This paper reflects the research and thoughts of a student at the time the paper was written for a course at Bryn Mawr College. Like other materials on Serendip, it is not intended to be "authoritative" but rather to help others further develop their own explorations. Web links were active as of the time the paper was posted but are not updated.
2000 Third Web Report
The first thing I needed to know in order to figure that out was how to view real stereograms, and why some people can't see the hidden image. The first step to viewing a stereogram is to have stereo vision-in other words, two eyes that function as a team (1). This leaves out people who have lost an eye, people with amblyopia (a "lazy eye") and people with strabismus (eye turns, such as "wall eyes" or "crossed eyes") (2). In theory, therefore, anyone who has two normal eyes can see a stereogram picture. Try to convince someone who's never been able to see one of that fact, however, and they'll never believe you. I know from personal experience that there are some people out there who, no matter how long they stare at a stereogram, simply don't see any hidden images, despite the fact that they have two functional eyes. This is probably because those people are unable to perfect the viewing technique-most stereograms are drawn so that in order to see the hidden image, you have to focus your eyes on a point about twice as far away from you as the picture itself. This is called "parallel viewing," because the lines of sight of the eyes are almost parallel where they intercept with the stereogram picture. Parallel viewing is difficult for many people, simply because it requires the viewer to focus on an invisible point different from what they are looking at. Another way of focusing on stereogram pictures is "cross viewing," in which the lines of sight of the eyes are crossed about halfway between the viewer and the picture. This way of viewing, however, produces images that look punched in rather than sticking out, unless the stereogram has been specifically made for cross viewing (3).
Fortunately, there are several tips that have been found to make parallel viewing easier. There's the pull-back method, in which the viewer puts their nose right up to the picture. The eyes can't focus on the image when it's that close, so when the viewer pulls slowly back from the stereogram, still looking through the picture and not at it, they should be able to see the hidden image. Another method is the wall method. In this method, the viewer focuses on something like a nail or a hook on a wall, slightly above the top edge of the picture. Then the viewer slowly lifts the stereogram, keeping the eyes focused on the more distant object. Hopefully, the viewer should then be able to see the hidden image (4). Another method that's often used is the glare method. This requires a piece of glass or plastic that produces a reflection. The viewer puts the image behind the reflective surface (stereograms on the computer screen work well, also), and focuses on their reflection in the glass rather than the picture itself. This produces the parallel viewing effect also. In addition to all of these methods to achieve parallel viewing, there is also a method to help the viewer achieve cross viewing, called the single finger method. This method requires four circles on a piece of paper, or on the computer screen, arranged in concentric pairs. The viewer puts a finger about six inches away from his or her face, then focuses on it. The viewer should then move his or her finger until it almost touches the circles, then shift the focus from the finger to the circles. There should appear to be three pairs of concentric circles, and the middle circle of the middle pair should appear to be popping out (3).
The second step to finding answers to my questions was to find out how stereograms are formed. As it turns out, they're not exactly random dot patterns. Back in 1959, a man named Dr. Bela Julesz discovered how to create a stereogram. You begin with a rectangle made up of dots placed into a random pattern. Then you pick out a group of dots that form a certain shape, such as a heart. Then you replicate the original rectangle but shift the dots within the heart shape to the left. When the rectangles are viewed side by side in the proper viewing method, the heart appears to "pop out." In 1979 a student of Dr. Julesz discovered that the offset method could be applied to a single image, and that was the first single-image, random dot stereogram (5). These pictures progressed from there, as different colors and more complicated hidden images were created, but as is evidenced by Dr. Steward Inglis on his website, it's easy to make your own simple stereogram (see linked site) (4).
The most crucial element to discovering answers to my previous questions, however, is understanding how the brain actually makes sense of 3D, both in life and in the stereogram pictures. In the case of a real three dimensional object, the views from each eye put together create not only x and y coordinates in the brain, but also a z coordinate, which is what gives us depth perception. This happens because the image in the left eye seems to shift when viewed with the right eye, and the larger the shift the closer the object is to the viewer. The brain, when given the two views from the eyes, associates the x's and the y's from each view, then makes sense of that information by perceiving the third dimension. Luckily for the Magic Eye company, the brain can easily be tricked. When the two views of a stereogram reach the brain, is matches up the x's and y's, and makes sense of the shift by producing a three dimensional image. Hooray for fooling the human brain (4)!
Based on all of this information, it's pretty easy to understand why, when I use the parallel method to look at something that wasn't meant to be a stereogram (for instance, the rug in the Bio 103 lecture room), my brain perceived waviness. All that's required is a pattern of randomly arranged dots, some of which are shifted to the left. In the example of the rug in the lecture room, there are probably some threads of the rug, which were shifted when it was manufactured. Any rug with a random pattern of different colored threads could be viewed this way; the shift could be produced by inexact manufacturing, or in the instance of a shag rug, by people treading on it. So, it seems obvious that any random dot pattern with some sort of shift can be viewed in three dimensions. Unfortunately, people who don't realize this are definitely going to wonder why I stare at carpeting....
2); Why Some People Can't See 3D-Lazy Eye, Amblyopia, Strabismus, Esotropia, Exotropia, Double Vision , A smaller part of site 1.
3) How to See 3D: Magic Eye 3D and More , Another smaller part of site 1.
4) Faber's Home Page-Stereogram FAQ , An FAQ site put up by a Computer Science PhD.
5) Frequently Asked Questions , ; the FAQ page on the Magic Eye website.
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