Quantifying the Ebbinghaus figure effect: target size, context size, and target-context distance determine the presence and direction of the illusion

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.

Valuations of target items are drawn towards unavailable decoy items due to prior expectations

When people make choices, the items they consider are often embedded in a context (of other items). How this context affects the valuation of the specific item is an important question. High-value context might make items appear less attractive because of contrast-the tendency to normalize perception of an object relative to its background-or more attractive because of assimilation-the tendency to group objects together. Alternatively, a high-value context might increase prior expectations about the item's value. Here, we investigated these possibilities. We examined how unavailable context items affect choices between two target items, as well as the willingness-to-pay for single targets. Participants viewed sets of three items for several seconds before the target(s) were highlighted. In both tasks, we found a significant assimilation-like effect where participants were more likely to choose or place a higher value on a target when it was surrounded by higher-value context. However, these context effects were only significant for participants' fastest choices. Using variants of a drift-diffusion model, we established that the unavailable context shifted participants' prior expectations towards the average values of the sets but had an inconclusive effect on their evaluations of the targets during the decision (i.e. drift rates). In summary, we find that people use context to inform their initial valuations. This can improve efficiency by allowing people to get a head start on their decision. However, it also means that the valuation of an item can change depending on the context.

Effects of cortical distance on the Ebbinghaus and Delboeuf illusions

The Ebbinghaus and Delboeuf illusions affect the perceived size of a target circle depending on the size and proximity of circular inducers or a ring. Converging evidence suggests that these illusions are driven by interactions between contours mediated by their cortical distance in primary visual cortex. We tested the effect of cortical distance on these illusions using two methods: First, we manipulated retinal distance between target and inducers in a two-interval forced choice design, finding that targets appeared larger with a closer surround. Next, we predicted that targets presented peripherally should appear larger due to cortical magnification. Hence, we tested the illusion strength when positioning the stimuli at various eccentricities, with results supporting this hypothesis. We calculated estimated cortical distances between illusion elements in each experiment and used these estimates to compare the relationship between cortical distance and illusion strength across our experiments. In a final experiment, we modified the Delboeuf illusion to test whether the influence of the inducers/annuli in this illusion is influenced by an inhibitory surround. We found evidence that an additional outer ring makes targets appear smaller compared to a single-ring condition, suggesting that near and distal contours have antagonistic effects on perceived target size.

Use of remote data collection methodology to test for an illusory effect on visually guided cursor movements

Investigating the influence of perception on the control of visually guided action typically involves controlled experimentation within the laboratory setting. When appropriate, however, behavioral research of this nature may benefit from the use of methods that allow for remote data collection outside of the lab. This study tested the feasibility of using remote data collection methods to explore the influence of perceived target size on visually guided cursor movements using the Ebbinghaus illusion. Participants completed the experiment remotely, using the trackpad of their personal laptop computers. The task required participants to click on a single circular target presented at either the left or right side of their screen as quickly and accurately as possible (Experiment 1), or to emphasize speed (Experiment 2) or accuracy (Experiment 3). On each trial the target was either surrounded by small or large context circles, or no context circles. Participants’ judgments of the targets’ perceived size were influenced by the illusion, however, the illusion failed to produce differences in click-point accuracy or movement time. Interestingly, the illusion appeared to affect participants’ movement of the cursor toward the target; more directional changes were made when clicking the Perceived Large version of the illusion compared to the Perceived Small version. These results suggest the planning of the cursor movement may have been influenced by the illusion, while later stages of the movement were not, and cursor movements directed toward targets perceived as smaller required less correction compared to targets perceived as larger.

Ebbinghaus Illusion

Abstract. For 25 years, the web has been used for psychological research ( Krantz et al., 1997 ; Reips, 1997 ). While many areas of psychology have benefitted from the increased access to participants and other benefits of web-based research, one area of psychology has rarely taken advantage of the online format, that is, sensation and perception. Largely, sensation and perception research has not used the web because of the need for carefully calibrated equipment to successfully run their experiments. However, there may be classes of phenomena in our sensory processes that might be studied online where the equipment and stimuli vary. Suppose the critical feature of the stimulus is an abstraction of the physical stimulus that does not vary with different displays. In that case, these features can be successfully studied online, meaning that results from online studies will match those from controlled laboratories. This study will examine the Ebbinghaus illusion to illustrate the successful use of the web for perceptual research. The implications and some discussion of types of perceptual studies conducted on the web will be discussed.

Learning to see the Ebbinghaus illusion in the periphery reveals a top-down stabilization of size perception across the visual field

Our conscious visual perception relies on predictive signals, notably in the periphery where sensory uncertainty is high. We investigated how such signals could support perceptual stability of objects' size across the visual field. When attended carefully, the same object appears slightly smaller in the periphery compared to the fovea. Could this perceptual difference be encoded as a strong prior to predict the peripheral perceived size relative to the fovea? Recent studies emphasized the role of foveal information in defining peripheral size percepts. However, they could not disentangle bottom-up from top-down mechanisms. Here, we revealed a pure top-down contribution to the perceptual size difference between periphery and fovea. First, we discovered a novel Ebbinghaus illusion effect, inducing a typical reduction of foveal perceived size, but a reversed increase effect in the periphery. The resulting illusory size percept was similar at both locations, deviating from the classic perceptual difference. Then through an updating process of successive peripheral-foveal viewing, the unusual peripheral perceived size decreased. The classic perceptual eccentricity difference was restored and the peripheral illusion effect changed into a fovea-like reduction. Therefore, we report the existence of a prior that actively shapes peripheral size perception and stabilizes it relative to the fovea.

