrical frames of reference. The illusion was reliably reduced with monocular presentation under conditions that affected the asymmetry of the phenomenal visual field.     

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.     

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.     

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°, 45°,90°, and 135° 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.     

Tendencies to eye movement,and misperception of curvature,direction, and length

From previous studies of eye movements, three types of eye-movement tendency can be inferred: (1) tendency to rectilinear eye movements, (2) tendency to horizontal or vertical eye movements, and (3) tendency to center-of-gravity fixations. The possible influence of these eye-movement tendencies on perception was investigated in two experiments. In Experiment 1, errors in perceived location of intersection in arc figures were studied varying arc-point distance and are length. Tendencies 1 and 2 accounted very well for the resultant S-shaped functions. In Experiment 2, the Müller-Lyer illusion with three different oblique angles and a line-segment illusion were measured as a function of the distance between the vertex and the center of gravity of the arrowhead. Tendency 3 accounted well for the inverted-U forms of the obtained functions but not for the increase of error with increasing angle.     

Vicario's illusion of sloping steps reexamined

If a few parallel horizontal rows of dots are set diagonally, like steps, across the visual field, the inner rows appear not to be horizontal but sloping up to one side; the effect holds as long as the vertical distances between the rows do not exceed a given visual angle. This illusion, described by Vicario in 1978, was never explained. An experiment is reported in which the illusion was still visible at row separations well in excess of the spatial limits originally considered, provided the stimulus elements were enlarged. The maximum illusion was obtained for length ratios (interrow distance to size of dots) identical to those which have been shown to produce the largest effects in a number of illusions of area and length. This suggests that Vicario's illusion is similar to other illusions of extent, and that it can be explained by a neural extent-coding model.     

Anomalous orientation effects in the Bourdon illusion

All current explanations of the Bourdon illusion imply that the illusion persists under mirror imaging over the vertical or horizontal axes. We tested this hypothesis in three experiments. For orientations of the standard Bourdon figure of about 135°, the illusion shows a dip, which is unexplainable in terms of current theories.     

Effects of visual-field inversions on the reverse-perspective illusion

The 'reverse-perspective' illusion entails the apparent motion of a stationary scene painted in relief and containing misleading depth cues. We have found that, using prism goggles to induce horizontal or vertical visual-field reversals, the illusory motion is greatly reduced or eliminated in the direction for which the goggles reverse the visual field. We argue that the illusion is a consequence of the observer's inability to reconcile changes in visual information due to body movement with implicit knowledge concerning anticipated changes. As such, the reverse-perspective illusion may prove to be useful in the study of the integration of linear perspective and motion parallax information.     

Spatial limits on the nonvisual self-touch illusion and the visual rubber hand illusion: Subjective experience of the illusion and proprioceptive drift

The nonvisual self-touch rubber hand paradigm elicits the compelling illusion that one is touching one’s own hand even though the two hands are not in contact. In four experiments, we investigated spatial limits of distance (15 cm, 30 cm, 45 cm, 60 cm) and alignment (0°, 90° anti-clockwise) on the nonvisual self-touch illusion and the well-known visual rubber hand illusion. Common procedures (synchronous and asynchronous stimulation administered for 60 s with the prosthetic hand at body midline) and common assessment methods were used. Subjective experience of the illusion was assessed by agreement ratings for statements on a questionnaire and time of illusion onset. The nonvisual self-touch illusion was diminished though never abolished by distance and alignment manipulations, whereas the visual rubber hand illusion was more robust against these manipulations. We assessed proprioceptive drift, and implications of a double dissociation between subjective experience of the illusion and proprioceptive drift are discussed.     

An analysis of illusion components with ⌞ and ⊥ - figures in active touch

The influence of radial movement in haptically explored ⌞ and ⊥-figures is investigated by tilting them from the frontoparallel to the horizontal plane. Inclining an upright ⌞-figure towards the horizontal plane leads to an illusion that increases with the degree of inclination (Experiment I). The same curve, only shifted upwards, is found with a ⊥-figure (Experiment II), indicating an additive bisection effect. A theoretical function relating illusion magnitude and angle of inclination is presented. The results confirm an interpretation of the illusion in terms of radial and tangential components of arm movements. The implications of these results are discussed in relation to theoretical explanations of the haptic and visual form of the horizontal-vertical illusion.     

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.     

