An autostereogram is a single-image stereogram (SIS), designed to create the visual illusion of a three-dimensional (3D) scene from a two-dimensional image in the human brain. In order to perceive 3D shapes in these autostereograms, the brain must overcome the normally automatic coordination between focusing and vergence.

The simplest type of autostereogram consists of horizontally repeating patterns and is known as a wallpaper autostereogram. When viewed with proper vergence, the repeating patterns appear to float above or below the background. The Magic Eye books feature another type of autostereogram called a random dot autostereogram. One such autostereogram is illustrated above right. In this type of autostereogram, every pixel in the image is computed from a pattern strip and a depth map. Usually, a hidden 3D scene emerges when the image is viewed with the correct vergence.

Autostereograms are similar to normal stereograms except they are viewed without a stereoscope. A stereoscope presents 2D images of the same object from slightly different angles to the left eye and the right eye, allowing the brain to reconstruct the original object via binocular disparity. With an autostereogram, the brain receives repeating 2D patterns from both eyes, but fails to correctly match them. It pairs two adjacent patterns into a virtual object based on wrong parallax angles, thus placing the virtual object at a depth different from that of the autostereogram image.

There are two ways an autostereogram can be viewed: "wall-eyed" and "cross-eyed". The terms "cross-eyed" and "wall-eyed" are borrowed from synonyms for various forms of strabismus, a condition where eyes do not point in the same direction when looking at an object. Wall-eyed viewing is informally known as parallel-viewing.] Most autostereograms (including those in this article) are designed to be viewed in only one way, which is usually wall-eyed. Wall-eyed viewing requires that the two eyes adopt a relatively parallel angle, while cross-eyed viewing requires a relatively convergent angle.


In 1838, the British scientist Charles Wheatstone published an explanation of stereopsis (binocular depth perception) arising from differences in the horizontal positions of images in the two eyes. He supported his explanation by showing pictures with such horizontal differences, stereograms, separately to the left and right eyes through a stereoscope he invented based on mirrors. When people looked at these flat, two-dimensional pictures, they experienced the illusion of three-dimensional depth.Pinker, S. (1997). The Mind's Eye. In "How the Mind Works" (pp. 211–233). ISBN 0-393-31848-6] [ [ - The Library: Wheatstone Paper 1838 ] ]

Between 1849 and 1850, David Brewster, a Scottish scientist, improved the Wheatstone stereoscope by using lenses instead of mirrors, thus reducing the size of the contraption.

Brewster also discovered the "wallpaper effect". He noticed that staring at repeated patterns in wallpapers could trick the brain into matching pairs of them as coming from the same virtual object on a virtual plane behind the walls. This is the basis of wallpaper-style "autostereograms" (also known as single-image stereograms).

In 1959, Bela Julesz, a vision scientist, psychologist and MacArthur Fellow, invented the random dot stereogram while working at Bell Laboratories on recognizing camouflaged objects from aerial pictures taken by spy planes. At the time, many vision scientists still thought that depth perception occurred in the eye itself, whereas now it is known to be a complex neurological process. Julesz used a computer to create a stereo pair of random-dot images which, when viewed under a stereoscope, caused the brain to see 3D shapes. This proved that depth perception is a neurological process.Julesz, B. (1971). "Foundations of Cyclopean Perception". Chicago: The University of Chicago Press. ISBN 0-226-41527-9] Shimoj, S. (1994). Interview with Bela Julesz. In Horibuchi, S. (Ed.), "Super Stereogram" (pp. 85–93). San Francisco: Cadence Books. ISBN 1-56931-025-4]

In 1979, Christopher Tyler of Smith-Kettlewell Institute, a student of Julesz and a visual psychophysicist, combined the theories behind single-image wallpaper stereograms and random-dot stereograms to create the first "random-dot autostereogram" (also known as single-image random-dot stereogram). This type of autostereogram allows a person to see 3D shapes from a single 2D image without the aid of optical equipment.Magic Eye Inc. (2004). "Magic Eye: Beyond 3D". Kansas City: Andrews McMeel Publishing. ISBN 0-7407-4527-1] Tyler, C.W. (1994). The Birth of Computer Stereograms for Unaided Stereovision. In Horibuchi, S. (Ed.), "Stereogram" (pp. 83–89). San Francisco: Cadence Books. ISBN 0-929279-85-9]

How they work

Simple wallpaper

Stereopsis, or stereo vision, is the visual blending of two similar but not identical images into one, with resulting visual perception of solidity and depth. [Cassin, B. and Solomon, S. "Dictionary of Eye Terminology". Gainsville, Florida: Triad Publishing Company, 1990.] In the human brain, stereopsis results from complex mechanisms that form a three-dimensional impression by matching each point (or set of points) in one eye's view with the equivalent point (or set of points) in the other eye's view. Using binocular disparity, the brain derives the points' positions in the otherwise inscrutable z-axis (depth).

When the brain is presented with a repeating pattern like wallpaper, it has difficulty matching the two eyes' views accurately. By looking at a horizontally repeating pattern, but converging the two eyes at a point behind the pattern, it is possible to trick the brain into matching one element of the pattern, as seen by the left eye, with another (similar looking) element, beside the first, as seen by the right eye. With the typical wall-eyed viewing, this gives the illusion of a plane bearing the same pattern but located behind the real wall. The distance at which this plane lies behind the wall depends only on the spacing between identical elements.Andrew A. Kinsman (1992). "Random Dot Stereograms". Rochester: Kinsman Physics. ISBN 0-9630142-1-8]

Autostereograms use this dependence of depth on spacing to create three-dimensional images. If, over some area of the picture, the pattern is repeated at smaller distances, that area will appear closer than the background plane. If the distance of repeats is longer over some area, then that area will appear more distant (like a hole in the plane).

