Lake Palanskoye in northern Kamchatka Peninsula was formed when a large landslide disrupted the drainage pattern, forming a natural dam. Depending on its elevation, each point in the image was shifted slightly. When stereoscopically merged, the result is a vertically exaggerated view of the Earth's surface in its full three dimensions.

A stereogram is an optical illusion of depth created from flat, two-dimensional image or images. Originally, stereogram referred to a pair of stereo images which could be viewed using stereoscope. Other types of stereograms include anaglyphs and autostereograms. Stereogram was discovered by Charles Wheatstone in 1838. He found an explanation of binocular vision which led him to construct a stereoscope based on a combination of prisms and mirrors to allow a person to see 3D images from two 2D pictures.^[1] Oliver Wendell Holmes, Sr. invented an improved form of stereoscope in 1861, which had no mirrors and was inexpensive to produce. These stereoscopes were immensely popular for decades.^[2]

Stereograms were re-popularized by the creation of autostereogram on computers, where a 3D image is hidden in a single 2D image, until the viewer focuses the eyes correctly. The Magic Eye series is a popular example of this. Magic Eye books refer to autostereograms as stereograms, leading most people to believe that the word stereogram is synonymous to autostereogram.^[3] Salvador Dalí created some impressive stereograms in his exploration in a variety of optical illusions.^[4] One of the most common ways to create a stereogram is to hold both of your index fingers in front of you with the tips touching and cross your eyes to create the illusion that you have an extra finger.

[edit] Types

Stereogram of an asiatic hybrid lilium. To view the image cross your eyes until four images appear, then allow the image to converge to a set of three, focusing on the centre image

• Stereoscopic imaging relies on the use of Stereoscope to present a slightly different image to each eye. The stereo pair can be viewed with the naked eye, if the images are placed side by side. The stereo pair is then viewed using the same viewing technique used to see autostereograms.
• Anaglyph images, also recognized as "red/green" or "magenta/cyan" images, combine two stereo images from slightly different viewpoints into a single image. These images may then be viewed with "anaglyph glasses", which use color filters to moderate the light reaching each eye to create the illusion of a three dimensional image.
• Random dot stereograms employ either two stereoscopic images or one anaglyph. The input image (or images) contain random dots with no discernible shapes. When the proper viewing device is used, a hidden 3D scene emerges from these random dots.
• Autostereograms produce an illusion of depth using only a single image. The image is usually generated by computer by repeating a narrow pattern from left to right. By decoupling eye convergence from focusing operations, a viewer is able to trick the brain into seeing a 3D scene.
• SIRDS (Single Image Random Dot Stereogram) is a form of autostereogram where each repeated pattern is altered slightly, creating a hidden image which is not discernible unless the right viewing technique is used.
• Wiggle-gram is an animated computer image which gives 3D percept without using glasses using only a single image. It usually contains a few frames.

[edit] Autostereograms

A random dot autostereogram encodes a 3D scene which can be 'seen' with proper viewing technique. Click on thumbnail to see full-size image.

An autostereogram is an optical illusion of depth usually observed by allowing the eyes to focus behind an image (diverge), but also sometimes in front of the image (converge). These two methods are also known as wall-eyed and cross-eyed, respectively. The slight differences in vertical repetitions of figures or random dots create the illusion of depth in the 2D image, just as the slight difference in perspective between one's eyes creates the perception of depth on 3D objects and scenes.

According to Magic Eye, a maker of autostereograms, "most people prefer the diverging method". However, with normal stereograms, this imposes a limit on the size of the image, since there is a limit to how much the eyes diverge; images created for the cross-eyed method can be larger. If a stereogram is viewed with the wrong method, the depth information is seen 'reversed'; points intended to be in the background appear in the foreground and vice versa.

In this Norman Rockwell painting, a boy is seen using a Holmes-type stereoscope to explore Egyptian historical sites.

[edit] Practical uses

While stereograms have typically been used for amusement, including "3D" movies using anaglyph motion pictures, posters and books of autostereograms, and historical replicas of early stereograms, there are also practical uses of the technologies.

[edit] Education

In the 19th Century, it was realized that stereoscopic images provided an opportunity for people to experience places and things far away, and many tour sets were produced, and books were published allowing people to learn about geography, science, history, and other subjects.^[5] Such uses continued till the mid 20th Century, with the Keystone View Company producing cards into the 1960's.

[edit] Space exploration

This image, captured on June 8, 2004, is an example of a composite anaglyph image generated from the stereo Pancam on Spirit, one of the Mars Exploration Rovers. It can be viewed stereoscopically with proper red/cyan filter glasses. A single 2D version is also available. Courtesy NASA/JPL-Caltech.

The Mars Exploration Rovers, launched by NASA in 2003 to explore the surface of Mars, are equipped with unique cameras that allow researchers to view stereoscopic images of the surface of Mars.

The two cameras that make up each rover's Pancam are situated 1.5m above the ground surface, and are separated by 30cm, with 1 degree of toe-in. This allows the image pairs to be made into scientifically useful stereoscopic images, which can be viewed as stereograms, anaglyphs, or processed into 3D computer images.^[6]

Curious rock with a jutting portion at "Home Plate" via the Mars Spirit Rover. (Animated GIF image for stereoscopic perception).

The ability to create realistic 3D images from a pair of cameras at roughly human-height gives researchers increased insight as to the nature of the landscapes being viewed. In environments without hazy atmospheres or familiar landmarks, humans rely on stereoscopic clues to judge distance. Single camera viewpoints are therefore more difficult to interpret. Multiple camera stereoscopic systems like the Pancam address this problem with unmanned space exploration.

[edit] Clinical uses

Stereograms cards are frequently used by orthoptists and vision therapists in the treatment of many binocular vision and accommodative disorders.^[7]

[edit] Mathematical, scientific and engineering uses

As in the stereopair image of the lake, stereopair photographs are sometimes used to help visualise aerial photographs. Cartographers may also generate stereopairs using computer programs in order to visualise topography in three dimensions.^[8] In biology and chemistry, complex molecular structures are often rendered in stereopairs. The same technique can also be applied to any mathematical (or scientific, or engineering) parameter that is a function of two variables, although in these cases it is more common for a three-dimensional effect to be created using a 'distorted' mesh or shading (as if from a distant light source).

[edit] References

[edit] Further readings

• Scott B. Steinman, Barbara A. Steinman and Ralph Philip Garzia. (2000). Foundations of Binocular Vision: A Clinical perspective. McGraw-Hill Medical. ISBN 0-8385-2670-5

[edit] External links

• BBC's h2g2 entry on 3D Stereograms
• How to create wiggle stereogram
• Make your own stereogram