Three elemental illusions determine the Zöllner illusion

We have discovered an apparent contraction illusion of acute angles in a special form of the Z?llner figure at the intersecting angles between 36 degrees and 83 degrees (i.e., a reversal of the Z?llner illusion). The necessary condition for this illusion is that inducing lines are long enough and the induced line (test line) is single. When an illusory line is used as the induced line, the magnitude of contraction increases. Short inducing lines give no illusion or a slight expansion of acute angles at the intersecting angle of 45 degrees. We have ascertained that the source of this expansion is the narrow region in the vicinity of the induced line, whereas the source of the contraction is much broader regions. Furthermore, we have discovered another expansion mechanism, which is generated by the symmetrical configuration of the standard Z?llner figure.     

Three elemental illusions determine theZöllner illusion

We have discovered an apparent contraction illusion of acute angles in a special form of the Zöllner figure at the intersecting angles between 36° and 83° (i.e., a reversal of the Zöllner illusion). The necessary condition for this illusion is that inducing lines are long enough and the induced Une (test line) is single. When an illusory line is usedas the induced line, the magnitude of contraction increases. Short inducing lines give no illusion or a slight expansion of acute angles at the intersecting angle of 45°. We have ascertained that the source of this expansion is the narrow region in the vicinity of the induced line, whereas the source of the contraction is much broader regions. Furthermore, we have discovered another expansion mechanism, which is generated by the symmetrical configuration of the standard Zöllner figure.     

The Sander illusion as a function of relative space and component lines

Magnitude of the Sander illusion was measured as a function of two variables: (1) the orientation of the line normally separating the two smaller parallelograms and (2) the presence or absence of the horizontal lines and of the diagonal test lines. The results showed that, as the angle of the dividing line varied so as to shift the relative sizes of the two parts of the figure toward equality, the illusion effect decreased, approaching zero when the two areas were equal. The illusory effect was enhanced by the removal of the two test lines. Results were discussed in relation to the problem of assimilation vs contrast effects.     

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.     

Depth separation and the Ponzo illusion

The Ponzo illusion refers to an apparent change in length of objectively equal parallel lines induced by enclosure within an acute angle. The present study investigated this illusory change in stimulus extent as a function of the relative depth positions of the parallel lines and the inducing angle. To permit facile and unconfounded manipulation of apparent depth, the stimuli comprising the Ponzo configuration were stereoscopic contours formed from dynamic random-element stereograms. The main results were: (1) apparent depth separation exerted a strong influence on illusion magnitude; (2) this influence was asymmetrical in that illusion magnitude decreased when the inducing angle appeared in depth behind the parallel lines and increased when the inducing angle appeared in depth in front of the lines. These data are consistent with a general theory of space perception that assumes that information about depth position is processed prior to information about stimulus characteristics.     

Brightness induction and the Café Wall illusion

The Café Wall illusion is a distortion illusion in which the parallel lines of a chessboard-like figure consisting solely of parallel and perpendicular line elements appear to converge in alternating rows, creating a wedge distortion similar to that of the well-known Z?llner illusion. Gregory and Heard have formulated an explanation for the Café Wall illusion which relies upon the operation of a 'border-locking mechanism' in the visual system. The results of the present experiment suggest an alternative explanation in which the operation of brightness induction within the mortar regions of the Café Wall produces a series of 'twisted cords' or slanted line elements akin to those of the Fraser or Z?llner figures. A series of such 'twisted cords' is shown to be capable of itself to produce an illusory convergence like that of the Café Wall. Manipulations of the luminance of discrete regions in the mortar lines of the Café Wall, designed either to augment or cancel the effects of brightness induction in the production of these slanted line elements, are successful in enhancing or reducing, respectively, the wedge distortion of this visual illusion.     

Illusory figures based on local kinematics.

