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See Inside July/August 2009

Seeing in Stereo: Illusions of Depth

Binocular vision gives us depth perception—and enables us to play some tricks

ALL PRIMATES, including humans, have two eyes facing forward. With this binocular vision, the views through the two eyes are nearly identical. In contrast, many other animal groups, especially herbivores such as ungulates (hooved animals, including cows, sheep and deer) and lagomorphs (rabbits, for example), have eyes pointing sideways. This perspective provides largely independent views for each eye and an enormously enlarged field of view overall. Why did primates sacrifice panoram­ic vision? What benefit did they gain?

We know binocular vision evolved several times independently in vertebrates. For example, among birds, predatory species such as owls and hawks have forward-pointing eyes. One theory is that the feature conferred a statistical advantage—two eyes are better than one—for detecting and discriminating objects, such as prey, in low light levels. But whatever the original reason for its emergence, the evolutionary novelty afforded a huge advantage: stereoscopic (literally, solid) vision.

Shifting Views
How does it work? Even though both your eyes point forward, they are separated horizontally so that they look at the world from two slightly different vantage points. It follows that each eye receives a slightly different picture of the three-dimensional scene around you; the differences (called retinal disparities) are proportional to the relative distances of the objects from you. Try this quick experiment to see what we mean: hold two fingers up, one in front of the other. Now, while fixating on the closer finger, alternately open and close each eye. You’ll notice that the farther the far finger is from you (don’t move the near finger), the greater the lateral shift in its position as you open and close each eye. On the retinas, this difference in line-of-sight shift manifests itself as disparity between the left and right eye images.

A simplified example shows this effect clearly. When you look at the pyramid, the right eye sees more of the right side than the left eye does, and vice versa; it is a simple consequence of geometric optics. Notice that the images in the two eyes are correspondingly different; the inner square is shifted right or left. This retinal disparity is proportional to the height of the pyramid. The brain measures the difference and experiences it as stereoscopic depth.

Although this explanation seems patently obvious today, it wasn’t elucidated until the 19th century. Leonardo da Vinci attempted to explain it several ­hundred years earlier and correctly observed that because the eyes normally receive different views of a 3-D scene, it is impossible, even in principle, to convey a full sense of 3-D on a 2-D canvas. Leo­nardo puzzled over how we can see a single world of solid objects given the different eye views (now known as Leonardo’s paradox), but he failed to grasp the critical point that retinal disparity is not a problem but is the basis for stereopsis.

This fact was finally made clear in 1838 by English physicist Charles Wheatstone, who published an elegant series of experiments on binocular vision. Recognizing the difference in perspective of the left and right eyes, he began by making line drawings of each eye’s view of simple objects. Then, employing a device he invented, called a mirror stereoscope, he presented these line drawings together to the viewer: left view to left eye alone; right view to right eye alone. Imagine his astonishment—and delight!—when he saw the skeletal outline of the object spring into 3-D relief, looking like he could almost reach out and grab it. It must have been the same sense of wonder every child experiences when playing with a stereo viewer such as the familiar View-Master. It seems like magic.

But how exactly does the brain blend the two eyes’ slightly different pictures harmoniously into a single fused picture? And how does it measure and extract the differences to allow for seeing in stereo? On one hand, it needs to unify the pictures; on the other hand, it needs to preserve and measure their differences.

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