Images commonly referred to as Magic EyeÒ images (after the company that produces them) are actually part of a wider range of computer generated imagery called stereograms, or more specifically Single Image Random Dot Stereograms (SIRDS), also called autostereograms.

Throughout history, people have developed ways to generate more lifelike two dimentional images. Precedents to stereograms include simple depth cues (as in art), stereoscopic photography (which used an instrument called a stereoscope to view two similar but different photographs simultaneously), anaglyphs (which require 3D glasses), and holograms, all of which produced in the viewer the perception of depth upon viewing a two dimentional image. 

Depth perception is ordinarily a result of two processes. The first process, called convergence, directs each eye to focus on a particular object, such that each eye has a different image of the same object. The second process, called stereopsis, is carried out by the brain, which fuses the two different images together to produce the perception of depth.

The research of Bela Julesz (1959) showed that the human brain could perceive depth information without adhering to visual cues. Julesz research centered on the development of random dot stereograms (RDS), which eliminated the depth cues inherent in recognizable images. First, Julesz would generate an image of random dots. Next, he would select a circular area of dots within the image and shift the area slightly to create a different, but similar image of random dots. Finally, Julesz would place the two images side by side to create a stereo pair (a pair of slightly different images). Upon viewing the stereo pair, the viewer would perceive a circle floating above the background. This is how the brain accounts for the difference in the stereo pair. 

Whereas Julesz research proved that depth perception could arise solely as a result of stereopsis, Tyler and Clarke, in 1979, discovered that a separate pair of images is not needed for stereopsis to occur. The research of Tyler and Clarke effectively explained the "wallpaper effect," a 3D effect produced by staring cross-eyed at wallpaper. Essentially, the "walpaper effect" is a focusing error. Typically, the eyes will converge onto a single point. But given a repeating pattern, the brain might be confused to the extent that the eyes "focus" onto two different, but identical points in the pattern. The brain will then perceive depth because the actual convergence point is somewhere behind the pattern. As a result, the perceived depth can be controlled by altering the period of the repeating pattern (the distance between each unit pair).

Single Image Random Dot Stereograms (SIRDS) make use of brain mismatching when viewing a repeating pattern. The difficulty in perceiving depth in SIRDS lies in the fact that the viewer’s eyes must lock onto different parts of the repeating pattern. Ordinarily, the eyes will converge onto the same point. By defocusing the eyes (one tactic is to look "through" the two dimensional image) it is possible to bypass convergence and experience depth in a repeating pattern. It is also possible to stare "cross-eyed" at an autostereogram to percieve depth, though the image you would percieve would be inverted from its intended depth. 

It is only possible to generate SIRDS by using computer imaging techniques. First, a three dimensional drawing is created. Next, a repeating pattern is generated to cover over the 3D image. Finally, the computer uses an algorithm to orient the period of the repeating pattern to the intended depth of the 3D image. In this way, the brain receives depth information from the repeating pattern, and from that information, generates the 3D image contained within. 

[Tony, Erin, Brian, Ryan]