Integration biases in the Ouchi and other visual illusions

A texture pattern devised by the Japanese artist H Ouchi has attracted wide attention because of the striking appearance of relative motion it evokes. The illusion has been the subject of several recent empirical studies. A new account is presented, along with a simple experimental test, that attributes the illusion to a bias in the way that local motion signals generated at different locations on each element are combined to code element motion. The account is generalised to two spatial illusions, the Judd illusion and the Z?llner illusion (previously considered unrelated to the Ouchi illusion). The notion of integration bias is consistent with recent Bayesian approaches to visual coding, according to which the weight attached to each signal reflects its reliability and likelihood.     

New illusions of sliding motion in depth

Apparent sliding motion in the so-called Ouchi illusion has been attributed to the global integration of local motion vectors arising from the aperture effect (Fermüller et al, 2000 Vision Research 40 77- 96; Mather, 2000 Perception 29 721-727). In a number of variants of the Ouchi illusion, we here demonstrate that sliding motion will also arise without a directional motion bias from local elements. Specifically, we show that in a disk-annulus pattern made from wiggly lines, sliding motion occurs although the local orientations within the disk and annulus are the same. We then argue that in an array of square-shaped checks, sliding motion originates from the interaction between the explicit orientation of the checks and the implicit orientation of the invisible diagonals. Finally, we demonstrate that a central array of filled black circles surrounded by a grey edge appears to slide relative to a surround of empty circles. We tentatively account for sliding motion in this figure by differences in speed signals, figure-ground segregation and apparent depth due to contrast polarity, edge blur, demarcation by a frame, and difference in shape.     

Spatial-frequency-contingent color aftereffects: Adaptation with two-dimensional stimulus patterns

The spatial-frequency theory of vision has been supported by adaptation studies using checkerboards in which contingent color aftereffects (CAEs) were produced at fundamental frequencies oriented at 45\dg to the edges. A replication of this study failed to produce CAEs at the orientation of either the edges or the fundamentals. Using a computer-generated display, no CAEs were produced by adaptation of a square or an oblique checkerboard. But when one type of checkerboard (4 cpd) was adapted alone, CAEs were produced on the adapted checkerboard and on sine-wave gratings aligned with the fundamental and third harmonics of the checkerboard spectrum. Adaptation of a coarser checkerboard (0.80 cpd) produced CAEs aligned with both the edges and the harmonic frequencies. With checkerboards of both frequencies, CAEs were also found on the other type of checkerboard that had not been adapted. This observation raises problems for any edge-detector theory of vision, because there was no adaptation to edges. It was concluded that spatial-frequency mechanisms are operating at both low- and high-spatial frequencies and that an edge mechanism is operative at lower frequencies. The implications of these results are assessed for other theories of spatial vision.     

Spatial-frequency-contingent color aftereffects: adaptation with two-dimensional stimulus patterns.

The spatial-frequency theory of vision has been supported by adaptation studies using checkerboards in which contingent color aftereffects (CAEs) were produced at fundamental frequencies oriented at 45 degrees to the edges. A replication of this study failed to produce CAEs at the orientation of either the edges or the fundamentals. Using a computer-generated display, no CAEs were produced by adaptation of a square or an oblique checkerboard. But when one type of checkerboard (4 cpd) was adapted alone, CAEs were produced on the adapted checkerboard and on sine-wave gratings aligned with the fundamental and third harmonics of the checkerboard spectrum. Adaptation of a coarser checkerboard (0.80 cpd) produced CAEs aligned with both the edges and the harmonic frequencies. With checkerboards of both frequencies, CAEs were also found on the other type of checkerboard that had not been adapted. This observation raises problems for any edge-detector theory of vision, because there was no adaptation to edges. It was concluded that spatial-frequency mechanisms are operating at both low- and high-spatial frequencies and that an edge mechanism is operative at lower frequencies. The implications of these results are assessed for other theories of spatial vision.     

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.     

Amplitude spectra of line-motion stimuli

The line-motion illusion has been regarded as the result of attention. An alternative interpretation is that the illusion is related to apparent motion which would predict the stimuli to contain motion energy associated with the direction of the illusory motion. In order to examine this possibility Fourier transforms of x-t plots of line-motion stimuli were generated under a variety of conditions. The sums of amplitudes associated with movement in the directions away from the cue relative to that towards the cue were compared to previously published psychophysical observations. It was found that the amplitude sums are largely consistent with the psychophysical results. In the few cases where there were discrepancies between results based on amplitude spectra and psychophysical findings, these discrepancies could be accounted for by making relatively simple and plausible assumptions. The present observations suggest that motion energy may be sufficient to account for the line-motion illusion.     

