The Ponzo illusion and the perception of orientation

Perceptual axioms are irreconcilable with Euclidean geometry

There are different definitions of axioms, but the one that seems to have general approval is that axioms are statements whose truths are universally accepted but cannot be proven; they are the foundation from which further propositional truths are derived. Previous attempts, led by David Hilbert, to show that all of mathematics can be built into an axiomatic system that is complete and consistent failed when Kurt Gödel proved that there will always be statements which are known to be true but can never be proven within the same axiomatic system. But Gödel and his followers took no account of brain mechanisms that generate and mediate logic. In this largely theoretical paper, but backed by previous experiments and our new ones reported below, we show that in the case of so-called 'optical illusions', there exists a significant and irreconcilable difference between their visual perception and their description according to Euclidean geometry; when participants are asked to adjust, from an initial randomised state, the perceptual geometric axioms to conform to the Euclidean description, the two never match, although the degree of mismatch varies between individuals. These results provide evidence that perceptual axioms, or statements known to be perceptually true, cannot be described mathematically. Thus, the logic of the visual perceptual system is irreconcilable with the cognitive (mathematical) system and cannot be updated even when knowledge of the difference between the two is available. Hence, no one brain reality is more 'objective' than any other.

Visual perceptual learning is effective in the illusory far but not in the near space

Visual shape discrimination is faster for objects close to the body, in the peripersonal space (PPS), compared with objects far from the body. Visual processing enhancement in PPS occurs also when perceived depth is based on 2D pictorial cues. This advantage has been observed from relatively low-level (detection, size, orientation) to high-level visual features (face processing). While multisensory association also displays proximal advantages, whether PPS influences visual perceptual learning remains unclear. Here, we investigated whether perceptual learning effects vary according to the distance of visual stimuli (near or far) from the observer, illusorily induced by leveraging the Ponzo illusion. Participants performed a visual search task in which they reported whether a specific target object orientation (e.g., triangle pointing downward) was present among distractors. Performance was assessed before and after practicing the visual search task (30 minutes/day for 5 days) at either the close (near group) or far (far group) distance. Results showed that participants that performed the training in the near space did not improve. By contrast, participants that performed the training in the far space showed an improvement in the visual search task in both the far and near spaces. We suggest that such improvement following the far training is due to a greater deployment of attention in the far space, which could make the learning more effective and generalize across spaces.

A review on various explanations of Ponzo-like illusions

This article reviews theoretical and empirical arguments for and against various theories that explain the classic Ponzo illusion and its variants from two different viewpoints concerning the role of perceived depth in size distortions. The first viewpoint argues that all Ponzo-like illusions are driven by perceived depth. The second viewpoint argues that the classic Ponzo illusion is unrelated to depth perception. This review will give special focus to the first viewpoint and consists of three sections. In the first section, the role of the number of pictorial depth cues and previous experience in the strength of all Ponzo-like illusions are discussed. In the second section, we contrast the first viewpoint against the theories that explain the classic Ponzo illusion with mechanisms that are unrelated to depth perception. In the last section, we propose a Bayesian-motivated reconceptualization of Richard Gregory's misapplied size constancy theory that explains Ponzo-variant illusions in terms of prior information and prediction errors. The new account explains why some studies have provided inconsistent evidence for misapplied size constancy theory.

A Cortical-Inspired Sub-Riemannian Model for Poggendorff-Type Visual Illusions

We consider Wilson-Cowan-type models for the mathematical description of orientation-dependent Poggendorff-like illusions. Our modelling improves two previously proposed cortical-inspired approaches, embedding the sub-Riemannian heat kernel into the neuronal interaction term, in agreement with the intrinsically anisotropic functional architecture of V1 based on both local and lateral connections. For the numerical realisation of both models, we consider standard gradient descent algorithms combined with Fourier-based approaches for the efficient computation of the sub-Laplacian evolution. Our numerical results show that the use of the sub-Riemannian kernel allows us to reproduce numerically visual misperceptions and inpainting-type biases in a stronger way in comparison with the previous approaches.

