Dynamic Amodal Completion Through the Magic Wand Illusion

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.


Dynamic Amodal Completion through the Magic Wand Illusion
This article provides an analysis of the Magic Wand illusion (Fig. 1), in which an object is revealed relative to its background by a 'Magic Wand' waving behind the object but in front of the background (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 across all parts of the object, allowing the whole structure to be completed by cumulation over time. In the terms developed by Michotte, Thinès & Crabbé (1964), the overlying triangle is perceived by modal completion (or illusory perception of the overlying implied object) while 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 illusion is subject to the same 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. (Although, 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.)

A B
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 Fig. 1B. Now the retinal afterimage in each stripe of the moving bar is cancelled 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.
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 non-intersecting 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 ( Fig. 2A). However, in combination with the solid block triangle figure elicited by the moving wand, the depth-ambiguous Impossible Triangle is revealed (Fig. 2B, 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 the Illusory Impossible Triangle is elicited by the occlusion of the three spheres in the movie (Film Clip V), designed to evoke the concept of the modal/amodal completion principles of the Kanisza Triangle in combination with the Impossible Triangle. This These two versions therefore a case ofshow the Magic Wand effect giving rise to the dynamic Illusory Impossible Triangle.

Relation to the Plateau illusion.
As early as 1829, Jean Plateau described a dynamic form of amodal completion (Plateau, 1829) that was a literal form of the Biblical metaphor of the "camel passing through the eye of a needle". A silhouette ("the camel") is passed behind a narrow vertical slit ("the needle"), such that the viewer only sees the upper and lower boundary points through the slit at any given moment in time. Cumulation of their positions over time can recover the full profile of the silhouette in perception, even though it never existed on the retina, constituting a dynamic form of amodal completion developed before the concept of amodal completion had been enunciated by Michotte, Thinès & Crabbé (1964) over a century later. Plateau's focus was on the compressive distortion of the form perceived under these conditions (termed the "anorthoscopic effect"), but no such distortion is evident in the inverse version described here, underlining a core difference between the two effects.