Effects of spatial filtering and lack of effects of visual imagery on pattern-contingent color aftereffects

Checkerboards contain fundamental two-dimensional Fourier components oriented 45° from the edges of individual checks. Previous studies have shown that contingent color aftereffects following adaptation to chromatic checkerboard stimuli were associated with the fundamental components rather than the edges, In the present experiments, we measured contingent color aftereffects, using the method of constant stimuli, after subjects adapted to unfiltered checkerboards and checkerboards with the fundamental Fourier components removed. The adaptation stimuli were magenta (or green) squares and green (or magenta) diamonds; the test stimuli were vertical or oblique sine-wave gratings with different saturations, After adaptation to unfiltered checkerboards, aftereffects contingent on the fundamental components were obtained. In contrast, after adaptation to filtered stimuli, aftereffects of smaller magnitude were found to be aligned with the edges. The data support the previous findings of spatial-frequency-contingent color after-effects with checkerboard adaptation stimuli and indicate that the aftereffects can be associated with edges if the fundamental components of adaptation stimuli are removed by spatial filtering. We reexamined the possibility of color aftereffects induced by imagery of checkerboards. Contrary to the previous reports, no significant aftereffects were obtained.     

The relationship between perceived length and egocentric location in Müller-Lyer figures with one versus two chevrons

We examined the apparent dissociation of perceived length and perceived position with respect to the Müller-Lyer (M-L) illusion. With the traditional (two-chevron) figure, participants made accurate open-loop pointing responses at the endpoints of the shaft, despite the presence of a strong length illusion. This apparently non-Euclidean outcome replicated that of Mack, Heuer, Villardi, and Chambers (1985) and Gillam and Chambers (1985) and contradicts any theory of the M-L illusion in which mislocalization of shaft endpoints plays a role. However, when one of the chevrons was removed, a constant pointing error occurred in the predicted direction, as well as a strong length illusion. Thus, with one-chevron stimuli, perceived length and location were no longer completely dissociated. We speculated that the presence of two opposing chevrons suppresses the mislocalizing effects of a single chevron, especially for figures with relatively short shafts.     

Motion versus position in the perception of head-centred movement

Abstract. Observers can recover motion with respect to the head during an eye movement by comparing signals encoding retinal motion and the velocity of pursuit. Evidently there is a mismatch between these signals because perceived head-centred motion is not always veridical. One example is the Filehne illusion, in which a stationary object appears to move in the opposite direction to pursuit. Like the motion aftereffect, the phenomenal experience of the Filehne illusion is one in which the stimulus moves but does not seem to go anywhere. This raises problems when measuring the illusion by motion nulling because the more traditional technique confounds perceived motion with changes in perceived position. We devised a new nulling technique using global-motion stimuli that degraded familiar position cues but preserved cues to motion. Stimuli consisted of random-dot patterns comprising signal and noise dots that moved at the same retinal 'base' speed. Noise moved in random directions. In an eye-stationary speed-matching experiment we found noise slowed perceived retinal speed as 'coherence strength' (ie percentage of signal) was reduced. The effect occurred over the two-octave range of base speeds studied and well above direction threshold. When the same stimuli were combined with pursuit, observers were able to null the Filehne illusion by adjusting coherence. A power law relating coherence to retinal base speed fit the data well with a negative exponent. Eye-movement recordings showed that pursuit was quite accurate. We then tested the hypothesis that the stimuli found at the null-points appeared to move at the same retinal speed. Two observers supported the hypothesis, a third partially, and a fourth showed a small linear trend. In addition, the retinal speed found by the traditional Filehne technique was similar to the matches obtained with the global-motion stimuli. The results provide support for the idea that speed is the critical cue in head-centred motion perception.     

Halt and recovery of illusory motion perception from peripherally viewed static images

We quantitatively investigated the halt and recovery of illusory motion perception in static images. With steady fixation, participants viewed images causing four different motion illusions. The results showed that the time courses of the Fraser-Wilcox illusion and the modified Fraser-Wilcox illusion (i.e., "Rotating Snakes") were very similar, while the Ouchi and Enigma illusions showed quite a different trend. When participants viewed images causing the Fraser-Wilcox illusion and the modified Fraser-Wilcox illusion, they typically experienced disappearance of the illusory motion within several seconds. After a variable interstimulus interval (ISI), the images were presented again in the same retinal position. The magnitude of the illusory motion from the second image presentation increased as the ISI became longer. This suggests that the same adaptation process either directly causes or attenuates both the Fraser-Wilcox illusion and the modified Fraser-Wilcox illusion.     

