On the notion of visual illusions

The usual definitions of illusions, as incorrect perceptions or cases of discrepancies between reality and our perception of reality, have been criticized as inadequate. The reason is that it is not clear how to apply this notion in a number of interesting cases. This paper is an attempt to provide an adequate definition of illusions, appropriate for many classical phenomena usually referred to as illusions.


Laboratory of experimental psychology, Department of Psychology, University of Belgrade, Serbia
The usual definitions of illusions, as incorrect perceptions or cases of discrepancies between reality and our perception of reality, have been criticized as inadequate.The reason is that it is not clear how to apply this notion in a number of interesting cases.This paper is an attempt to provide an adequate definition of illusions, appropriate for many classical phenomena usually referred to as illusions.
Illusions of the senses are usually thought of as instances of non-veridical (incorrect) perception, or cases of discrepancies between reality and our perception of reality, when we do not perceive objects as they actually are.However, such a notion of illusion was criticized by pointing out that it is not clear how to apply this concept consistently in a number of interesting cases (see Morgan, 1996;Rogers, 2010Rogers, , 2014)).For example, is all perception of color illusory, given that there are features of spectral luminance distributions that are not recoverable by our color mechanisms?Does a pair of flat stereo images that mimic the actual input to the two eyes from a 3D body provide a veridical or an illusory experience of depth?In what precise sense does our perception deviate from reality in illusions?What would it even mean to experience the world veridically, as it 'actually' is in reality?Such questions suggest that the notion of illusions is muddled and should perhaps be dismissed as a scientifically useless concept.
My goal here is to show that this concept can in fact be properly defined in such a manner that it applies for some salient cases of illusions, that is, for a set of phenomena which includes a number of classical and well-known effects traditionally explicitly labeled as illusions.Namely, the notions of correct / incorrect perceptions as instances of agreement / disagreement of perception with reality can be defined as follows: perception is illusory when two objects are physically equal with respect to some feature but appear different, and also when they are physically different but appear equal; perception is veridical when two objects are physically equal with respect to some feature and appear equal, and also when they are physically different and appear different.A four-part scheme or format Corresponding Author: Dejan Todorović (dtodorov@f.bg.ac.rs) will be used for the illustration of this definition, with the help of which cases of veridicality and illusions can be presented in a systematic manner.Examples of the application of this scheme, adapted from Todorović (2010Todorović ( , 2014)), will first be provided for some illusions of size, orientation and lightness.
The Ebbinghaus illusion.As the first example, consider Figure 1, which is divided into four panels.In panel 1a there are two disks that have equal physical size, which also look equal (or certainly very similar) in size.In panel 1c there are also two disks, one of which is the same as in panel 1a and the other which is physically somewhat larger (its radius is 20% longer), and also looks a bit larger.In these two panels reality and appearance are in agreement, in the sense that objects appear as they are: when they are the same they look the same (panel 1a), and when they are different they look different (panel 1c).Cases of such agreement of physical and phenomenal features are instances of veridical perception.Consider now panel 1b.It contains the same two physically equal disks as in panel 1a.However, in this panel they are surrounded by additional disks, forming two different contexts: in one case the surrounding disks are larger than the central disk and in the other case the surrounding disks are smaller.The two different contexts cause the two identical central disks to appear different: the central disk surrounding by larger disks looks smaller than the central disk surrounded by smaller disks.This is an example of a well-known visual illusion, named after Hermann Ebbinghaus.In spite of the fact that the observer knows well that the disks have the same size, they still look different, in other words, this visual effect is cognitively impenetrable.On the other hand, in panel 1d the situation is in a sense opposite than in panel 1b.Here the two central disks are the same as the two physically different disks in panel 1c, but the surrounding disks are the same as in panel 1b; thus panels 1b and 1d have the same constituents, except for the central disk surrounded by larger disks, which is physically larger in panel 1d than in panel 1b.In panel 1d the two central disks appear approximately similar in size, although physically they are different (and although in panel 1c this difference is noticeable).The physical difference in size is perceptual compensated by the difference of the two contexts, that is, the presence of different surrounding disks.In sum, in panels 1b and 1d reality and appearance are not in agreement.Objects that are physically equal appear different (panel 1b) and, conversely, objects that are physically different appear the same or very similar (panel 1d).Cases of such disagreement of physical and phenomenal features are instances of illusory perception.
Note that the configuration in panel 1b is useful to demonstrate the illusion, since it is easily shown that the disks are physically the same but appear different.On the other hand, the configuration in panel 1d is useful to measure the illusion, since it is easy to establish the difference in physical size of two objects that appear equal (or very similar) in size.How big the physical difference needs to be for the disks to appear equal is an empirical matter, established in experiments, for example by asking subjects to vary the size of the central disk surrounded by larger disks until it perceptually matches in size the other central disk.