Illusory size determines the perception of ambiguous apparent motion

The visual system constructs perceptions based on ambiguous information. For motion perception, the correspondence problem arises, i.e., the question of which object went where. We asked at which level of processing correspondence is solved – lower levels based on information that is directly available in the retinal input or higher levels based on information that has been abstracted beyond the input directly available at the retina? We used a Ponzo-like illusion to manipulate the perceived size and separations of elements in an ambiguous apparent motion display. Specifically, we presented Ternus displays – for which the type of motion that is perceived depends on how correspondence is resolved – at apparently different distances from the viewer using pictorial depth cues. We found that the perception of motion depended on the apparent depth of the displays, indicating that correspondence processes utilize information that is produced at higher-level processes.

Influences of orientation on the Ponzo, contrast, and Craik-O'Brien-Cornsweet illusions

Explanations of the Ponzo size illusion, the simultaneous contrast illusion, and the Craik-O'Brien-Cornsweet brightness illusions involve either stimulus-driven processes (assimilation, enhanced contrast, and anchoring) or prior experiences. Real-world up-down asymmetries for typical direction of illumination and ground planes in our physical environment should influence these illusions if they are experience based, but not if they are stimulus driven. Results presented here demonstrate differences in illusion strengths between upright and inverted versions of all three illusions. A left-right asymmetry of the Cornsweet illusion was produced by manipulating the direction of illumination, providing further support for the involvement of an experience-based explanation. When the inducers were incompatible with the targets being located at the different distances, the Ponzo illusion persisted and so did the influence from orientation, providing evidence for involvement of processes other than size constancy. As defined here, upright for the brightness illusions is consistent with an interpretation of a shaded bulging surface and a 3D object resulting from a light-from-above assumption triggering compensation for varying illumination. Upright for the Ponzo illusion is consistent with the inducers in the form of converging lines being interpreted as railway tracks receding on the ground triggering size constancy effects. The implications of these results, and other results providing evidence against experience-based accounts of the illusions, are discussed.

The Moon Illusion as (Partly) an Error in Apparent Visual Angle: A New Possibility

An illusory exaggeration of the horizon moon’s visual angle (together with an apparently larger physical size) may account for its dramatic appearance.

Effects of Color and Luminance Contrast on Size Perception-Evidence from a Horizontal Parallel Lines Illusion

The present study investigated a size illusion composed of two horizontal lines that were vertically separated and parallel to each other. When the two lines were of equal length, the upper line was consistently perceived to be a little longer than the lower line, therefore it was termed as horizontal parallel lines (HPL) illusion. We investigated the effect of color and luminance contrast on the HPL illusion by manipulating the color and luminance of the two lines. Results indicated the following: (1) differences in color between the two lines reduced the illusion; (2) differences in luminance between the two lines reduced the illusion; (3) Effect 1 was greater than Effect 2; (4) the illusory effect could not be affected as long as both of the lines were of the same color or luminance. The results suggest that the color or luminance contrast may contribute to the overall decrease in the illusory effect for lines with different colors/luminances, but generally the illusion decreases as the two lines are less similar to each other. These findings indicate that the similarity or ‘sameness’ effect dominates the effect of color/luminance contrast on the size illusion over the effect resulted from contrast difference or depth perception.

Illusory Distance Modulates Perceived Size of Afterimage despite the Disappearance of Depth Cues

