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by W.A. Steer  PhD


Stereograms: introduction

A general introduction to stereograms and their properties, with an example. I attempt a non-technical explanation of how they work and how they are created.

What is an autostereogram?

Autostereograms represent one of the latest approaches to creating the illusion of three dimensions. First seen in their current form in 1990, they differ from earlier 3D technologies in that no special viewing aids are required. All that is necessary is to diverge ones eyes as if looking through the screen or paper showing the picture (which is, admittedly, easier said than done until you get the hang of it).

Blue & black Escher-style swans
Fig.1: Stereogram of rippled surface. The central peak should come towards you. If the centre peak goes away from you then you're looking cross-eyed rather than wide-eyed. Try again!

Note that the depth in a stereogram becomes more pronounced as you move further away, and shallower as you bring your face up to the picture. Try it!

The type of stereograms these articles are concerned with are also known as Single Image Stereograms (SIS), or Single Image Random Dot Stereogram (SIRDS) if the pattern consists of randomly coloured dots. Various companies have produced posters and books of stereograms, under the such names as "Hollusion" and "Magic Eye". Some of the best posters are made by NVision Graphics.

How do autostereograms work?

In normal vision, when looking at a page of text for example, both eyes look at exactly the same place. With a flat page both eyes see practically the same thing and hence the brain concludes that the page is indeed flat. Now an autostereogram picture is basically made up of a pattern which repeats across the width of the page. When you diverge your eyes to "see" it each looks at adjacent repeats of the pattern, but the brain is fooled into believing that both eyes are still looking at exactly the same thing. Since the pattern is not just copied but is subtly distorted on each repeat, (in accordance with the three dimensional image represented), the two eyes see slightly different images. At this point, human perception takes over and the brain concludes that the differing images arise from looking at a three dimensional object, whose form it decodes in an instant. Hence the 3D illusion occurs.

...and how are they made?

By computer of course! Actually, the process is rather simpler than you would imagine. Since the illusion requires you look 'through' the picture, start by considering a pane of glass in place of the picture. Now imagine a pin placed behind the sheet of glass, and a ray drawn from the pin-head to each eye (most peoples eyes are separated by about 7cm or 2.5 inches). Consider the points where the two rays pass through the glass. If the observer and the glass are fixed, then as the pin is moved back those points move apart. When the pin is brought forward, the points come together. Both points always lie on a horizontal line. The distance between the two points on the glass is related to the distance of the pin behind the glass by a simple mathematical formula, known generally as 'similar triangles'.

A stereogram is made by starting with a depth-map describing how deep each part of the scene is. Frequently this can be seen as a grey-scale picture with dark areas representing regions that are furthest away, and nearer objects shown in lighter shades.

Concentric rings in shades of grey!
Fig.2: Depth-map for the above "ripples" stereogram (fig.1).

For each point on the depth-map, corresponding pairs of points on the screen are identified, their separation depending on the depth, and their mean position coinciding with the original point on the depth-map. The pattern is then applied, subject to the constraint that both points in any pair must have the same colour. (Since there are no constraints in the vertical direction, this process can be worked on a line by line basis.)

See also technical description of my algorithms and programs.

Stereo index Homepage

Created: June 1996
Last modified: 23 March 2002

Source: http://www.techmind.org/stereo/sintro.html

©2001 William Andrew Steer