Illusion-Destruction by Appropriate Scaling

Shrinkage in the apparent size of cylindrical objects

A novel illusion in apparent size is reported. We asked observers to estimate the width and depth of vertically oriented elliptic cylinders depicted with texture or luminance gradients (experiment 1), or the height of horizontally oriented elliptic cylinders depicted with binocular disparity (experiment 2). The estimated width or height of cylinders showed systematic shrinkage in the direction of the gradual depth change. The dissimilarity of 2-D appearance amongst our stimuli implies a large variation in spatial-frequency components and brightness contrasts, eliminating the possibility that these parameters contributed to the illusion. Also, the mechanism inappropriately triggered by pictorial depth cues (eg size scaling) may be irrelevant, because the illusion was obtained even when binocular disparity alone specified the shape of the cylinders. The illusion demonstrated here suggests that our visual system may determine the size of 3-D objects by accounting for their depth structures.

The Medawar Lecture 2001 knowledge for vision: vision for knowledge

An evolutionary development of perception is suggested-from passive reception to active perception to explicit conception-earlier stages being largely retained and incorporated in later species. A key is innate and then individually learned knowledge, giving meaning to sensory signals. Inappropriate or misapplied knowledge produces rich cognitive phenomena of illusions, revealing normally hidden processes of vision, tentatively classified here in a 'periodic table'. Phenomena of physiology are distinguished from phenomena of general rules and specific object knowledge. It is concluded that vision uses implicit knowledge, and provides knowledge for intelligent behaviour and for explicit conceptual understanding including science.

Evidence for the correcting-mechanism explanation of the Kanizsa amodal shrinkage

An object phenomenally shrinks in its horizontal dimension when shown on a 2-D plane as if the central portion of the object were partially occluded by another vertical one in 3-D space (the Kanizsa amodal shrinkage). We examined the predictions of the correcting-mechanism hypothesis proposed by Ohtsuka and Ono (2002, Proceedings of SPIE 4864 167-174), which states that an inappropriate operation of the mechanism that corrects a phenomenal increase in monocularly visible areas accompanied by a stereoscopic occluder gives rise to the illusion. In this study we measured the perceived width (or height in experiment 3) of a square seen behind a rectangle, while controlling other factors which potentially influence the illusion, such as the division of space or depth stratification. The results of five experiments showed that (a) the perceived width was not influenced when the occluder had a relatively large binocular disparity, but was underestimated when the occluder did not have disparity, and (b) the shrinkage diminished when the foreground rectangle was transparent, was horizontally oriented, or contained no pictorial occlusion cues. These results support the hypothesis that the correcting mechanism, triggered by pictorial occlusion cues, contributes to the Kanizsa shrinkage.

Geometrical haptic illusions: The role of exploration in the Müller-Lyer, vertical-horizontal, and Delboeuf illusions

This article surveys studies of the occurrence, in the haptic modality, of three geometrical illusions well known in vision, and it discusses the nature of the processes underlying these haptic illusions. We argue that the apparently contradictory results found in the literature concerning them may be explained, at least partially, by the characteristics of manual exploratory movements. The Müller-Lyer illusion is present in vision and in haptics and seems to be the result of similar processes in the two modalities. The vertical-horizontal illusion also exists in vision and haptics but is due partly to similar processes (bisection) and partly to processes specific to each modality (anisotropy of the visual field and overestimation of radial vs. tangential manual exploratory movements). The Delboeuf illusion seems to occur only in vision, probably because exploration by the index finger may exclude the misleading context from tactile perception. The role of these haptic exploratory movements may explain why haptics is as sensitive as vision to certain illusions and less sensitive to others.

A test of size-scaling and relative-size hypotheses for the moon illusion

In two experiments participants reproduced the size of the moon in pictorial scenes under two conditions: when the scene element was normally oriented, producing a depth gradient like a floor, or when the scene element was inverted, producing a depth gradient like a ceiling. Target moons were located near to or far from the scene element. Consistent with size constancy scaling, the illusion reversed when the "floor" of a pictorial scene was inverted to represent a "ceiling." Relative size contrast predicted a reduction or increase in the illusion with no change in direction. The relation between pictorial and natural moon illusions is discussed.

The tilt-constancy theory of visual illusions

The authors argue that changes in the perception of vertical and horizontal caused by local visual cues can account for many classical visual illusions. Because the perception of orientation is influenced more by visual cues than gravity-based cues when the observer is tilted (e.g., S. E. Asch & H. A. Witkin, 1948), the authors predicted that the strength of many visual illusions would increase when observers were tilted 30 degrees. The magnitude of Zöllner, Poggendorff, and Ponzo illusions and the tilt-induction effect substantially increased when observers were tilted. In contrast, the Müller-Lyer illusion and a size constancy illusion, which are not related to orientation perception, were not affected by body orientation. Other theoretical approaches do not predict the obtained pattern of results.