The Zöllner illusion.Figure 2 contains an example involving perception of orientation, presented in the same general format as the size illusion in Figure 1.Panel 2a contains two parallel lines, which also look parallel.Panel 2c contains two lines which are not parallel and also don't look parallel; their orientations are different, and the lines subtend an angle of 3 degrees, converging from left to right.Panel 2b contains the same two parallel lines as in panel 1a, but here they are presented in the context of additional short crossing lines, which have different orientations for the two lines.The consequence is the well-known Zöllner illusion: the parallel lines don't appear as parallel but as diverging from left to right.Panel 2d contains the same two converging lines as in panel 2c, but crossed with the same two sets of short lines as in panel 2b.In this panel the two lines appear parallel or nearly so, or at least more parallel than the same two lines in panel 2c.The difference in the orientations of the two lines, that is, their physical convergence, is perceptually compensated by the illusion-inducing effect of the different orientations of the crossing lines, causing the perception of their divergence.Similarly as in Figure 1, panel 2b is useful for demonstrating the illusion, since it is easily shown that the perceptually converging lines are physically parallel, and panel 2d is useful for measuring the illusion, since it is easy to establish the difference in physical orientation of the two parallelappearing lines, although the required angle may be somewhat different for different subjects.The simultaneous lightness contrast illusion.Figure 3 presents an example from the domain of lightness perception.Panel 3a contains two disks with the same luminance (amount of reflected light).They also look the same in lightness (perceived shade of gray).In panel 3c one disk is the same as in panel 3a, but the luminance of the other disk is higher, and the two disks, correctly, appear to have to have different shades of gray.Panel 3b contains the same physically equal disks from panel 3a, but here they are placed on backgrounds of different luminance.As a consequence of this difference of contexts the disks appear different, such that the one on the darker background looks lighter; this is an instance of the simultaneous lightness contrast illusion.Panel 3d contains the two different disks from panel 3c, but placed on two different backgrounds, same as in panel 3b.As a consequence, the two disks appear much more similar in lightness in this panel than in panel 3c.The presentations of the three illusions from different perceptual domains (size, orientation, lightness) have shared the same format.The two objects in the first row are physically the same in both panels (a, b), and in the second row they are physically different in both panels (c, d).In the first column the two objects are placed in the same context in both panels (a, c), and in the second column they are placed in different contexts in the two panels (b, d).The two objects appear equal (or approximately equal) with respect to some attribute in two panels (a, d), and appear different in the two other panels (b, c).The perceptual judgments agree with physical reality when objects are in the same contexts (a, c); these are cases of veridical perception.Reality and perception disagree when the objects are placed in different contexts (b, d); these are cases of illusory perception.
Two types of object features were invoked in this discussion, as well as two types of relations between them.The two types of features were physical features (size, orientation, luminance), as measured by physical instruments (measuring tape, protractor, photometer), and perceptual features (perceived size, perceived orientation, lightness), as assessed by recording observer judgments.The relations were comparisons of physical features (physical equality and physical difference) and comparisons of perceptual features (perceived equality and perceived difference).Furthermore, the two comparisons were themselves compared by establishing whether they agree or disagree, with two possible outcomes.First, the physical comparison and the perceptual comparison could agree with each other; this could happen in two ways, when the two objects were both physically equal and perceptually equal (panel a), and also when the two objects were both physically and perceptually different (panel c).Second, the two comparisons could disagree with each other; this could also happen in two ways, when the two objects were physically equal but perceptually different (panel b), and when, conversely, the two objects were physically different but perceptually equal (panel d).The first outcome corresponds to veridical perception and the second outcome corresponds to illusory perception.In this way both veridical and illusory perception are defined for this class of stimuli.
Three illusions were used as illustrations here, but many other classical visual illusions can also be presented in the exact same way (and several were presented in this manner in Todorović, 2010Todorović, , 2014)).They include size illusions such as the Müller-Lyer illusion, the Sander illusion and the Ponzo illusion, location illusions such as the Judd illusion and the Oppel-Thiéry-Wundt illusion, orientation and shape illusions such as the Café wall illusion and the Hering-Wundt illusion, direction illusions such as the Poggendorff illusion, as well as some lightness and color illusions.
The purpose of the preceding considerations was to show how the notions of veridical and illusory perception can be defined clearly and unambiguously, using a general formal presentation scheme applicable to many classical illusions.However, not all illusions can be presented in exactly this way, nor are all phenomena that can be presented in this format necessarily illusions.Namely, the above scheme is tailored to illustrate effects of context, but not all illusions are necessarily context effects, nor are all context effects necessarily illusions, as illustrated below.