Amplitude and phase in the Müller-Lyer illusion

It has previously been claimed that the Müller-Lyer illusion is the result of low-pass spatial filtering. One way to understand this would be that the distribution of amplitudes is what generates this illusion. This possibility was investigated by computing the 2-D Fourier transforms of the two Müller-Lyer stimuli and extracting their phase and amplitude spectra. These spectra were combined to create hybrid spectra having the phase of one Müller-Lyer figure and the amplitudes of the other. Images were then created by computing the inverse Fourier transform of the hybrid spectra. Except in cases where the analysis was performed patchwise on very small patches, the figures generated with the phase spectrum of the stimuli having outward-pointing fins appear the longer. This was also the case when stimuli were generated with flat amplitude spectra. Because they show that the Müller-Lyer illusion does not depend on any particular distribution of amplitudes, these demonstrations do not support the theory that the Müller-Lyer illusion is the result of low-frequency filtering.     

Relative spatial expansion and contraction within the Müller-Lyer and Judd illusions

The shaft portions of Müller-Lyer (M-L) figures, one-ended M-L figures, Judd figures, and their respective control (tails-up) figures were divided by subjects into eight equal-appearing intervals by means of successive bisections. For most of the control stimuli the length of the left half of the shaft tended to be overestimated relative to the length of the right side. For the tails-out version of the M-L figure, there was relative overestimation of segments of the shaft adjacent to the tails, while for the tails-in version there was relative underestimation of these segments. These results indicate that the distortion of perceived length in the M-L illusion is not distributed evenly along the shaft. For the one-ended M-L figures the apparent overestimations and underestimations extended further along the shaft than for the standard figures. For the Judd figure perceived length varied systematically along the length of the shaft from underestimation near the tails-in end of the figure to overestimation near the tails-out end. These results are contradictory to the hypothesis that the M-L illusion results from inappropriate size scaling produced through the operation of size-constancy mechanisms, since this conjecture would predict uniform expansion or contraction. The results are compared with findings that localization responses are accurate for M-L figures but biased for one-ended M-L figures and Judd figures.     

Detection of counter-changing contrast: second-order apparent motion without postrectification motion-energy analysis or salience mapping/feature tracking

The perception of 2nd-order, texture-contrast-defined motion was studied for apparent-motion stimuli composed of a pair of spatially displaced, simultaneously visible checkerboards. It was found that background-relative, counter-changing contrast provided the informational basis for the perception of 2nd-order apparent motion; motion began where contrast changed toward the contrast value of the background checkerboard and ended where contrast changed away from the background value. The perceived apparent motion was not attributable to either postrectification motion-energy analysis or salience-mapping/feature-tracking mechanisms. Parallel results for 1st-order, luminance-defined motion (H. S. Hock, L. A. Gilroy, & G. Harnett, 2002) suggest that counter-changing activation provides a common basis for the perception of both luminance- and texture-contrast-defined apparent motion.     

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.     

Apparent rotation and jazzing in Leviant's Enigma illusion

In 1981 Leviant devised Enigma, a figure that elicits perceived rotary motion in the absence of real motion. However, despite its striking appearance there is no good explanation for this motion illusion to date. Gregory (1993 Proceedings of the Royal Society of London B 253 123) pointed out a similarity to MacKay's 'complementary' afterimage in his ray pattern and suggested accommodative fluctuations and small eye movements as a potential origin for these phenomena. Furthermore, Zeki et al (1993 Proceedings of the Royal Society of London B 252 215-222) found PET-activation in response to Enigma in visual area V5 and immediately surrounding areas (called V5 complex) suggesting that the illusory motion could be mediated by the same neurons as real motion. In the experiments reported here, I show that the rotary motion is perceived on coloured as well as achromatic annuli intercepting the radial lines. More importantly, the illusory streaming motion continues to be seen with a cycloplegic lens as well as through a pinhole (ie ruling out transient changes of accommodation), and in the positive after-image (ie in the absence of eye movements). Apparent rotation is strongest with radial inducers impinging at right angles onto the annuli, but persist, although to a lesser degree, when the inducing lines are tilted in opposite directions, non-collinear, or replaced by dotted lines or lines with rounded terminators. For an explanation, the Enigma illusion requires a neural mechanism that uses lines abutting an empty annulus to elicit orthogonal streaming motion in one or the other direction.     

The fluttering-heart illusion: a new hypothesis

The fluttering-heart illusion is a perceived lagging behind of a colour target on a background of a different colour when the two are oscillated together. It has been proposed that the illusion is caused by a differential in the perceptual latencies of different colours (Helmholtz 1867/1962), a differential in rod-cone latencies (von Kries 1896) and rod-cone interactions (von Grünau 1975, 1976 Vision Research 15 431-436, 437-440; 16 397-401; see list of references there). The purpose of this experiment was to assess the hypothesis that the fluttering-heart illusion is caused by a differential in the perceived velocities of chromatic and achromatic motion. To evaluate this hypothesis, we tested observers possessing normal colour vision and deuteranopes. The perceived delay of a chromatic target relative to an achromatic target was measured as a function of background cone contrast and target colour. For observers with normal colour vision, the perceived delay of the chromatic target is greater in the L-S than the L-M testing conditions. The reverse is observed in deuteranope observers. We suggest that this is caused by the absence of an L-M opponent mechanism contributing to chromatic motion in deuteranopes. Greater background cone contrasts tended to yield smaller perceived delays in both normal and deuteranope observers, indicating that greater chromatic modulation decreases the perceived delay of the colour target. These results support the hypothesis that the fluttering-heart illusion can be explained by a differential in the perceived velocities of chromatic and achromatic motion.     

