Feature

Eyeing Up the Magic Eye

Everyone's going cross-eyed over autostereograms.

Stuart Inglis and Ian Witten

Binocular vision is a useful thing, giving animals, including humans, the ability to perceive depth and distance in everyday life. The slightly different images of the world received by each eye are "fused" cooperatively to produce a single image with all the depth cues that make up the three-dimensional world. It's a little trickier to produce the same depth in the two-dimensional world of a flat image, but recent developments overseas and in New Zealand have provided the opportunity to open a "magic eye" onto the world of autostereograms.

Stereo pictures began with Wheatstone's invention in 1838 of the "stereoscope", an optical instrument similar to binoculars through which a viewer looks at a pair of photographs taken from differing viewpoints and fuses them into a full three-dimensional image. An early suggestion for a colour stereo display involved a rotating colour filter wheel in front of the eyes. In 1962 Bela Julesz, a psychologist, discovered that the 3D illusion can be sustained even when the photographs in a stereoscope are replaced by random dot images, provided that the dots are displaced slightly in a way that simulates the viewing of a cloud of points from different eye positions.

Until recently it seemed that stereo viewing inevitably required two separate pictures, or at least some method of splitting a single picture into two to give each eye a different view (using, for instance, red/green filters, polarized light, or interference as in holograms). However, in 1990 two US researchers discovered that it is possible to combine a pair of random dot stereograms together into one image, the result being called a "single image random dot stereogram" (SIRDS) or an "autostereogram". To generate an autostereogram, each point on the solid object to be viewed is mapped on to two points in the image plane.

It turns out that very convincing images with vivid depth can be constructed in this way, and the advantage of this ingenious approach is that no special viewing equipment is required. It is this technique that has been utilised in the popular Magic Eye series of books and stationery items. It does take a little practice to see depth in the pictures, but the experience is very satisfying when first achieved.

The process of viewing three dimensional pictures from single paper or screen images has recently been refined by researchers in the computer science department at Waikato University. In collaboration with colleague Harold Thimbleby during his recent visit from Stirling University in Scotland, we have developed a new way of generating these autostereograms.

Last year, we were able to make several improvements to the original autostereogram generation algorithm. We corrected the depth calculation and fixed an asymmetry in the viewing calculation. The asymmetry meant that some people could see the intended image only when the picture was held upside down, as the initial randomly selected strip of dots has a directional bias.

We also incorporated the removal of the "hidden surfaces" that are caused by one part of a 3D scene obscuring another. It might be only a technical detail but it has the advantages of simplifying the "coding" of the image and providing greater flexibility in allocating colours when these are used. It also removes visible "echoes" which can combine in complex and systematic ways across an autostereogram in a distracting or misleading fashion.

As well as providing a popular pastime and some interesting possibilities for artists, autostereograms are opening up a new line of interesting experiments with optical illusions that could teach us more about the meeting place between the geometry and perception of vision.

An Example

Consider the following situation. In the background there is a solid object with two black dots on it. Between the object and the viewer's eyes, there is a sheet of glass (the "image plane"). Assume the eyes stay focused on the object.

Draw a line from each eye to each dot. These four lines all pass through the sheet of glass If you put black dots on the glass where the lines pass through, the eyes get the same information from the dots on the glass as they do from the dots on the object.

If the dots are carefully placed on the object, the lines from the left eye to the right dot and right eye to left dot intersect as they pass through the glass -- thus there need only be three dots on the glass, as one of them is doing double duty.

Now put more carefully-placed pairs of dots on the object. You can then put more triplets of dots on the glass, as above. The dots on the glass still convey the same information as the dots on the object as long as the eyes stay focused on the position of the object. Each dot in a pair must be the same colour for this to work, though different pairs can be different colours.

Do this with enough dots on the object, and the dots on the glass will contain a reasonable 3-D image of the object. Now take the real object away. As long as the eyes stay focused correctly, they still perceive the object in three dimensions. Looking at the glass won't work -- it's necessary to look beyond it to where the object used to be.

Stuart Inglis works in Waikato University's Department of Computer Science.
Ian Witten works in Waikato University's Department of Computer Science.