The Effect of Size Statistics of the Background Texture on Perceived Target Size

We investigated the effect of the size distribution statistics of background elements on the perceived size of a target. We manipulated the first, second, and third order statistics (i.e., mean, variance, and skewness) of the background element size distribution. We used a two-interval forced-choice paradigm to measure perceived target size at different background size distributions. In each trial, a standard disk, or target, was presented in one interval with a textured background and a comparison disk, on a blank background, in the other. The task for the observers was to determine which interval contained a larger disk. We measured the point of subjective equality for the perceived target size with a staircase procedure. The perceived target size decreased with the increment of mean background disk size. The variance and skewness of the background element size did not affect the perceived target size. Our results showed that only the first order statistics of the background modulated the perceived target size, not the higher order statistics. A computational model, in which the visual system extracts size information by averaging the responses of different size channels, whose response is modulated by the size of the background elements, can account for the results.

Perception of contextual size illusions by honeybees in restricted and unrestricted viewing conditions

How different visual systems process images and make perceptual errors can inform us about cognitive and visual processes. One of the strongest geometric errors in perception is a misperception of size depending on the size of surrounding objects, known as the Ebbinghaus or Titchener illusion. The ability to perceive the Ebbinghaus illusion appears to vary dramatically among vertebrate species, and even populations, but this may depend on whether the viewing distance is restricted. We tested whether honeybees perceive contextual size illusions, and whether errors in perception of size differed under restricted and unrestricted viewing conditions. When the viewing distance was unrestricted, there was an effect of context on size perception and thus, similar to humans, honeybees perceived contrast size illusions. However, when the viewing distance was restricted, bees were able to judge absolute size accurately and did not succumb to visual illusions, despite differing contextual information. Our results show that accurate size perception depends on viewing conditions, and thus may explain the wide variation in previously reported findings across species. These results provide insight into the evolution of visual mechanisms across vertebrate and invertebrate taxa, and suggest convergent evolution of a visual processing solution.

Is the Ebbinghaus illusion a size contrast illusion?

The Ebbinghaus illusion, in which a central target surrounded by larger context figures looks smaller than when surrounded by smaller context figures, is usually classified as a size contrast illusion. Thus "size contrast" is the dominant account of this effect. However, according to an alternative "contour interaction" account this phenomenon has little to do with size contrast but is rather caused by distance-dependent attractive and repulsive interactions between neural representation of contours. Here evidence is presented against the size contrast account and consistent with the contour interaction account. Experiment 1 was a control study confirming that the illusion can be obtained using displays consisting only of squares, which are more convenient to manipulate than the standardly used circles. In Experiment 2, the standard configuration involving small context figures surrounding the target was compared to a novel configuration, which involved many "spread" small context figures. The illusory effect of the standard context was stronger than the illusory effect of the spread context, in accord with the prediction of the contour interaction account, and contrary to the prediction of the size contrast account. In Experiment 3 two novel configurations were used, based on standard and spread contexts. The results were in accord with the prediction of the contour interaction account, whereas the size contrast account had no prediction because the stimuli did not involve conventional size contrast. Additional aspects of the stimuli and an account of the illusion based on a perspective interpretation are also discussed.

Ebbinghaus figures that deceive the eye do not necessarily deceive the hand

In support of the visual stream dissociation hypothesis, which states that distinct visual streams serve vision-for-perception and vision-for-action, visual size illusions were reported over 20 years ago to ‘deceive the eye but not the hand’. Ever since, inconclusive results and contradictory interpretations have accumulated. Therefore, we investigated the effects of the Ebbinghaus figure on repetitive aiming movements with distinct dynamics. Participants performed a Fitts’ task in which Ebbinghaus figures served as targets. We systematically varied the three parameters which have been shown to influence the perceived size of the Ebbinghaus figure’s target circle, namely the size of the target, its distance to the context circles and the size of the context circles. This paper shows that movement is significantly affected by the context size, but, in contrast to perception, not by the other two parameters. This is especially prominent in the approach phase of the movement towards the target, regardless of the dynamics. To reconcile the findings, we argue that different informational variables are used for size perception and the visual control of movements irrespective of whether certain variables induce (perceptual) illusions.

Interaction of Perception and Action in Discrete and Continuous Rapid Aiming Tasks

Previously, we have shown that discrete and continuous rapid aiming tasks are governed by distinct visuomotor control mechanisms by assessing the combined visual illusion effects on the perceived and effective index of difficulty (ID). All participants were perceptually biased by the combined visual illusion before they performed the rapid aiming tasks. In the current study, the authors manipulated the order of performing perceptual and motor tasks to examine whether perceptual or motor experience with the illusory visual target would influence the subsequent perceived and effective ID in discrete and continuous tapping tasks. The results supported our hypothesis showing that perceptual experience with the illusory visual target in the discrete condition reduced the effective ID in the subsequent discrete tapping task, and motor experience with the illusory visual target in the continuous condition reduced the illusion effects on the perceived ID in the subsequent perceptual judgment task. The study demonstrates the coinfluence of perception and action, and suggests that perception and action influence one another with different magnitude depending on the spatial frame of reference used to perform the perceptuomotor task.