Variation of the magnitude of the horizontal-vertical illusion with retinal eccentricity

The horizontal-vertical illusion was studied as a function of retinal eccentricity. It was found that the relation of illusion magnitude to vertical eccentricity is described by a U-shaped function with large amounts of reversed illusion for the more eccentric positions. Substantial effects due to horizontal eccentricity were also obtained, but these were not consistent across subjects. It is suggested that the flattening of the peripheral zones of the refracting surfaces of the eye may be involved in the variation of the illusion with retinal position, and that the astigmatic properties of the central portions of these surfaces may be a prime factor in the usual horizontal-vertical illusion.     

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.     

The influence of figure size and orientation on the magnitude of the horizontal-vertical illusion

Two experiments were performed to examine the effect of display size and figure orientation on the horizontal-vertical illusion. According to the visual field hypothesis of Künnapas (1957a, 1957b) if the relation of the figure components to the surrounding frame is held invariant neither experimental manipulation should exert an appreciable influence. However, both manipulations produced significant effects indicating that the visual field hypothesis is untenable as the primary determinant of the horizontal-vertical illusion. An alternative explanation was discussed.     

Errors of the standard in the horizontal-vertical illusion

Three experiments were conducted to test the claim that the magnitude of the horizontal-vertical illusion in an L figure varies as a function of which component is used as standard. No difference was found in Experiment 1, in which a staircase procedure was used to establish the PSE. However, by the use of a method of adjustment, the magnitude of illusion was affected by the component used as standard in Experiment 2. The results of Experiment 3, in which a staircase procedure was used with S in upright and recumbent body postures, confirmed those of Experiment 1. It was concluded that earlier differences associated with the standard were a methodological accompaniment of the psychophysical technique used.     

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.     

An illusion of eccentricity

The illusion investigated here is that two concentric arcs, drawn in different (though possibly overlapping) circular sectors and having the same angular extent, appear to be eccentric. Three possible explanations of the illusion are tested. The first hypothesis is that concentricity judgments are made by elongating the arcs to see if they intersect, the illusion being due to the tendency, when elongating a curve, to follow the end-tangent. The second hypothesis is that concentricity judgments are based on a test of coincidence of centers, the illusion being due to the overestimation of the radius of short arcs. The third hypothesis is that both of these factors contribute in equal measure. These hypotheses make different predictions about the effect (on the magnitude of the illusion) of the following variables: (1) the angular distance between the arcs; (2) the radial distance between the arcs; (3) the degree of curvature of the arcs; and (4) the angular extent of the arcs. The observed values of the illusion angle (obtained by the method of limits) in relation to these variables did not uniformly support any of the hypotheses. A more complex model that is consistent with the observed results is therefore proposed.     

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 effect of retinal location on the magnitude of the Poggendorff illusion

The effect of retinal locus on the magnitude of the Poggendorff illusion was investigated. A significant illusion was found to occur in the fovea and in undiminished magnitude at the peripheral locations horizontally displaced from the fovea. No significant illusion was induced at the vertically displaced positions. It is suggested that the results obtained at the positions displaced from the fovea may be attributable to the refracting surfaces of the cornea, and that these findings lend support to an account of the Poggendorff illusion which emphasizes the significant involvement of peripheral mechanisms.     

Handgrip maximum force and the visual horizontal-vertical illusion

The visual horizontal-vertical illusion (HVI) refers to the tendency to overestimate vertical distances relative to horizontals in both 2-D and 3-D presentations. Although the HVI is evident across a wide range of different stimuli, no general theoretical account fully explains the illusion. Some recent authors have proposed the 'effort' account of HVI, contending that vertical overestimation is mediated by effort assessment of gravitational challenges offered by the stimulus. The theory has been supported by a set of studies showing that the height overestimation of large-scale 3-D objects is inversely related to perceivers' fitness and strength. We explored if the large-scale HVI/strength dependence extends to the evaluation of small-scale 2-D line stimuli, traditionally used in HVI studies. We measured the maximum handgrip strength, and assessed the HVI with a computerised line-adjustment task in thirty-two individuals. Compatible with earlier findings in the context of large-scale 3-D stimuli, a significant negative correlation was found between the strength of the dominant hand and amount of HVI. In addition, the variability of HVI was negatively correlated with maximum grip strength of both hands. The results are discussed with reference to the 'effort' account of HVI.     

