Completion Illusion

[Assunta Gergely]

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A striking example of the constructive nature of visual perception is how the human visual system completes contours of occluded objects. To date, it is unclear whether perceptual completion emerges during early stages of visual processing or whether higher-level mechanisms are necessary. To answer this question, we used transcranial magnetic stimulation to disrupt signaling in V1/V2 and in the lateral occipital (LO) area at different moments in time while participants performed a discrimination task involving a Kanizsa-type illusory figure. Results show that both V1/V2 and higher-level visual area LO are critically involved in perceptual completion. However, these areas seem to be involved in an inverse hierarchical fashion, in which the critical time window for V1/V2 follows that for LO. These results are in line with the growing evidence that feedback to V1/V2 contributes to perceptual completion.

Looking at a web page is much like looking at a landscape through a set of binoculars. A small part of that landscape is in your immediate view, but often you have to pan up and down, or side to side to see it all. Similarly, on a web page, to discover all the available content, users may need to scroll up and down, or even swipe or scroll side to side.

Although users are accustomed to scrolling vertically on the web, scrolling (or swiping) horizontally is still not an expected way to interact with a desktop page. Even on mobile devices, where the horizontal-swipe gesture is fairly common, interfaces that rely on these gestures need strong signifiers to indicate the direction of interaction to users.

It is less common that an entire website be laid out horizontally, requiring users to use a horizontal scroll bar to view all of the content. Occasionally designers and creative businesses take this direction on their sites to showcase their creative design abilities. For mainstream sites, relying on horizontal scrolling is discouraged. The horizontal scrollbar is cumbersome because it requires constant attention and physical effort to steer the cursor within a narrow tunnel. And sites that are based on horizontal scrolling can easily make the same visual-design mistakes that create illusion of completeness on the vertical dimension.

In the Magic Wand effect, an overlying figure of the same color as its background is revealed by the motion of a wand behind it. The occluding figure is inferred by integration of the occluding edge information over time. The overlying figure is perceived by modal completion, while the wand and the background underneath are perceived by amodal completion. This illusion is compared with its predecessor from nearly two centuries ago, the Plateau Anorthoscopic Illusion, in which an object is recognizable when moved behind a slit.

This article provides an analysis of the Magic Wand illusion (Figure 1), in which an object is revealed relative to its background by a Magic Wand waving behind the object region but in front of its background region (see Tyler, 2011). At any given moment, only a small part of the object is revealed in this way, but the motion of the wand carries it around all parts of the object, allowing the whole structure to be completed by cumulation over time. In the terms developed by Michotte, Thins, and Crabb (1964), the overlying triangle is perceived by modal completion (or illusory perception of the overlying implied object), while the hidden part of the wand and the background underneath it are perceived by amodal completion (or perception of the spatial configuration of the implied object without perception of its modal properties such as color; Scherzer & Ekroll, 2015).

In this form, the revealed shape could be carried by retinal persistence of the edge information. If the eyes maintain fixation at any point in the field, the edge contours will build up over time on the retina. With sufficient persistence, the entire outline could build up as a brightening luminance retinal afterimage. (Note that the actual appearance is of a dark shadow induced on the inside of the triangle near the wand as it moves, with only a minimum of the predicted afterimage brightening in the region just vacated by the wand.)

To determine whether these luminance-induced effects are a significant factor in the illusion, a version with equiluminant stripes in the wand is depicted in Figure 1(b). Now the retinal afterimage in each stripe of the moving bar is canceled by the following stripe, leaving no net afterimage. Only some form of cortical persistence of the second-order contrast modulation could provide the information for building up the occluding structure. Observation of this condition in Film Clip II makes it clear that the perception of the triangle is just as strong as with the first-order luminance wand, and thus that that it reveals a true modal/amodal completion mechanism without the aid of a retinal afterimage (see Supplemental material).