Correspondence matching in long-range apparent motion precedes featural analysis

It has been suggested that correspondence matching in long-range motion is mediated by a perceptually high-level, 'intelligent' system. This suggestion is based on findings that long-range motion can be perceived between stimuli that could not be detected by lower-level motion mechanisms acting on Fourier motion energy, and that correspondence matching is affected by featural similarities between motion tokens that would be invisible to low-level (Fourier) motion detectors. Here, the effects of spatial-frequency content, color, and binocular disparity on correspondence matching are investigated. It is shown that the effects of featural matches between motion tokens develop only over time and lag behind the effects of the relative proximity between motion tokens in the retinal projection. This suggests that correspondence matching in long-range apparent motion is mediated by a mechanism which acts initially on the retinal coordinates of the motion tokens only, but may be biased to favor matching tokens that are featurally similar through a slower top-down influence by higher-level processes.     

Illusory temporal order for stimuli at different depth positions

We used four experiments to examine how the perceived temporal order of two visual stimuli depends on the depth position of the stimuli specified by a binocular disparity cue. When two stimuli were presented simultaneously at different depth positions in front of or around a fixation point, the observer perceived the more distant stimulus before the nearer stimulus (Experiments 1 and 2). This illusory temporal order was found only for sudden stimulus presentation (Experiment 3). These results suggest that a common processing, which is triggered by sudden luminance change, underlies this illusion. The strength of the illusion increased with the disparity gradient and the disparity size (Experiment 4). We propose that this illusion has a basis in the processing of motion in depth, which would alert the observer to a potential collision with an object that suddenly emerges in front of the observer.     

The directional tuning of the barber-pole illusion.

In order to study the integration of local motion signals in the human visual system, we measured directional tuning curves for the barber-pole illusion by varying two crucial aspects of the stimulus layout independently across a wide a range in the same experiment. These were the orientation of the grating presented behind the rectangular aperture and the aspect ratio of the aperture, which in combination determine the relative contributions of local motion signals perpendicular to the gratings and parallel to the aperture borders, respectively. The strength of the illusion, ie the tendency to perceive motion along the major axis of the aperture, obviously depends on the spatial layout of the aperture, but also on grating orientation. Subjects were asked which direction they perceived and how compelling their motion percept was, revealing different strategies of the visual system to deal with the barber-pole stimulus. Some individuals respond strongly to the unambiguous motion information at the boundaries, leading to multistable percepts and multimodal distributions of responses. Others tend to report intermediate directions, apparently being less influenced by the actual boundaries. The general pattern of deviations from the motion direction perpendicular to grating orientation--a decrease with aspect ratio approaching unity (ie square-shaped apertures) and with gratings approaching parallel orientation to the shorter aperture boundary--is discussed in the context of simple phenomenological models of motion integration. The best fit between model predictions and experimental data is found for an interaction between two stimulus parameters: (i) cycle ratio, which is the sine-wave gratings equivalent of the terminator ratio for line gratings, describing the effects from the aperture boundaries, and (ii) the grating orientation, responsible for perpendicular motion components, which describes the influence of motion signals from inside the aperture. This suggests that the most simple cycle (terminator) ratio explanation cannot fully account for the quantitative properties of the barber-pole illusion.     

Visible persistence and form correspondence in Ternus apparent motion.

Visual stimuli remain visible for some time after their physical offset (visible persistence). Visible persistence has been hypothesized to play an important role in determining the pattern of correspondence matching in the Ternus apparent-motion display. In this display, one or more elements reappears in overlapping locations at different times, whereas another element appears alternately to the right or the left of these elements. Usually either the elements are perceived to move coherently as a group (group motion), or one element may be perceived to hop over one or more other elements (element motion). According to the visible-persistence account of the perceptual organization of the Ternus display, element motion is seen when the temporal gap between elements in overlapping locations is small enough to be bridged by visible persistence; if it is not, group motion is seen. We conducted four experiments to test this visible-persistence account. In Experiments 1 and 2, a form correspondence cue (line length) was introduced to bias the visual system toward the element-motion interpretation, while visible persistence was either reduced or eliminated. The element-motion percept dominated despite the elimination of visible persistence. In Experiments 3 and 4, we found that Ternus elements presented without interruption, and thus presumably persisting over time, can be perceived in group motion. Together, the results indicate that visible persistence is neither necessary nor sufficient to account for the pattern of correspondence matches in the Ternus display.