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.     

An investigation of several parameters of the horizontal-vertical illusion

Length of standard line, degrees of lateral separation of H and V stimuli, and which line served as standard or comparison stimulus were systematically varied in a 4 by 3 by 2 factorial design on the horizontal-vertical illusion. When illusion affects were averaged under H- and V-standard conditions, a negative relationship obtained between magnitude of illusion and length of line. With. vertical as standard, the illusion increased as a function of lateral separation of stimuli, but decreased with horizontal as standard. These differential trends for H- and V-standard conditions contributed to the unsystematic relationship between the size of the illusion and progressive displacement of H and V lines. The illusion curves for three lengths of standard line across degrees of lateral separation were similar. The findings are viewed as incompatible with explanations of the H-V illusion involving the so-called “error of the standard.”     

Analysis of individual variations in the classical horizontal-vertical illusion

In the horizontal-vertical illusion (HVI), the length of the vertical line is overestimated, whereas in the bisection illusion (BI), the horizontal bisecting line is expected to be overestimated. Here, only half of our 22 observers showed the expected BI, whereas the other half underestimated the bisecting line. Observers also differed in their judgments of the strength of the HVI: The HVI was stronger for observers showing the classical bisection effect, and weaker or absent for those underestimating the bisecting line. To account for these results, we used a linear model to individually estimate the strength of two putative factors underlying both illusions. Whereas the strength of the HVI and BI were highly correlated, the estimated factors were uncorrelated. Therefore, in two control experiments, we then measured the pure horizontal-vertical (pHVI) and bisection (pBI) illusions. A significant correlation between the estimated factors and the measured illusion variants was found. Results were robust against variations of contrast, repetitive presentations, and choice of adjusted line. Thus, the classical HVI as an additive combination of two independent factors was confirmed, but we found considerable interindividual variations in the strength of the illusions. The results stress the importance of analyzing individual data rather than taking sample means for understanding these illusions.     

Effect of the standard on size of the horizontal-vertical illusion

70 subjects participated in a study designed to replicate the 1968 claim of Gardner and Long that the horizontal-vertical illusion is larger with the vertical than with the horizontal as standard. The effect did not appear in Exp. 1 when subjects made judgments under both the reproduction and graded-series methods but did in a pilot study and in Exp. 2, although more strongly with the method of reproduction.     

Stimulus configuration and line orientation in the horizontal-vertical illusion

The method of average error was used with a mixed design to measure the horizontal-vertical illusion (HVI) for 40 Ss. Six stimulus configurations (?, ?,?, ?, ⊥, +) were combined with seven angular orientations of the upright standard, and on each trial the variable horizontal was adjusted to appear equal to the standard in length. Results showed that for no stimulus configuration did the vertical orientation of the standard yield the greatest illusion. The magnitude of the HVI was dependent upon the stimulus configuration, upon the orientation of the standard, and upon an interaction between these variables. For the ⊥ and +, equal inclinations of the standard to either side of the vertical yielded equal effects; for the other figures, asymmetrical effects were produced. The results are discussed in relation to the perspective theory of visual illusions.     

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.     

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° to 80° 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°–30° 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°-80° 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, θ′=a+bθ+cθ² (where θ is the visual angle; θ′, the obtained angle;a, b, andc, constants). (2) The linear coefficientb is larger than unity and is steeper for vertical direction than for horizontal direction. (3) The quadratic coefficientc 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.