It is known that the perceived size of an afterimage is modulated by the perceived distance between the observer and the depth plane on which the afterimage is projected (Emmert's law). Illusions like Ponzo demonstrate that illusory distance induced by depth cues can also affect the perceived size of an object. In this study, we report that the illusory distance not only modulates the perceived size of object's afterimage during the presence of the depth cues, but the modulation persists after the disappearance of the depth cues. We used an adapted version of the classic Ponzo illusion. Illusory depth perception was induced by linear perspective cues with two tilted lines converging at the upper boundary of the display. Two horizontal bars were placed between the two lines, resulting in a percept of the upper bar to be farther away than the lower bar. Observers were instructed to make judgment about the relative size of the afterimage of the lower and the upper bars after adaptation. When the perspective cues and the bars were static, the illusory effect of the Ponzo afterimage is consistent with that of the traditional size-distance illusion. When the perspective cues were flickering and the bars were static, only the afterimage of the latter was perceived, yet still a considerable amount of the illusory effect was perceived. The results could not be explained by memory of a prejudgment of the bar length during the adaptation phase. The findings suggest that cooccurrences of depth cues and object may link a depth marker for the object, so that the perceived size of the object or its afterimage is modulated by feedback of depth information from higher-level visual cortex even when there is no depth cues directly available on the retinal level.

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.

Testing the Tilt-Constancy Theory of Visual Illusions

Prinzmetal and Beck (2001) Journal of Experimental Psychology: Human Perception and Performance27 206–217) argued that a subset of visual illusions is caused by the same mechanisms that are responsible for the perception of vertical and horizontal—a theory they referred to as the tilt-constancy theory of visual illusions. They argued that these illusions should increase if the observer's head or head and body are tilted because extra reliance would then be placed on the illusion-inducing local visual context. Exactly that result had previously been reported in the case of the tilted-room and the rod-and-frame illusions. Prinzmetal and Beck reported similar increases in the tilt illusion (TI), as well as the Zöllner, Poggendorff, and Ponzo illusions. In two experiments, we re-examined the effect of head tilt on the TI. In experiment 1, we used more conventional TI stimuli, more standard experimental methods, and a more complete experimental design than Prinzmetal and Beck, and additionally extended the investigation to attraction as well as repulsion effects. Experiment 2 more closely replicated the Prinzmetal and Beck stimuli. Although we found that head tilt did increase TIs in both experiments, the increases were of the order of 1°–2°, more modest than the 7° reported by Prinzmetal and Beck. Significantly, the TI increase was larger when inducing tilts and head tilts were in the same direction than when they were in opposite directions, suggesting that the tilt-constancy theory may be oversimplified. In addition, because previous evidence renders unlikely the claim that the Poggendorff illusion can be explained simply in terms of misperceived orientation of the transversals, the question arises whether there might be some other explanation for the increase in the Zöllner, Poggendorff, and Ponzo illusions with body tilt that Prinzmetal and Beck reported.

Immediate susceptibility to visual illusions after sight onset

The dominant accounts of many visual illusions are based on experience-driven development of sensitivity to certain visual cues. According to such accounts, learned associations between observed two-dimensional cues (say, converging lines) and the real three-dimensional structures they represent (a surface receding in depth) render us susceptible to misperceiving some images that are cleverly contrived to contain those two-dimensional cues. While this explanation appears reasonable, it lacks direct experimental validation. To contrast it with an account that dispenses with the need for visual experience, it is necessary to determine whether susceptibility to the illusion is present immediately after birth; however, eliciting reliable responses from newborns is fraught with operational difficulties, and studies with older infants are incapable of resolving this issue. Our work with children who gain sight after extended early-onset blindness, as part of Project Prakash, provides a potential way forward. We report here that the newly sighted children, ranging in age from 8 through 16 years, exhibit susceptibility to two well-known geometrical visual illusions, Ponzo [1] and Müller-Lyer [2], immediately after the onset of sight. This finding has implications not only for the likely explanations of these illusions, but more generally, for the nature-nurture argument as it relates to some key aspects of visual processing.