A new type of motion-induced illusory figure determined by local kinematic information is investigated. The new figure is induced by radial line patterns subjected to either figure motion (the lines change as if they were stationary and a triangle was rotating in front of them) or background motion (the lines change as if they were being rotated behind a stationary triangle). Although the two kinds of motion are equivalent from the viewpoint of relative displacements, perceptually they yield very different results. With background motion, observers tend to perceive rigid figures that have a triangular shape. With figure motion, observers report seeing deforming figures with shapes that vary depending on the number of lines in the display. We consider two alternative accounts for this asymmetry which we term the background superiority effect (BSE). The first account proposes that the effect is due to retinal persistence and to figure stability. Against this line of explanation, we demonstrate that observers also see rigid triangular shapes in displays where both the figure and the radial lines rotate (double motion displays). The second account proposes that the effect depends on the availability of local kinematic information constraining contour orientation. This second line of explanation is consistent with observers' reports of bowed edges in double motion displays rotating in phase or in counterphase. Candidate mechanisms for extracting local kinematic information are discussed.     

Factors affecting perceived orientation of the Poggendorff transversal

The Poggendorff figure was simplified by removing the right transversal segment. When Ss judged the distance between a dot located on the right parallel and the imagined point where the left transversal, if extended, would intersect the right parallel, the error was independent of dot location. This result is consistent with the idea that the Poggendorff figure is processed asymmetrically by (mis)projecting one of the transversals across to the opposite parallel. Systematically omitting line segments reduced (and sometimes reversed) illusory effects. The most critical Poggendorff feature was the obtuse angle formed between transversal and parallel. Ss vertically adjusted one of two dots to apparent collinearity with an implied transversal, the tip of an intervening vertical line and the other (stationary) dot. Which dot was stationary proved critical. This primitive Poggendorff display generated no illusion unless the implied transversal, defined by the stationary dot, was the one that formed an obtuse angle with the vertical line. This result also strongly supports asymmetric active processing ideas. Perceived orientation is a property of directed line segments.     

The role of structural components in the Mueller-Lyer illusion

In order to assess the role of the structural components of the Mueller-Lyer illusion, subjects reproduced the central extent of standard Mueller-Lyer figures and configural variations. Illusory magnitude of the underestimated wings-in and overestimated wings-out figures was examined with selective amputations of the oblique wings and central line segment (shaft). Variations were presented at 0, 45, 90, and 135 deg from vertical. Orientation had no reliable effect on illusory magnitude. Elimination of the shaft effected a decrease in the apparent extent for all variations, presumably due to the addition of the filled-unfilled space illusory effect to the standard Mueller-Lyer effect. A second study corroborated this finding The decrease in apparent extent consequent to shaft removal occurred independently of any response factor. Selective wing removal differentially decreased the illusory magnitude of the standard Mueller-Lyer figures; this was discussed with regard to a dual-illusion hypothesis. Finally, variations that contained no intersecting lines produced a significant illusion in the direction of the standard Mueller-Lyer figures, suggesting the involvement of higher level, nonperipheral distortion mechanisms.     

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.     

A new explanation for the Poggendorff illusion

Kanizsa (1972, 1974) has observed that the surface upon which a figure is amodally completed undergoes shrinkage. That observation is investigated here as a possible explanation of the Poggendorff illusion, on the assumption that the shrinkage of the surface behind the surface defined by the two vertical parallel lines results in displacement of the two visible segments of the oblique line. The first two experiments attempted to quantify the shrinkage of the amodal surface by measuring the enlargement of the vertical strip required to achieve perceived collinearity; the oblique lines intercepted the vertical strip at 45- and 30-deg angles. In both cases, the enlargement required to counterbalance the assumed amodal shrinkage was approximately 30%. In the third experiment, the oblique line was rotated to the horizontal, and again the perceived shrinkage of the amodal surface was approximately 30%. The application of this explanation to the Poggendorff illusion is discussed, as well as the relevance of this explanation to the common experimental finding that magnitude of the illusion is dependent upon the slope of the oblique line.     

Can subthreshold summation be observed with the Ehrenstein illusion?