People who have never been able to perceive 3D shapes hidden within an autostereogram find it hard to understand remarks such as, "the 3D image will just pop out of the background, after you stare at the picture long enough", or "the 3D objects will just emerge from the background". It helps to illustrate how 3D images "emerge" from the background from a second viewer's perspective. If the virtual 3D objects reconstructed by the autostereogram viewer's brain were real objects, a second viewer observing the scene from the side would see these objects floating in the air above the background image.

The 3D effects in the example autostereogram are created by repeating the tiger rider icons every 140 pixels on the background plane, the shark rider icons every 130 pixels on the second plane, and the tiger icons every 120 pixels on the highest plane. The closer a set of icons are packed horizontally, the higher they are lifted from the background plane. This repeat distance is referred to as the depth or z-axis value of a particular pattern in the autostereogram. The depth value is also known as Z-buffer value.

Autostereograms where patterns in a particular row are repeated horizontally with the same spacing can be read either cross-eyed or wall-eyed. In such autostereograms, both types of reading will produce similar depth interpretation, with the exception that the cross-eyed reading reverses the depth (images that once popped out are now pushed in).

However, icons in a row do not need to be arranged at identical intervals. An autostereogram with varying intervals between icons across a row presents these icons at different depth planes to the viewer. The depth for each icon is computed from the distance between it and its neighbor at the left. These types of autostereograms are designed to be read in only one way, either cross-eyed or wall-eyed. All autostereograms in this article are encoded for wall-eyed viewing, unless specifically marked otherwise. An autostereogram encoded for wall-eyed viewing will produce incoherent 3D patterns when viewed cross-eyed. [If a two-image stereogram designed for wall-eyed viewing is viewed cross-eyed, all details on the Z-axis will be reversed - objects that were meant to be seen to rise above the background will appear to sink into it. However, in an autostereogram, repeated patterns generally interfere with one another, causing incoherent 3D shapes.] Most Magic Eye pictures are also designed for wall-eyed viewing.

The following wall-eyed autostereogram encodes 3 planes across the x-axis. The background plane is on the left side of the picture. The highest plane is shown on the right side of the picture. There is a narrow middle plane in the middle of the x-axis. Starting with a background plane where icons are spaced at 140 pixels, one can raise a particular icon by shifting it a certain number of pixels to the left. For instance, the middle plane is created by shifting an icon 10 pixels to the left, effectively creating a spacing consisting of 130 pixels. The brain does not rely on intelligible icons which represent objects or concepts. In this autostereogram, patterns become smaller and smaller down the y-axis, until they look like random dots. The brain is still able to match these random dot patterns.

The distance relationship between any pixel and its counterpart in the equivalent pattern to the left can be expressed in a "depth map". A depth map is simply a grayscale image which represents the distance between a pixel and its left counterpart using a grayscale value between black and white. By convention, the closer the distance is, the brighter the color becomes.

Using this convention, a grayscale depth map for the above autostereogram can be created with black, gray and white representing shifts of 0 pixels, 10 pixels and 20 pixels, respectively. A depth map is the key to creation of random-dot autostereograms.




When a series of autostereograms are shown one after another, in the same way moving pictures are shown, the brain perceives an animated autostereogram. If all autostereograms in the animation are produced using the same background pattern, it is often possible to see faint outlines of parts of the moving 3D object in the 2D autostereogram image without wall-eyed viewing; the constantly shifting pixels of the moving object can be clearly distinguished from the static background plane. To eliminate this side effect, animated autostereograms often use shifting background in order to disguise the moving parts.

When a regular repeating pattern is viewed on a CRT monitor as if it were a wallpaper autostereogram, it is usually possible to see depth ripples. This can also be seen in the background to a static, random-dot autostereogram. These are caused by the sideways shifts in the image due to small changes in the deflection sensitivity (linearity) of the line scan, which then become interpreted as depth. This effect is especially apparent at the left hand edge of the screen where the scan speed is still settling after the flyback phase. This effect is absent from a TFT LCD.

This technique was used as one of the possible 3-D viewing methods in the Magic Carpet series.

Mechanisms for viewing

Much advice exists about seeing the intended three-dimensional image in an autostereogram. While some people can simply see the 3D image in an autostereogram, others must learn to train their eyes to decouple eye convergence from lens focusing.

Not every person can see the 3D illusion in autostereograms. Because autostereograms are constructed based on stereo vision, persons with a variety of visual impairments, even those affecting only one eye, are unable to see the three-dimensional images.

People with amblyopia (also known as lazy eye) are unable to see the three-dimensional images. Children with poor or dysfunctional eyesight during a critical period in childhood may grow up stereoblind, as their brains are not stimulated by stereo images during the critical period. If such vision problem is not corrected in the early childhood, the damage becomes permanent and the adult will never be able to see autostereograms. It is generally thought that amblyopia is a permanent condition, but [ NPR] reports a case where a patient with amblyopia regains stereo vision] It is estimated that some 1% to 5% of the population is affected by amblyopia. [cite web|url= |title=Amblyopia - prevalence, natural history, functional effects and treatment |accessdate=2006-07-17 |first=Ann |last=Webber |coauthors=Joanne Wood | work=Clinical and Experimental Optometry | year=2005 |month=November]

3D perception

Depth perception results from many monocular and binocular visual clues. For objects relatively close to the eyes, binocular vision plays an important role in depth perception. Binocular vision allows the brain to create a single Cyclopean image and to attach a depth level to each point in the Cyclopean image.

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