The working memory Ponzo illusion: Involuntary integration of visuospatial information stored in visual working memory

Visual working memory (VWM) has been traditionally viewed as a mental structure subsequent to visual perception that stores the final output of perceptual processing. However, VWM has recently been emphasized as a critical component of online perception, providing storage for the intermediate perceptual representations produced during visual processing. This interactive view holds the core assumption that VWM is not the terminus of perceptual processing; the stored visual information rather continues to undergo perceptual processing if necessary. The current study tests this assumption, demonstrating an example of involuntary integration of the VWM content, by creating the Ponzo illusion in VWM: when the Ponzo illusion figure was divided into its individual components and sequentially encoded into VWM, the temporally separated components were involuntarily integrated, leading to the distorted length perception of the two horizontal lines. This VWM Ponzo illusion was replicated when the figure components were presented in different combinations and presentation order. The magnitude of the illusion was significantly correlated between VWM and perceptual versions of the Ponzo illusion. These results suggest that the information integration underling the VWM Ponzo illusion is constrained by the laws of visual perception and similarly affected by the common individual factors that govern its perception. Thus, our findings provide compelling evidence that VWM functions as a buffer serving perceptual processes at early stages.

Combinatorial neural codes from a mathematical coding theory perspective

Shannon's seminal 1948 work gave rise to two distinct areas of research: information theory and mathematical coding theory. While information theory has had a strong influence on theoretical neuroscience, ideas from mathematical coding theory have received considerably less attention. Here we take a new look at combinatorial neural codes from a mathematical coding theory perspective, examining the error correction capabilities of familiar receptive field codes (RF codes). We find, perhaps surprisingly, that the high levels of redundancy present in these codes do not support accurate error correction, although the error-correcting performance of receptive field codes catches up to that of random comparison codes when a small tolerance to error is introduced. However, receptive field codes are good at reflecting distances between represented stimuli, while the random comparison codes are not. We suggest that a compromise in error-correcting capability may be a necessary price to pay for a neural code whose structure serves not only error correction, but must also reflect relationships between stimuli.

On depth processing in the production of the Ponzo illusion: two problems and a solution

Certain phenomenological difficulties for the depth-processing/size-scaling theory of the Ponzo illusion can be resolved if those theoretical activities are carried out in Milner and Goodale's proposed vision-for-action cortical pathway.

Neglect's perspective on the Ponzo illusion

Visual illusions have been used to explore implicit perception in neglect. Previous studies have highlighted differences between length and surface illusion perception in neglect, but much less is known about depth illusion perception. In the Ponzo illusion (a classic depth illusion), two converging oblique lines modulate the perceived length of two horizontal lines. In the current study, we presented modified versions of the Ponzo illusion in which only one of the converging oblique lines was presented (alternatively the right or the left one). This manipulation allowed us to explore (1) how acute patients with neglect process depth illusions, and (2) whether awareness of both converging lines is necessary for the full effect of the illusion. To examine these questions, we had participants (i.e. healthy controls, patients with neglect and right brain-damaged patients) to make a perceptual judgment regarding the perceived length of the upper versus lower horizontal line within the Ponzo frame in four conditions: (1) the classic Ponzo illusion, (2) a "modified left" Ponzo illusion with a single oblique line on the left, (3) a "modified right" Ponzo illusion with a single oblique line on the right and (4) a control condition with parallel lines. The results indicated that all participants perceived the canonical Ponzo illusion and the modified right illusion. Critically, patients with neglect did not perceive the modified left illusion. In addition, for neglect patients, there was no difference in the strength of the perceived illusion when comparing the canonical illusion with the modified right illusion. Importantly, single case analysis revealed a high degree of variability in the neglect group that seemed to be linked with the amount of damage to occipital areas. Overall our results indicate that: (1) the classic Ponzo illusion might be perceived in neglect patients based solely on perception of the right side of the stimulus configuration, and (2) differences between types of illusions (i.e. depth vs. length), and variability between patients suggest that caution is needed when utilizing these kinds of illusions to assess implicit processing in neglect.