The vertical-horizontal illusion.The issue here is that, unlike in the previous examples, the pairs of objects in panels 4a and 4b are not physically identical in every way except for the different contexts, since they also differ in orientation and mutual spatial relation; the same is true for the pairs of objects in panels 4c and 4d.Furthermore, again unlike in the previous examples, it is not appropriate to describe the pairs of lines in panels 4a and 4c as being in the same context, and as being in different contexts in panels 4c and 4d.However, although this phenomenon thus does not quite fit the above formal scheme, it nevertheless still is properly described as an illusion, because objects that are the same with respect to a feature (here size) appear as being different (panel 4b), and vice versa (panel 4d).
An alternative way to present this illusion would be to turn line CD by 90 o in panels 4a and 4c.However, although in this case the pairs of lines in panels 4a and 4b, as well as in panels 4c and 4d, would be more similar than in current Figure 4, they still would not be identical.Furthermore, in this arrangement the lines AB and CD in panel 4a, with the same length but different orientation, would not look identical in length, because the horizontal-vertical illusion is present, although in a weaker form, even when the two lines do not touch in the form of an inverted T, as in panel 4b.
The Wollaston effect.Figure 5 presents a converse case compared to figure 4, in that it follows the above format, but does not necessarily involve an illusion.The objects are pairs of pairs of eyes in cartoon faces.In panel 5a the two eye pairs are identical (with irises centered in the eye opening), and are also presented in the same context, meaning that they are both placed symmetrically within the ellipses that represent head outlines.The perceptual feature of interest here is the perceived direction of gaze of the two faces, which is the same.In panel 5c the two eye pairs are also placed symmetrically within the head outline but are not identical (irises are centered in one eye pair but shifted rightwards in the other pair), and they are also not perceived to gaze in the same direction.Panel 5b contains the same two identical pairs of eyes as panel 5a, but here they are presented in two different contexts: in one face the eyes are positioned symmetrically, as in panel 5a, and in the other face they are both (together with the 'nose' and the 'mouth') shifted leftwards, towards the oval outline.In consequence the two faces are not perceived to gaze in the same direction: one face appears to look at the observer, and the other appears to look leftwards.This is an instance of the Wollaston (1824) effect.Finally, panel 5d contains the same two different pairs of eyes as panel 5c, but presented in the same two different contexts as in panel 5b.Here both faces seem to look in the same or nearly the same direction, at the observer.Although the Wollaston effect is often classified as an illusion, I have argued that it is not (Todorović, 2014).Note that the placement of the eyes within the oval outline can be regarded as a crude but effective way to convey the orientation of the head for cartoon faces: symmetrical placement is a cue that the head is oriented frontally, whereas sideways placement is a cue that the head is tilted.Thus in panel 5b, although the pairs of eyes are the same (the irises are in the same relative positions within the eye opening), they belong to two differently oriented heads.In such a case it is only logical that the gaze directions would be different, because the eyes are in the head and have to turn together with it, even when they themselves don't move with respect to the head; therefore the fact that the perceived gaze directions are different is not an illusion.Conversely, in panel 5d the face in which the head is turned leftwards and the eyes rightwards is as legitimate a case of gazing at the observer as the other face in which the head is frontal and the eyes symmetrical; therefore the fact that the gaze directions are perceived as same (or very similar) is also not an illusion.
One possible criticism of the definition of veridical and illusory perception proposed above is that some illusions may not necessarily be presented as comparisons of two objects.For example, the Zöllner illusion may be illustrated with an example in which a horizontal line crossed with small oblique lines does not look horizontal but tilted.This case does not involve comparison of orientation of two lines but judgment of orientation of a single line.However, as shown above, this phenomenon can also be presented as a comparison of two lines, thus fitting the proposed definition.It remains to be shown whether such a procedure is feasible for other types of illusions.
Another possible criticism concerns one of the four possibilities in the above scheme, that is, the claim that the case when two objects are different and also appear different is a case of veridical perception (panel c).The problem is that such a notion of veridicality seems to be too coarse-grained, particularly when compared to the other case of veridical perception, when two objects are equal and also appear equal (panel a).However, this difference is a consequence of an asymmetry between the relations of equality and inequality, in that, given an object, the potential set of objects equal to it is more restricted that the potential set of objects different from it.
The proposed definition invokes only the relations of equality and inequality.Borrowing a term from the domain of measurement scales, such relations are only nominal.However, perceptual judgments are not restricted to claims of equality and inequality.Thus an object can be judged not just as different in length from another object, but also as longer or shorter (ordinal judgment), or, although such tasks are rarely used in psychophysical experiments, as twice or half as long (ratio judgments), or being 5 cm long and the other being 6 cm long.Such judgments can be correct or incorrect, thus being veridical or illusory.Although such aspects could be taken into account in a more developed

