Novel visual illusions related to Vasarely's 'nested squares' show that corner salience varies with corner angle

Vasarely's 'nested-squares' illusion shows that 90 degrees corners can be more salient perceptually than straight edges. On the basis of this illusion we have developed a novel visual illusion, the 'Alternating Brightness Star', which shows that sharp corners are more salient than shallow corners (an effect we call 'corner angle salience variation') and that the same corner can be perceived as either bright or dark depending on the polarity of the angle (ie whether concave or convex: 'corner angle brightness reversal'). Here we quantify the perception of corner angle salience variation and corner angle brightness reversal effects in twelve naive human subjects, in a two-alternative forced-choice brightness discrimination task. The results show that sharp corners generate stronger percepts than shallow corners, and that corner gradients appear bright or dark depending on whether the corner is concave or convex. Basic computational models of center surround receptive fields predict the results to some degree, but not fully.     

BOLD activation varies parametrically with corner angle throughout human retinotopic cortex

The Alternating Brightness Star (ABS) is an illusion that provides insight into the relationship between brightness perception and corner angle. Recent psychophysical studies of this illusion have shown that corner salience varies parametrically with corner angle, with sharp angles leading to strong illusory percepts and shallow angles leading to weak percepts. It is hypothesized that the illusory effects arise because of an interaction between surface corners and the shape of visual receptive fields: sharp surface corners may create hotspots of high local contrast due to processing by center-surround and other early receptive fields. If this hypothesis is correct, early visual neurons should respond powerfully to sharp corners and curved portions of surface edges. Indeed, the primary role of early visual neurons may be to localize the discontinuities along the edges of surfaces. If so, all early visual areas should show greater BOLD responses to sharp corners than to shallow corners. On the other hand, if corner processing is exclusively constrained to certain areas of the brain, only those specific areas will show greater responses to sharp vs shallow corners. To address this we explored the BOLD correlates of the ABS illusion in the human visual cortex using fMRI. We found that BOLD signal varies parametrically with corner angle throughout the visual cortex, offering the first neurophysiological correlates of the ABS illusion. This finding provides a neurophysiological basis for the previously reported psychophysical data that showed that corner salience varied parametrically with corner angle. We propose that all early visual areas localize discontinuities along the edges of surfaces, and that specific cortical corner-processing circuits further establish the specific nature of those discontinuities, such as their orientation.     

The illusion of clarity: Image segmentation and edge attribution without filling-in

It comes as no surprise that viewing a high-resolution photograph through a screen reduces its clarity. Yet when a coarsely quantized (i.e., pixelated) version of the same photo is seen through a screen its clarity is increased. Six experiments investigated this illusion of clarity. First, the illusion was quantified by having participants rate the clarity of quantized images with and without a screen (Experiment 1). Interestingly, the illusion occurs both when the wires of the screen are aligned with the blocks of the quantized image and when they are shifted horizontally and vertically (Experiments 2 and 3), casting doubt on the hypothesis that a local filling-in process is involved. The finding that no illusion occurs when the photo is blurred rather than quantized (Experiment 4) and that the illusion is sharply reduced when visual attention is divided (Experiment 5) argue for an image segmentation process that falsely attributes the edges of the quantized blocks to the screen. Finally, the illusion is larger when participants adopt an active rather than a passive cognitive strategy (Experiment 6), pointing to the importance of cognitive control in the illusion.     

A new variant of the Ouchi illusion reveals Fourier-component-based processing

We report that anomalous motion illusion in a new variant of the Ouchi figure is well predicted by the strength of its Fourier fundamentals and harmonics. The original Ouchi figure consists of a rectangular checkerboard pattern surrounded by an orthogonal rectangular checkerboard pattern, in which illusory relative motion between the two regions is perceived. Although this illusion has been explained in terms of biases in integrating one-dimensional motion signals to determine the two-dimensional motion direction, the physiological mechanism has not been clarified. With our new stimuli, which consisted of thin lines instead of rectangles, we found that the perceived illusion is drastically reduced when the position of each line element is randomly shifted. This is not predicted by simple models of local motion integration along the visible edges. We demonstrate that the relative amplitude of the relevant Fourier fundamentals and harmonics leads to a quantitative prediction. Our analysis was successfully applied to other variants of the Ouchi figure (Khang and Essock 1997 Perception 26 585-597), closely predicting the reported rating. The results indicate that the underlying physiological mechanism is sensitive to the Fourier components of the stimuli rather than the visible edges.     