The relationship between vertical stimulation and horizontal attentional asymmetries

The original aim was to examine the effect of perceived distance, induced by the Ponzo illusion, on left/right asymmetries for line bisection. In Experiment 1, university students ( n = 29) made left/right bisection judgements for lines presented in the lower or upper half of the screen against backgrounds of the Ponzo stimuli, or a baseline. While the Ponzo illusion had relatively little effect on line bisection, elevation in the baseline condition had a strong effect, whereby the leftward bias was increased for upper lines. Experiment 2 ( n = 17) eliminated the effect of elevation by presenting the line in the middle and moving the Ponzo stimuli relative to the line. Despite this change, the leftward bias was still stronger in the upper condition in the baseline condition. The final experiment ( n = 17) investigated whether upper/lower visual stimulation, which was irrelevant to the task, affected asymmetries for line bisection. The results revealed that a rectangle presented in the upper half of the screen increased the leftward line bisection bias relative to a baseline and lower stimulation condition. These results corroborate neuroimaging research, showing increased right parietal activation associated with shifts of attention into the upper hemispace. This increased right parietal activation may increase the leftward attentional bias—resulting in a stronger leftward bias for line bisection.

Perceiving the present: systematization of illusions or illusion of systematization?

Mark Changizi et al. (2008) claim that it is possible systematically to organize more than 50 kinds of illusions in a 7 × 4 matrix of 28 classes. This systematization, they further maintain, can be explained by the operation of a single visual processing latency correction mechanism that they call "perceiving the present" (PTP). This brief report raises some concerns about the way a number of illusions are classified by the proposed systematization. It also poses two general problems-one empirical and one conceptual-for the PTP approach.

Functional magnetic resonance imaging of a child with Alice in Wonderland syndrome during an episode of micropsia

BACKGROUND

Alice in Wonderland syndrome is a perceptual disorder involving brief, transient episodes of visual distortions (metamorphopsia) and can occur in conjunction with certain viral infections. We used functional magnetic resonance imaging to examine visual processing in a 12-year-old boy with viral-onset Alice in Wonderland syndrome during an episode of micropsia (reduction in the perceived size of a form).

METHODS

Functional magnetic resonance imaging was conducted in response to a passive viewing task (reversing checkerboard) and an active viewing task (line-length decisions in the context of the Ponzo illusion).

RESULTS

In both tasks, the child with Alice in Wonderland syndrome showed reduced activation in primary and extrastriate visual cortical regions but increased activation in parietal lobe cortical regions as compared with a matched control participant.

CONCLUSIONS

The active experience of micropsia in viral-onset Alice in Wonderland syndrome reflects aberrant activity in primary and extrastriate visual cortical regions as well as parietal cortices. The disparate patterns of activity in these regions are discussed in detail.

Bracket placement in lingual vs labial systems and direct vs indirect bonding

OBJECTIVE

To examine the ultimate accuracy of bracket placement in labial vs lingual systems and in direct vs indirect bonding techniques.

MATERIALS AND METHODS

Forty pretreatment dental casts of 20 subjects were selected. For each dental cast, four types of bracket placement were compared: labial direct (LbD), labial indirect (LbI), lingual direct (LgD), and lingual indirect (LgI). Direct bonding was performed with the casts held in a mannequin head. Labial brackets were oriented with a Boone gauge, and lingual brackets were oriented with the Lingual-Bracket-Jig System. Torque error (TqE) and rotation deviation (RotD) were measured with a torque geometric triangle and a toolmaker's microscope, respectively. Both torque and rotational measurements were evaluated statistically as algebraic and absolute numeric values, using analysis of variance with repeated measures.

RESULTS

Absolute TqE and RotD were significantly (P < .001) higher in direct than in indirect bonding techniques higher in both the labial and lingual bracket systems by twofold and threefold, respectively (LbD = 7.26 degrees , 1.06 mm; vs LbI = 3.02 degrees , 0.75 mm; LgD = 8.42 degrees , 1.13 mm; vs LgI = 3.18 degrees , 0.55 mm). No statistically significant difference was found between labial and lingual systems for the same bonding technique. Maxillary incisors demonstrated the largest RotD angle (eg, right lateral: 12.04 degrees ). A distal off-center RotD was predominant in the mandibular dentition.

CONCLUSIONS

Labial and lingual systems have the same level of inaccuracy. For both systems, indirect bonding significantly reduces absolute TqE and RotD. The TqE found can cause transverse discrepancy (scissors or crossbite) combined with disclusion with antagonist teeth. The RotD found can result in irregular interproximal contact points.