Cool Visual Illusions: Depth Perception and The Power of Shadows

I frequently hear people imply, if they don't state directly, that two working eyes are required for depth perception. This is surprising because with a moment's reflection, it's easy to see that there are depth cues that don't require both eyes. In fact, out of the many, many cues to depth that our visual system uses, only a couple -- convergence, or the relative position of the two eyes, and disparity (though there are two or three different kinds of disparity, depending on who you ask) -- require both eyes. The rest are all monocular.

The most obvious monocular depth cues are size (objects appear larger when they're close than when they're far away) and perspective (as in the converging railroad tracks). Other fairly obvious monocular cues include occlusion, close objects can block parts or all of objects further away, and blur, or as the Wikipedia article calls it, "distance fog," because far off objects appear blurrier than close objects. Then there's my favorite, because the name just sounds cool: motion parallax.

But this post isn't about any of those. It's about shadows. Again, a moment's reflection should make it clear (if you didn't already know) that shadows are good depth cues. An object in front of you that's casting a shadow on another object in front of you is probably in front of that object, and the size and spread of the shadow will tell you something about the distance between the two objects, given a stationary light source, at least. What may surprise you, though, is how powerful a depth cue shadow can be. It's so powerful that it can override many of the more obvious depth cues. So powerful, in fact, that you can get really cool illusions just from mucking around with shadows. Like, say, this one:

This is a simple and, when done right (I couldn't get the damn shadow to blur right, so it's not as strong in my image), a very striking illusion first demonstrated in the lab by Kersten et al.(1. What you should see is a square going up and down. It's strongest, I've found, if you look at the cross in the middle of the square (if you don't see it, try the original. Despite the strong (at least in the original) perception that the square is going up and down, the only thing actually moving in the image is the shadow.

Why does the moving shadow cause the illusory motion of the square? Well, under ordinary circumstances (i.e., when we're not deliberately tricking our visual systems), there are a few conditions under which shadows can move the way they are in the demonstrations: either the light source is moving relative to the shadow-casting object, the viewer is moving relative to the object, the background is moving relative to the object, or the object itself is moving. The illusion implies that our default assumption is that the light source is stationary and the object is moving. Not a bad assumption, really, given that we evolved in an environment consisting almost entirely of stationary,or at least slow-moving, light sources, like the sun or the moon.

My favorite shadow-induced illusory motion demonstrations, however, are the ones that involve moving objects and shadows (first, second, third, fourth) from Kersten, Mamassian, and Knill(2). Stationary versions of the first video show the effect really well (the image is from a PowerPoint presentation by Lawrence Cormack):

The shadows make the balls, which are in fact in the same positions in the two images, look like they're in very different positions. When you add motion, the different positions of the shadows cause the balls to appear as though they're moving on very different trajectories. Perhaps most striking is the fact that, as the second and fourth videos above show, you can make it look like the balls, which in fact follow a straight trajectory, turn, just by changing the position of the shadow at one or more points. These illusions make it appear that our visual system, presumably at a fairly low level, is making assumptions about how objects and their shadows go together, and interpreting scenes accordingly. This interpretation then gets fed into the visual system's (high-level) motion processing, resulting in the illusions.

¹Kersten, D., Knill, D. C., Mamassian, P. and Bülthoff, I. (1996). Illusory motion from shadows. Nature, 279, (6560), 31.
²Kersten, D., Mamassian, P., & Knill, D.C. (1997). Moving cast shadows induce apparent motion in depth. Perception, 26, 171-192.