Figure 1 .
Figure 1.The Ebbinghaus illusion.Two equal disks (panel a) appear different when surrounded by disks of different size (panel b).Two different disks (panel c) appear same or approximately same when surrounded by disks of different size (panel d).

Figure 2 .
Figure 2. The Zöllner illusion.Two parallel lines (panel a) don't appear parallel when crossed by short lines of different orientations (panel b).Two non-parallel lines (panel c) appear approximately parallel when crossed by short lines of different orientations (panel d).

Figure 3 .
Figure 3.The simultaneous lightness contrast illusion.Two disks of the same luminance (panel a) appear differently light when placed on different surrounds (panel b).Two disks of different luminance (panel c) appear similarly light when placed on different surrounds (panel d).
Figure 4 is an attempt to present the horizontal-vertical illusions in the above format, but it is only partially successful.As in the previous examples, the two objects in panel 4a are the same and look the same (in length) and in panel 4c they are different and look different.In panel 4b the two lines have the same length but the vertical line looks longer; this is an instance of the well-known vertical-horizontal illusion.Finally, in panel 4d the two lines have the same lengths as in panel 4c, that is, they are different, but look the same (or very similar in length).

Figure 4 .
Figure 4.The horizontal-vertical illusion.Two lines of same length (panel a) appear differently long when one is horizontal and the other is vertical (panel b).Two lines of different lengths (panel c) appear equally or similarly long when one is horizontal and the other is vertical (panel d).

Figure 5 .
Figure 5.The Wollaston effect.Two faces with eyes with same positions of irises (panel a) appear to look in different directions when the eyes are placed in different positions within the head outline (panel b).Two faces with eyes with different positions of irises (panel c) appear to look in same or similar directions when the eyes are placed in different positions within the head outline (panel d).