The horizontal-vertical illusion in photographs of concrete scenes with and without depth information

On the basis of the hypothesis of misapplied constancy scaling, the perception of an abstract horizontal-vertical illusion figure embedded in photographs of natural scenes with depth cues is investigated. The effect is compared with that of a figure on photographs containing no depth information and with a figure on a neutral surface. It is shown that the magnitude of the illusion in the perspective scenes is greater than in the other two conditions. The results are considered compatible with a constancy theory of the illusion. Finally, the evidence for misapplied constancy scaling in the horizontal-vertical illusion in relation to a retinal theory is discussed.     

Retinal projection or size constancy as determinants of the horizontal-vertical illusion?

To compare the influence of the projected retinal size and of the figure size on the perception of the horizontal-vertical illusion, the target size, the viewing distance, and the slant of an illusion figure were varied. In the first experiment the illusion produced by two figures of the same object size but of different retinal size was compared with that of two figures projecting the same retinal size but differing in object size. The illusion diminished when the size of the retinal projection was increased, whereas a change in figure size did not change the illusion. In Exp. II the illusion figure was tilted backwards which reduced the retinal projection of the 'vertical' figure limb. The illusion decreased and became negative as a function of the retinal projection, but this decrease was relatively small compared with the reduction of the retinal image. The results are interpreted as supporting a retinal origin as an explanation of the illusion. Although there is strong evidence for size-constancy scaling in a tilted figure, constancy scaling is considered of minor importance as a determinant of the usual illusion.     

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.     

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.     

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 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.     

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.     

Horizontal-vertical illusion: continuous decrement or the deviant first guess?

Numerous studies have reported that repetitive or extensive inspection leads to short-term decrement of the horizontal-vertical illusion. The present experiment explored whether this decrement reflects a gradual decline, as previously assumed, or is better described as a singular drop-off beyond the initial evaluation. 111 student participants adjusted vertical or horizontal lines such that they appeared equally long with a perpendicular standard. There were 8 successive adjustment trials for each subject. The results suggest that a substantial component of the illusion depends on the first impression assessment. The earlier anatomical and cognitive theories of the horizontal-vertical illusion cannot incorporate this datum. However, recent findings suggest that a motor theory of illusion might accommodate the observed one-step decrement in the illusion.     

Attenuating the haptic horizontal—vertical curvature illusion

In a number of experiments, blindfolded subjects traced convex curves whose verticals were equal to their horizontal extent at the base. Overestimation of verticals, as compared with horizontals, was found, indicating the presence of a horizontal-vertical illusion with haptic curves, as well as with visible curves. Experiment 1 showed that the illusion occurred with stimuli in the frontal plane and with stimuli that were flat on the table surface in vision and touch. In the second experiment, the stimuli were rotated, and differences between vision and touch were revealed, with a stronger illusion in touch. The haptic horizontal-vertical illusion was virtually eliminated when the stimuli were bimanually touched using free exploration at the body midline, but a strong illusion was obtained when curves were felt with two index fingers or with a single hand at the midline. Bimanual exploration eliminated the illusion for smaller 2.5- through 10.2-cm stimuli, but a weakened illusion remained for the largest 12.7-cm patterns. The illusion was present when the stimuli were bimanually explored in the left and right hemispace. Thus, the benefits of bimanual exploration derived from the use of the two hands at the body midline combined with free exploration, rather than from bimanual free exploration per se. The results indicate the importance of haptic exploration at the body midline, where the body can serve as a familiar reference metric for size judgments. Alternative interpretations of the results are discussed, including the impact of movement-based heuristics as a causal factor for the illusion. It was suggested that tracing the curve’s peak served to bisect the curve in haptics, because of the change in direction.     

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.     

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.     

Mechanisms in the haptic horizontal-vertical illusion: Evidence from sighted and blind subjects

The haptic horizontal-vertical illusion was studied in two experiments. In Experiment 1, the illusion was relatively weak in sighted subjects and depended on stimulus size and the nature of the figure, that is, whether the pattern was an inverted-T or L shape. Experiment 2 compared early blind and late blind subjects. The illusion was present for an inverted-T figure but absent for an L figure in late blind subjects. However, the early blind subjects treated both the L and T figures as similar and showed the illusion to both. These results support the idea that visual experience may alter haptic judgments in sighted and late blind subjects.     

The role of figure orientation and apparent depth in the perception of the horizontal-vertical illusion.

An experiment was performed which examined the role of figural orientation directly, and the role of an inappropriately invoked size-constancy mechanism indirectly, in the actuation and magnitude of the horizontal-vertical illusion. When the vertical line of the stimulus figure was aligned above the horizontal line, the illusory effect was significant and positive; in contrast, when the vertical line was located below the horizontal line, the illusion was negative. Under the assumption that a vertical line can appear as a foreshortened line in depth, these findings support an explanation based on the operation of a misapplied size-constancy mechanism.     

Three-dimensional Müller-Lyer illusion

Three-dimensional (3-D) variants of the Müller-Lyer pattern were created to address the question of where along the path of information flow in the visual system the illusion might occur. These variants, which yielded a robust illusion, included dihedral angles in place of the arrowheads of the classical pattern. The enormous difference in the shape of the resulting retinal image, compared with that of the classical pattern, makes it difficult to explain the present illusion by resorting to image-processing theories such as selective filtering (Ginsburg, 1984, 1986) or depth processing (Gregory, 1963, 1966, 1968). It was also shown that this 3-D illusion is homologous with the classical illusion, and that the two may thus share a common causal mechanism. A new type of 3-D figure, which yielded the same retinal image as did the classical pattern, was then employed. However, since the figure was 3-D, its shape in spatial coordinates was very different compared to that of the classical pattern. The magnitude of the illusion obtained with this figure was half that of the classical pattern. This finding suggests that the illusion might be caused by processes that occur after the computation of depth. All three experiments indicated that the illusion may be produced later in the processing stream than has previously been suggested.     

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.     

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.     

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.     

The discrimination of heading from optic flow is not retinally invariant.

Three experiments were conducted to determine whether the discrimination of heading from optic flow is retinally invariant and to determine the importance of acuity in accounting for heading eccentricity effects. In the first experiment, observers were presented with radial flow fields simulating forward translation through a three-dimensional volume of dots. The flow fields subtended 10 degrees of visual angle and were presented at 0 degree, 10 degrees, 20 degrees, and 40 degrees of retinal eccentricity. The observers were asked to indicate whether the simulated movement was to the right or the left of a target that appeared at the end of the display sequence. Eye movements were monitored with an electrooculogram apparatus. In a second experiment, static acuity thresholds were derived for each of the observers at the same retinal eccentricities. There was a significant increase in heading detection thresholds with retinal eccentricity (from 0.92 degree at 0 degree retinal eccentricity to 3.47 degrees at 40 degrees). An analysis of covariance indicated that the variation in sensitivity to radial flow, as a function of retinal eccentricity, is independent of acuity. Similar results were obtained when the Vernier acuity of observers was measured. These results suggest that the discrimination of heading from radial flow is not retinally invariant.     

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.