The Ponzo illusion and the perception of orientation

A new theory, called the tilt constancy theory, claims that the Ponzo illusion is caused by the misperception of orientation induced by local visual cues. The theory relates the Ponzo illusion-along with the Zöllner, Poggendorff, Wündt-Hering, and cafe wall illusions-to the mechanisms that enable us to perceive stable orientations despite changes in retinal orientation or body orientation. In Experiment 1, the magnitude of the misperception of orientation was compared with the magnitude of the Ponzo illusion. In Experiment 2, predictions of the tilt constancy theory were compared with accounts based on (1) low spatial frequencies in the image, (2) memory comparisons (pool-and-store model), and (3) relative sizejudgments. In Experiment 3, predictions of the tilt constancy theory were tested against predictions of the assimilation theory of Pressey and his colleagues. In the final experiment, the orientation account was compared with theories based on linear perspective and inappropriate size constancy. The results support the tilt constancy theory.

Slope and the Zöllner illusion

Informal observation suggests that the magnitude of the Zöllner illusion is reduced when the figure is viewed on a sloping plane. The hypothesis that this effect derives from the enlargement of the acute angle of intersection between the obliques and the verticals in the figure when it is viewed on a sloping plane is here investigated. The magnitude of the Zöllner illusion was measured with the use of a visual analogue scale. The results show that the change in the magnitude of the Zöllner effect as a function of the slope of the figure is different from that for corresponding figures, with enlarged angles of intersection between the obliques and the verticals, presented vertically. It is concluded that the enlargement of the angles of intersection can only partly account for the reduction of the Zöllner effect when the figure is viewed under slope, and that some other factor must be involved. An alternative hypothesis is evaluated whereby the effects result from the diminution in the contrast of the obliques when the figure is viewed under slope. Data are also presented to show that observers are able to perceive the enlarged or foreshortened angles of intersection veridically.

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

If a standard Zöllner 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 Schröder 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 Zöllner 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 Zöllner 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.

Knowledge in perception and illusion

Following Hermann von Helmholtz, who described visual perceptions as unconscious inferences from sensory data and knowledge derived from the past, perceptions are regarded as similar to predictive hypotheses of science, but are psychologically projected into external space and accepted as our most immediate reality. There are increasing discrepancies between perceptions and conceptions with science's advances, which makes it hard to define 'illusion'. Visual illusions can provide evidence of object knowledge and working rules for vision, but only when the phenomena are explained and classified. A tentative classification is presented, in terms of appearances and kinds of causes. The large contribution of knowledge from the past for vision raises the issue: how do we recognize the present, without confusion from the past. This danger is generally avoided as the present is signalled by real-time sensory inputs-perhaps flagged by qualia of consciousness.

The Müller-Lyer contrast illusion: a computational approach

When a temporal delay is interposed between the contextual elements (wings) and the focal element (central axis) of the Müller-Lyer figures, the usual assimilation illusion changes to an illusion of contrast; that is, judged axis length is contrasted away from rather than assimilated toward the context provided by parallel extents between wings. Presentation time for the preceding contextual wings on the order of 1 sec or more was needed to produce contrast effects in judgments of the following focal axis (Experiment 3) and, given sufficient presentation time, these contrast effects were largely unaffected by the length of the temporal delay between contextual and focal elements, appearing equally strong for delays between 0 and 2 sec (Experiments 1 and 2). These results are consistent with a representational basis for these contrast effects that is high-level and long-lived. The Müller-Lyer contrast illusion may reflect the inadvertent error arising from basing judgments about particular objects on information about attribute differences among objects. Such judgmental errors may be the natural consequence of constrained computations that make explicit information required for certain common tasks, but at the expense of obscuring information required for less common tasks.

Length illusion in fractional Müller-Lyer stimuli: an object-perception approach

Length judgments were compared for Müller-Lyer stimuli and figures which had line junctions at only one end of the central shaft. A length illusion occurred for fractional figures, only slightly reduced in magnitude from the usual illusion, and the largest reduction occurred for fractional figures with fork junctions. These results are consistent with an hypothesis (drawn from artificial intelligence algorithms for interpreting line drawings) that isolated line junctions are treated as boundary junctions with constrained interpretations of convex and concave edges for the shafts of arrow and fork junctions, respectively. Information about relative position of edges may be used to constrain computation of metric properties and consequential differences in size scaling would be responsible for the illusion. Illusions can arise when information well suited for one kind of task (eg object recognition) is employed in tasks for which it is not well suited (eg size perception).

Three-space inference from two-space stimulation

Oblique contours sloping at 30 degrees with respect to the horizontal were presented alone, in combination to form chevrons, or with a vertical line to form arrowhead or Y patterns; they were projected onto a screen in the frontal parallel plane and viewed from positions that gave viewing angles of 90 degrees (normal to the screen's surface), 53 degrees, or 34 degrees. The perceived orientation of the contours, as assessed by a movable arm that the subjects set to be parallel to the obliques, changed monotonically as a function of viewing angle. The change was as great for single obliques as for combinations of obliques within the chevron, arrowhead, and Y patterns. The results of Experiment 1 were extended in Experiment 2, in which obliques at 30 degrees and 50 degrees with respect to the horizontal were presented singly or in combination as chevron patterns. It is argued that the results of both experiments indicate that single two-space oblique lines are immediately interpreted as lying in three-space and that the changes in perceived orientation are a consequence of this perceptual inference.