A further elaboration of the effect was a finalist in the 2011 Best Illusion of the Year contest (Tyler, 2011). This version used a triplet of three nonintersecting lines as the seed for completion of an Illusory Impossible Triangle figure (Penrose & Penrose, 1958, Film Clip III). In themselves, the three lines specify only a flat, unambiguous triangular figure (Figure 2(a)). However, in combination with the solid block triangle figure elicited by the moving wand, the depth-ambiguous Impossible Triangle is revealed (Figure 2(b), Film Clip IV). Any one vertex of the triangle has a defined depth structure, but each is incompatible with the depth structure of the other two, so the depth rotates according to which vertex is being fixed at any given time. The same impression of an illusory Impossible Triangle is elicited by the occlusion of three spheres in the Supplemental Material (Film Clip V), designed to evoke the concept of the modal/amodal completion principles of the Kanizsa Triangle in combination with the Impossible Triangle. These two versions therefore show the Magic Wand effect giving rise to the dynamic Illusory Impossible Triangle.

Michotte A., Thins G., Crabb G. (1964). Les complments amodaux des structures perceptives [Amodal completions of perceptual structures]. Louvain, Belgium: Publications Universitaires, Studia Psychologica.

You will likely experience illusory discs where the lines would intersect. These will appear 'filled-in' with a brighter white than the surrounding area. You may also experience these discs as 'figures' which sit in a higher depth plane than the lines and so occlude them.

Experiences of the Ehrenstein figure exhibit both modal and amodal completion of objects. In modal completion one has a visual experience as of an object in virtue of experiencing edges that appear to be created by a luminance, colour or texture boundary. On reflection, one can tell that there is no such boundary and there is not a difference in luminance, colour or texture where there appears to be one; but, nonetheless, that is what we experience. For example, look at the Kanizsa triangle on the right. The triangle that one seems to see pointing upwards, in virtue of a difference in luminance between it and the background, is a classic example of modal completion. The apparent discs in the Ehrenstein figure are also an example of modal completion, as they are experienced in virtue of experiencing an apparent lightness boundary where none is present.

Perceptual filling-in is a well-attested phenomenon. For example, if a subject is presented with the stimulus of a green disc surrounded by a red annulus, and the green region is retinally fixed (moves with the eye), after a short time the subject will report that they see only a red disc (Krauskopf 1963). This is because retinally fixed stimuli quickly fade from the visual field due to neural adaptation (see the entries for the Troxler Effect and Negative Afterimages). In the Krauskopf experiment, the green disc was filled in by the surrounding red in a process similar to the filling-in of the blind spot which is inherent in the anatomy of the human eye. The physiological mechanisms of filling-in are unclear; Friedman et al. (2003) suggest that visual perception is based on a neural image operating as a 2-dimensional array, in which colour signals diffuse in all directions until meeting a contour signal. It can be assumed that the filling-in of the apparent discs in the Ehrenstein figures is mediated by the same mechanism, although in this case the contour is illusory rather than actual. For more detailed discussion, see Grossberg (2015) for an accessible introduction to the FACADE (Form and Colour and DEpth) neural model, which predicts perceptual filling-in as well as the apparent brightness increase and figure-ground effects seen in Ehrenstein figures.

It is a given of life that nothing is permanently and finally satisfying or fulfilling. It is a given of the mind that somewhere there is a person or thing that will be permanently satisfying or fulfilling. Such a chimerical belief and the restless desperate seeking that may follow it can be deeply disheartening and self-defeating.

The search for completion in life is a red-herring. In the context of feeling and purpose, completion is the idea that life will be fundamentally different later, after something is completed. For instance, one may feel that social relations will be different after one has 'completed' getting married, or that life will be different after one 'completes' making a lot of money, or that one can start expecting to be treated well after one 'completes' proving oneself. Circumstances change of course, but the feeling of completion never comes. One occaisionally meets people who can report 'content' but never one who can report 'completion.'

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