EARLY GESTALT psychologists—including Stuart Anstis of the University of  California, San Diego, and the late Hans Wallach—were intrigued by what they referred to as the Barber Pole Illusion (a). A vertical cylinder with spiraling red and white stripes painted on its surface is made to spin on its long axis. Even though the stripes are actually moving horizontally, around the pole, they appear to move vertically (up or down the pole, depending on direction of spin).

The illusion is a powerful demonstration of the point we have made repeatedly in this column—perception does not mimic physics. It involves the brain’s interpretation—derived from an image on the retina located at the back of the eye—to pass judgment on what is happening out there in the world. But what causes the illusion?

Let us consider a simpler case: a card painted with vertical stripes moving horizontally behind a circular aperture (b). Here the outer margins of the striped card are shown schematically to make it clear what is going on behind the aperture. They would not be visible, however, when the actual display is viewed. You can make this simple setup at home by cutting from a large piece of cardboard a circular aperture, say one to two inches in diameter. Then use a second, smaller cardboard with vertical stripes, alternating white and red, about four to six stripes to an inch. Have someone else move the striped card back and forth along any axis while you look at the stripes within the aperture and judge their direction of motion.

If the striped cardboard is moved horizontally, then, not surprisingly, you will see the stripes moving horizontally. But if the stripes were actually moving diagonally at a faster speed, the stimulus on the retina would be exactly the same. In fact, there is a family of vectors (that is, directional movements) of varying speeds and orientations that would all produce the same changing image on the retina. This family of vectors is indicated in b by arrows of different lengths, which represent speed and direction. Yet even though the stimulus itself is ambiguous, your perception is not; you always see the stripes moving orthogonally to their orientation; it seems to be the default for our perception, other things being equal. You do not see the stripes moving diagonally at a higher speed. The brain solves the so-called aperture problem by assuming a default.

Inside the Box
Now let us reconsider a stimulus like the barber pole—that is, one in which the aperture is rectangular and vertical, and the stripes are diagonally oriented (c). As you try the same experiment with this new setup, you might expect that the default perception will be the same—of motion perpendicular to the stripes’ orientation. But it is not; you do not see diagonal motion. Instead, these stripes invariably appear to move vertically along the aperture’s long axis (as in the barber pole). Why?

One reason may be that there is an additional factor at work in this case. Notice that even though the direction (and velocity) the stripes move in is still ambiguous, the tips (or sharp endpoints) of the lines are moving unambiguously upward along the long axis of the aperture (or cylinder, in the case of a real barber pole). The motion of these “terminators” may help disambiguate the direction of movement; the tips “drag” the stripes in a single upward direction, an effect that some researchers refer to as “motion capture.” This phenomenon explains the Barber Pole Illusion. You might say that unambigious motion tips off the brain and dictates that the entire stripe pattern be seen moving (arrows in c) along the length of the pole, whether that pole is horizontal or vertical.

We can challenge the visual system by creating a display such as d, which is made of a randomly scattered group of vertical and horizontal apertures behind all of which stripes are moving diagonally. If you focus on any one of the openings, you will see either horizontally or vertically moving stripes, as expected. But with a bit of effort, you can make yourself see the entire display as a “whole.” In that case, you perceive the tout ensemble as a single large diagonally moving set of stripes seen through a giant opaque card from which horizontal and vertical apertures have been cut out in random locations. Your visual system “thinks” this perception is a more economical description of the data than is the vision of independent barber poles scattered in the world in precisely this manner by some mad Martian intent on confusing you. Your immunity to seeing independent barber poles implies that some fairly complex rules of image segmentation (including “completion” of the striped surface behind horizontal and vertical windows) must be wired into the visual system.

Where Constraints Intersect
Or take another example. In e you will tend to see motion 45 degrees up and to the right, and in f 45 degrees down and to the right, as indicated by the arrows.

Now what if you superimpose the two? Do you see them sliding past each other at right angles? The answer is no; you see the plaid moving horizontally (indicated by arrow in g). Perception researchers Edward H. Adelson of the Massachusetts Institute of Technology and J. Anthony Movshon of New York University have done some clever experiments to show that, contrary to naive intuition, this effect does not happen simply by averaging the vectors of the two stripes. It happens because of a principle they dubbed “intersection of constraints.” Each grating’s motion is compatible with a family of vectors, and the region of overlap—where the two families overlap—is taken as the “true” direction of motion. Intriguingly, motion-sensitive cells in areas of the brain (including one called MT) at work early in the visual hierarchy of motion processing respond to the direction of each grating separately (“component motion”), whereas cells at a higher level respond to the overall direction of the plaid (“plaid motion”). It is as though the cells were integrating the output of the component sensitive cells by deploying the intersection-of-constraints algorithm.

There is an alternative model to the intersection of constraints. Notice in g that even though the motion of the component stripes is ambiguous the intersections between the lines are moving unambiguously horizontally. These crossover points might “capture” and drag along the gratings horizontally (analogous to the role of the sharp tips in the vertical aperture or barber pole).

At present, no compelling reason exists to choose one model over the other; the former (intersection of constraints) is more mathematically elegant and might appeal to a cosmologist, whereas the latter (a messy “shortcut”) might appeal to a biologist.

The original barber pole pattern is supposed to depict blood and bandages, harking back to an era when barbers were also surgeons. Little did they realize that the illusion could provide such razor-sharp insights into human motion perception.