Constancy scaling and conflict when the Zöllner illusion is seen in three dimensions

If a standard Z?llner illusion is seen as a staircase in depth, pairs of long lines flanking convex stair edges appear to diverge as usual, but divergence in pairs flanking concave edges can appear reduced. If the stair is reversed perceptually in the manner of the Schr?der staircase, convex and concave shapes exchange and the extent of apparent divergence in the long line pairs exchanges with them. The effect is enhanced if explicit stair edges are added, and reduced if the standard Z?llner pattern is replaced by one in which segments of the long lines are offset in the direction of the usual illusory effect. The observations suggest that the three-dimensional potential of the pattern cannot be excluded from explanations of the illusion, and are compatible with the view of Gregory and Harris that inappropriate constancy scaling is its primary cause, triggered 'bottom-up' by pattern properties or 'top-down' by cognitive inference. However, these two mechanisms would have to be acting in conflict to generate suppression of divergence in the concave steps. Pattern processing for properties, such as orientation, that are not associated with the potential of the Z?llner illusion as a three-dimensional configuration, but that have been suggested as sources of the illusion in recent studies, could also be acting in opposition to hypothesis scaling in the concave steps.     

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.     

Object and spatial representations in the corner enhancement effect

Cole, Gellatly, and Blurton have shown that targets presented adjacent to geometric corners are detected more efficiently than targets presented adjacent to straight edges. In six experiments, we examined how this corner enhancement effect is modulated by corner-of-object representations (i.e., corners that define an object's shape) and local base-level corners that occur as a result of, for instance, overlapping the straight edges of two objects. The results show that the corner phenomenon is greater for corners of object representations than for corners that do not define an object's shape. We also examined whether the corner effect persists within the contour boundaries of an object, as well as on the outside. The results showed that a spatial gradient of attention accompanies the corner effect outside the contour boundaries of an object but that processing within an object is uniform, with no corner effect occurring. We discuss these findings in relation to space-based and object-based theories of attention.     

The Bourdon illusion occurs with straight-, right-angle-, and parallel-edge figures

The Bourdon illusion is the apparent bentness of the straight edge of a figure consisting of two elongated triangular components arranged apex to apex. In three experiments, the illusion was shown to occur in the opposite direction, with the components arranged base to base. It was also shown to occur with the component edges at right angles and parallel. With the edges at right angles, the illusion also occurred in one direction when the components were apex to apex and occurred in the opposite direction when they were base to base. Supplementary observations indicated that the illusion is stronger when the components are relatively small and widely separated and eliminated when one of the two edges is curved.     

Kanizsa's shrinkage illusion produced by a misapplied 3-D corrective mechanism

In order to include the monocular areas from the left and the right eye in the cyclopean view, the visual system displaces the occluded elements which would result in a horizontal elongation of the shape but does not occur thanks to a correction mechanism which preserves the shape. We hypothesised that this mechanism causes Kanizsa's amodal shrinkage illusion (the apparent elongation of a partially occluded square) when it is incorrectly applied by the visual system to a two-dimensional stimulus. Four experiments tested this hypothesis: (i) one-eyed observers were less susceptible to the illusion than people with normal binocular vision because, for them, the correction for shape is unnecessary; (ii) the illusion was stronger with binocular than with monocular vision since binocularity induces the visual system to correct for the shape distortion; (iii) the illusion diminished when the stimulus was rotated 90 degrees given that displacement and compression are not required for vertical occlusion; (iv) the magnitude of the illusion was a function of the width of the occluder because, as previous research has shown, the edges of a partially occluded square are less displaced the farther they are from the edges of the occluder. The data from the four experiments support our hypothesis even though no condition was able to eliminate the illusion; other possible causes are discussed.     

Orientation misperceptions induced by contrast polarity: comment on "Contrast polarities determine the direction of Café Wall tilts" by Akiyoshi Kitaoka, Baingio Pinna, and Gavin Brelstaff (2004)

According to Kitaoka et al (2004, Perception 33 11-20), the Café Wall illusion can be reduced to misalignment effects produced locally by a large shape on a line passing nearby. I demonstrate here that the interacting units are edges and not whole shapes, and that the source of the illusion does not consist in a local tilt but in a tendency of the edges to join when they have the same contrast polarity.     