The visuomotor system resists the horizontal-vertical illusion

The effect of the horizontal-vertical illusion on the visual and visuomotor systems was investigated. Participants (N = 8) viewed horizontal and vertical lines in an inverted-T stimulus and judged whether the two line segments were the same or different lengths. Participants also reached out and grasped either the vertical or the horizontal line segment of the stimulus. Perceptually, participants succumbed to the illusion; that is, they judged Ts of equal horizontal and vertical line lengths to be different and Ts of unequal line lengths to be the same. When reaching toward the same stimuli, however, the size of their grip aperture was scaled appropriately for the various line lengths. Thus, whereas the perceptual system succumbed to the illusion, the visuomotor system did not. Those results support a model proposed by M. A. Goodale and A. D. Milner (1992), who posited separate cortical pathways for visual perception and visually guided action.     

Left of centre: asymmetries for the horizontal vertical line illusion

This study explored the mechanisms that underlie asymmetries for the horizontal vertical illusion (HVI), which deceives length perception, so that a vertical line is perceived as longer than a horizontal line of equivalent length. In Experiment 1, university students (n = 14) made length judgements for vertical and horizontal lines. The vertical line was shifted in eight steps from the far left of the horizontal line (⌊) to the far right (⌋). An HVI was observed for the medial positions (⊥), which diminished towards the lateral positions. The HVI was also stronger when the vertical line was on the left. Because the left/right asymmetry changed as a function of lateral/medial position, the asymmetry within the HVI stimulus is most likely the result of pseudoneglect, which affects judgements of horizontal length. In Experiment 2, participants (n = 15) made judgements for HVI stimuli presented to the left- and right-hemispace and the midline. The HVI was stronger in the left hemispace. Because the asymmetry between the left- and right-hemispaces did not interact with the asymmetry within the stimuli, it was concluded that the asymmetry between hemispatial positions was the result of right hemisphere susceptibility to illusory geometrical effects whereas the asymmetry within the stimulus is related to an object-centred attentional asymmetry. The HVI is affected by asymmetries in length judgements and susceptibility to illusions and may provide interesting insights into attentional disorders in clinical populations, such as neglect.     

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.     

The spacing illusion: a spatial aperture problem?

A geometrical illusion in which the horizontal spacing between adjacent parallel lines in a row is underestimated when the lines are tilted away from vertical in a chevron configuration was investigated in two experiments. The perceived spacing was found to decrease as the tilt angle increased, consistent with the idea that separation judgements are influenced by the normal spacing between lines ie at right angles to the line orientation. It is proposed that this illusion reveals an analogue in spatial perception to the well-known aperture problem in motion perception. In establishing the separation of nearby or overlapping shapes in an image, the visual system cannot only rely upon the normal separation of contours belonging to each shape (as would be visible through small spatial apertures or receptive fields), since this varies with contour orientation. The system is therefore faced with a spatial aperture problem. The spacing illusion may arise because information usually available to solve the problem is absent in the illusion figure, or it may reflect a bias in favour of the orthogonal, which is adopted in the face of the ambiguity.     

Associative and categorical relations in the associative memory illusion

What kinds of associations underlie the associative memory illusion? In Experiment 1, lists composed of horizontal, or coordinate, free associates elicited false recognition of critical lures much more often than did lists composed of vertical, or subordinate, category instances. Experiment 2 replicated this result, and showed that the difference between free associates and category instances was not an artifact of differential levels of forward or backward associative strength. Associative structure plays an important role in the associative memory illusion: The illusion is strongest when the critical lure lies at the same level of categorization as the studied items.     

Effects of illusory stripes on the Helmholtz illusion

This study examined the Helmholtz illusion by using "illusory stripes." A square patch is perceived as wider when vertical lines are drawn on it and is perceived as taller when horizontal lines are drawn on it, i.e., Helmholtz illusion. With vertical lines curved sinusoidally, horizontal "illusory stripes" are perceived; and with horizontal lines curved sinusoidally, vertical "illusory stripes" are perceived. The purpose of the present study was to test whether the "illusory stripes" produce the Helmholtz illusion. We measured the apparent size of a square patch filled with sinusoidal lines. Our subjects (N=27) judged the patch with horizontal "illusory stripes" taller than the square patch filled with vertical straight lines. The subjects also judged the square patch with vertical "illusory stripes" wider than the square patch filled with horizontal straight lines. These results demonstrate that "illusory stripes" can produce the Helmholtz illusion.