Subthreshold summation between physical target lines and illusory contours induced by edges such as those produced in the Kanizsa illusion has been reported in previous studies. Here, we investigated the ability of line-induced illusory contours, using Ehrenstein figures, to produce similar subthreshold summation. In the first experiment, three stimulus conditions were presented. The target line was superimposed on the illusory contour of a four-arm Ehrenstein figure, or the target was presented between two dots (which replaced the arms of the Ehrenstein figure), or the target was presented on an otherwise blank screen (control). Detection of the target line was significantly worse when presented on the illusory contour (on the Ehrenstein figure) than when presented between two dots. This result was consistent for both curved and straight target lines, as well as for a 100 ms presentation duration and unlimited presentation duration. Performance was worst in the control condition. The results for the three stimulus conditions were replicated in a second experiment in which an eight-arm Ehrenstein figure was used to produce a stronger and less ambiguous illusory contour. In the third experiment, the target was either superimposed on the illusory contour, or was located across the central gap (illusory surface) of the Ehrenstein figure, collinear with two arms of the figure. As in the first two experiments, the target was either presented on the Ehrenstein figure, or between dots, or on a blank screen. Detection was better in the dot condition than in the Ehrenstein condition, regardless of whether the target was presented on the illusory contour or collinear with the arms of the Ehrenstein figure. These three experiments demonstrate the ability of reduced spatial uncertainty to facilitate the detection of a target line, but do not provide any evidence for subthreshold summation between a physical target line and the illusory contours produced by an Ehrenstein figure. The incongruence of these results with previous findings on Kanizsa figures is discussed.     

Spatial factors of brightness illusion in the Ehrenstein figure

The strength of brightness illusion in an Ehrenstein figure has been examined as a function of two variables--inducing line length and gap size--by a two-alternative forced-choice procedure. The results show an interaction between the two variables; the length of the inducers and gap size are both involved in the formation of the brightness illusion, with gap size as the stronger factor. A spatial limit (corresponding to a gap size of 2.4 deg) was found, below which the illusion is always present regardless of the length of the inducers. An area ratio, defined as the ratio of the area of the ring formed by the four inducing lines of an Ehrenstein figure to the area of the illusory surface, takes into account the different spatial factors studied in the experiment and the global size of the Ehrenstein figure. The strength of the illusion was found to increase linearly with increasing values of the area ratio.     

A wave-line colour illusion

A new colour-spreading illusion is reported. Illusory colours appear on a white background when three unconnected sinusoidal curves are aligned in parallel when the central line is of a different colour than the other two lines. For some combinations of colours, illusory colours appear not only around the central line but also around the other lines.     

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.     

The Poggendorff illusion: Apparent misalignment which is not attributable to apparent orientation of the transversals

Subjects while looking down were required to adjust a horizontal field of parallel lines (Experiment I) or a single line (Experiment II) to the apparent sagittal direction with and without a superimposed rectangle in the centre of a circular field. The rectangle was tilted at 20, 30 or 40° to the parallels and at 20° to the line. For the 20° condition the parallel lines were apparently oriented at about half a degree compared with the field without a rectangle but in the direction opposite to that necessary to account for the Poggendorff misalignment effect. For the 30 and 40° conditions the lines did not change in apparent orientation. The orientation of the single line did not change. Almost all subjects readily reported an apparent misalignment between the collinear parallels and line separated by the oblique rectangle. It is concluded that the Poggendorff misalignment illusion occurs without apparent regression of the lines to right angles with the figure.     

Real and subjective contour Poggendorff illusions: no differences based on eye color

Measures of illusion magnitude for a real contour and two subjective contour Poggendorff figures were obtained from a large number of dark-eyed and light-eyed undergraduates. Illusion magnitude varied as a function of figure type. However, eye color neither had a significant overall effect on illusion magnitude, nor did it interact with the figure-type variable. These data indicate that the presence of intersecting lines is not the basis of the iris-pigmentation effect reported by Coren and Porac.     

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 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.     

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.