Anomalous contours and illusion of angularity: phenomenal and theoretical comparisons.

Many experimental comparisons between real and anomalous contours have proven the functional equivalence of the two conditions; however, there are some contradictory findings. One of these is obtained by analyzing the anomalous contours in the light of a new illusion, called the 'illusion of angularity'. A circle becomes a polygon when it covers the centre of a radial arrangement of black stripes, and a polygon changes its perceptual shape depending on its orientation with respect to the same radial arrangement. Phenomenally, it appears like a very pointed polygon, in which every side is concave or, alternatively, a shape that looks like a circle with angles added in the spaces between the radial stripes, or a polygonal shape in which every side is convex. The reciprocal anomalous counterparts of these conditions, obtained by removing the geometrical/polygonal contours, reveal different results. In the first case, one sees a perfect circle; in the second case, a polygon with blunted vertices, or a circular shape with angular protrusions; in the third case, a deformed circle. These results are inconsistent with some theoretical models proposed to explain the emergence of anomalous contours, namely, all the top-down models expressed in terms of cognitive constructions and perceptual hypotheses, or in terms of global figural organizations. Rather, these comparisons suggest a different interpretation for the two phenomena (the illusion of angularity and anomalous contours). This interpretation is based on dynamic interactions or on network computations that synthesize both real and anomalous contours.     

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 corner Poggendorff

With the classic Poggendorff illusion a set of parallel 'induction lines' will cause a set of oblique line segments to look misaligned even though they are collinear. A different kind of misalignment can be produced by placing the induction lines so that they form a corner. Under these conditions the obliques will appear to be angled slightly, one relative to the other. The effects are small, but can be seen and reliably reported by a group of naive subjects. The influence of the induction lines drops sharply as their relative position is moved from parallel to orthogonal, but there is a small residual influence which may be called the corner Poggendorff effect.     

The effect of spectral difference on auditory saltation

Auditory saltation is a spatiotemporal illusion in which the judged positions of sound stimuli are shifted toward subsequent stimuli that follow closely in time and space. In this study, the "reduced-rabbit" paradigm and a direct-location method were employed to investigate the effect of spectral sound content on the saltation illusion. Eighteen listeners were presented with sound sequences consisting of three high-pass or low-pass filtered noise bursts. Noise bursts within a sequence were either the same or differed in frequency. Listeners judged the position of the second sound using a hand pointer. When the time interval between the second and third sound was short, the target was shifted toward the location of the subsequent stimulus. This displacement effect did not depend on the spectral content of the first sound, but decreased substantially when the second and third sounds were different. The results indicated an effect of spectral difference on saltation that is discussed with regard to a recently proposed stimulus integration approach in which saltation was attributed to an interaction between perceptual processing of temporally proximate stimuli.     

Apparent distance reduction with moving stimuli (Tandem Effect): Evidence for an attention-shifting model

Summary When two vertical rods move through a horizontal window in close succession, the Tandem Effect can be observed. It consists of a spatial illusion (distance between the rods looking smaller than it actually is) and a temporal illusion (under certain conditions both rods are seen simultaneously in the window, though the first rod has left the window before the second rod enters it). We report six experiments that explored the distance-reduction illusion and tested an attentional model of the effect. It assumes that attention is initially focused on the first rod and then shifted to the second, when it enters the window. The percept of the pair of rods is integrated from the first rod's position at the beginning, and the second rod's position at the end, of the focus shift. Consequently their subjective distance will be smaller than their physical distance by the distance that they travel during the focus shift. Experiments 1 and 2 established the Tandem Effect as an empirical phenomenon and showed that its size depends on stimulus parameters such as window size and movement speed. Experiments 3–5 tested specific predictions from the attentional model. Experiment 6 examined a further illusion, the Fröhlich Effect, and showed that it can be subsumed under the model. The experiments produced some unexpected effects and some predictions from the model were only partly confirmed. It is shown that the main findings can be combined into two quantitative functions that describe the course of focusing. One implication is that visual attention does not move from one object to another; rather all attention shifts originate in the fovea. We discuss several alternative interpretations of our data and show that they are less satisfactory than the attentional model.     