The creation and reversal of the Müller-Lyer illusion through attentional manipulation

A configuration is presented in which both the overestimated and the underestimated portions of the Müller-Lyer illusion are embedded. In free viewing no distortion of length occurs; however, overestimation or underestimation illusions can be produced by simple manipulation of the attentional set, thus demonstrating one cognitive component in the formation of the Müller-Lyer distortion.

Inappropriate constancy scaling theory and the Mueller-Lyer illusion

Gregory's Inappropriate Constancy Scaling explanation for visual illusion was investigated. If perceptual experience with real-life edges and angles, near and far, leads to constancy scaling which is inappropriately applied to the Mueller-Lyer configuration, then configurations which are based upon angles of regard in between the two extreme field patterns would produce illusory effects between the two conventional Mueller-Lyer effects. A model representing one edge of a cubic figure, i.e., one vertical and four horizontal lines, was constructed of wooden dowel rods and photographed at predetermined angles. Transparencies based on the photographed images were then used to determine the PSE at each of these angles. Generally, we interpret out results as supportive of the theory, since PSEs increase as a function of angular change from 0 degrees to 180 degrees. The linear trend is complicated by an unexpected cubic trend, but an explanation is proposed.

Two categorical stages of object recognition

Visual object recognition was investigated in a group of eighty-one patients with right- or left-hemisphere lesions. Two tasks were used, one maximizing perceptual categorization by physical identity, the other maximizing semantic categorization by functional identity. The right-hemisphere group showed impairment on the perceptual categorization task and the left-hemisphere group were impaired on the semantic categorization task. The findings are discussed in terms of categorical stages of object recognition. A tentative model of their cerebral organization is suggested.

The role of apparent depth and context in the perception of the Ponzo illusion

The role of apparent depth features and the proximity of the test lines to the adjacent contours in the actuation of the Ponzo illusion was examined. Six versions of the Ponzo figure were employed: a standard Ponzo figure and five modified figures in which the test lines varied in orientation (horizontal or vertical) and in location (inside or outside the converging contours). Both manipulations resulted in a significant decrease in the magnitude of the illusion in comparison to the standard Ponzo figure. The results suggest that the Ponzo illusion is significantly affected by contextual factors.

Müller-Lyer illusions: their origin in processes facilitating object recognition

Perspective theories for the Müller-Lyer illusions have considered them to reflect constancies normally permitting the viewer to compensate for distance in estimating the true size of three-dimensional objects. Our experiments suggest a rather different perspective theory involving object recognition.

A novel experimental procedure was used. Each of the separate groups of thirty subjects viewed only one of nineteen experimental drawings based on the Müller-Lyer figures. They judged the overall length of the shaft and divided it into subjectively equal quarters. The major findings were that the effect of each component angle was generally independent of other angles and independent of any overall perspective appearance of the figure. The shortening effect produced by an acute angle was limited to the contiguous quarter, whüe the lengthening effect of an obtuse angle extended undiminished from the contiguous quarter to the next quarter.

Perspective photographs are shown, demonstrating that these angle-induced changes in apparent length can compensate selectively for the different perspective distortions occurring for the component parts of a single three-dimensional object. Such expansions and contractions provide no direct help in estimating overall size or distance of the object. But they do make possible recognition of the actual shape of the object and its orientation to the viewer, as well as producing errors when judging the length of Müller-Lyer figures.

The geometry of the correspondence between two retinal projections

Since each retinal projection of an object has some definite geometric relation to it, the two projections of a same object are related to each other. The correspondences between points, linear segments, and orientations on the two retinas are discussed thoroughly in three-dimensional geometry, and the constraints that tie the projections (the 'projective invariants') are presented. Some widely held conceptions on disparity or the ambiguity problem in binocular stereopsis appear to be based upon representation that are correct in particular situations, but are misleading in the general case. I suggest that in order to achieve binocular stereopsis, the brain does not proceed by complete trial and error, but may guide its search for correspondences by taking advantage of the geometric constraints. There are at least four major possible strategies: (i) a metric strategy, as initially proposed by Julesz; (ii) a projective strategy based on the law of invariance of the anharmonic ratio and Desargue's theorem; (iii) a perspective strategy discussed in relation to the homology relationships between vanishing points and in relation to physiological studies on cells of visual cortex; and (iv) a more dynamic strategy based upon the geometric properties of the Zöllner illusion.

The Poggendorff illusion with subjective contours

Gregory (1972) has claimed that the Poggendorff misalignment effect occurs when the collinear obliques are separated by subjective rather than real contours. He used two figures to demonstrate this variant of the illusion. Two experiments to test the claim are reported. The first showed that apparent misalignment in one of the two original figures is no greater than that with two obliques alone (the oblique line effect), but misalignment in the other is greater than with two oblique lines and than with a control without subjective contours. The second experiment showed that apparent misalignment in the second figure was less than in two control figures without subjective contours. Since this reduced effect was probably due to the nature of the intersection between the oblique and a semi-circular element, the role of subjective contours remains unsettled.