Contrast polarities determine the direction of Café Wall tilts

We propose an explanatory approach to Café Wall type illusions that is simple yet fairly comprehensive. These illusions are constructed out of basic elementary units in a jigsaw-like manner. Each unit, in general, contains both a solid body and a thin tail: the contrast polarity between the two determines the direction of the contributory illusory tilt produced by that element-according to a heuristic rule illustrated in figure 1. Ensembles of these elements exhibit illusory tilts only when the tails of the elements align along a common line in an additive manner. When elements of opposing polarity alternate, the illusion is cancelled. This approach extends and supersedes those presented in Pinna's illusion of angularity and Kitaoka's 'acute' corner effect. Furthermore, it appears to be, in part, compatible with existing mechanisms proposed to account for the emergence of local tilt cues, and it suggests several novel variations on the Café Wall theme.     

The effect of eccentricity and the adapting level on the café wall illusion

The café wall pattern is composed of rows of alternating light and dark tiles, and alternate rows are shifted by one fourth of a cycle. The rows of tiles are separated by narrow horizontal mortar lines whose luminance is between those of the dark and the light tiles. Although the mortar lines are physically parallel, they are perceived to be tilted, which is known as the café wall illusion. In this study, an energy-based model for encoding orientation is implemented in order to estimate the strength of the café wall illusion, and it is shown that the estimated orientation depends on the spatial frequency to which each orientation-encoding unit is tuned. The estimation of mortar line orientation from an orientation-encoding unit tuned to a lower spatial frequency was greater than that from a unit tuned to a higher spatial frequency. It is assumed that the perceived mortar line orientation is the result of an integration of responses from the orientation-encoding units tuned to various spatial frequencies. This leads to the prediction that under viewing conditions in which responses from orientation-encoding units tuned to a higher spatial frequency are presumably weakened, the strength of the café wall illusion increases. In agreement with this prediction, it is shown that the café wall illusion is stronger when the café wall image is presented at the periphery or is observed under low luminance levels. On the other hand, the weighted averaging of the estimated mortar orientations across spatial frequencies overestimates the perceived orientation of the mortar lines. This suggests that the final percept of the café wall illusion could be determined by some kind of nonlinear interaction, such as an inhibitory interaction, between orientation-encoding units.     

Subjective contours and the Poggendorff illusion

Poggendorff illusions were generated by real edges, subjective contours, and various control patterns. Using both magnitude estimation and reproduction measures of illusion strength, it was found that subjective contours produced a reliable Poggendorff illusion. This clarifies previous reports which could not demonstrate a subjective contour-based illusion.     

Attentional control settings modulate susceptibility to the induced Roelofs effect

When a visible frame is offset laterally from an observer's objective midline, the subjective midline is pulled toward the frame's center, causing the frame and any enclosed targets to be misperceived as being shifted somewhat in the opposite direction. This illusion, the Roelofs effect, is driven by environmental (bottom-up) visual cues, but whether it can be modulated by top-down (e.g., task-relevant) information is unknown. Here, we used an attentional manipulation (i.e., the color-contingency effect) to test whether attentional filtering can modulate the magnitude of the illusion. When observers were required to report the location of a colored target, presented within an array of differently colored distractors, there was a greater effect of the illusion when the Roelofs-inducing frame was the same color as the target. These results indicate that feature-based attentional processes can modulate the impact of contextual information on an observer's perception of space.     

Straightness as the main factor of the hErmann grid illusion

The generally accepted explanation of the Hermann grid illusion is Baumgartner's hypothesis that the illusory effect is generated by the response of retinal ganglion cells with concentric ON-OFF or OFF-ON receptive fields. To challenge this explanation, we have introduced some simple distortions to the grid lines which make the illusion disappear totally, while all preconditions of Baumgartner's hypothesis remain unchanged. To analyse the behaviour of the new versions of the grid, we carried out psychophysical experiments, in which we measured the distortion tolerance: the level of distortion at which the illusion disappears at a given type of distortion for a given subject. Statistical analysis has shown that the distortion tolerance is independent of grid-line width within a wide range, and of the type of distortion, except when one side of each line remains straight. We conclude that the main cause of the Hermann grid illusion is the straightness of the edges of the grid lines, and we propose a theory which explains why the illusory spots occur in the original Hermann grid and why they disappear in curved grids.