Perspective Projection - Transformations and Projections in Computer Graphics - page 136

Dot Stereograms
Figure 3.56 illustrates the principle of this interesting method (for a complete descrip-
tion, see [Thimbleby et al. 94]). A three-dimensional scene is projected on a screen and
apoint P 1 is selected at random. The two eyes of the viewer see point P 1 projected
at points Q 1 and Q 2 . We now select another point P 2 such that its projections for the
two eyes are Q 2 and Q 3 .Thus,point Q 2 is both the left-eye projection of P 1 and the
right-eye projection of P 2 .( P 2 must be at the same height as P 1 , which is not obvious
in our two-dimensional figure.) A little thinking shows that most points on the screen
do similar “double duty.” The exceptions are points close to the edges of the screen,
or points whose P 1 or P 2 are hidden by other parts of the scene. Since Q 2 is common
to P 1 and P 2 , we face the question of what color to paint it. In fact, Q 1 , Q 2 ,and Q 3
have to be painted the same color.

Left eye

Q 3

Scene

Q 2

P 2

P 1

Q 1

Right eye

Figure 3.56: Dot Stereograms: The Principle.

The algorithm described in [Thimbleby et al. 94] has to decide what color to paint
each point (dot) on the screen and also to determine the two parents, P 1 and P 2 ,of
each point on the screen.
The result of this algorithm is a stereogram that consists of dots and can be watched
in three dimensions by crossing the eyes, without the need for special glasses or any other
device. There are three types of dot stereograms, as we now discuss.
SIRDS (Single Image Random Dot Stereograms) . This is the oldest type. It
goes back to the pioneering work of Bela Julesz in the 1960s. Such a stereogram consists
of a random pattern of dots, each representing two pixels of the object. Figure 3.57 is
an example of this type of stereogram.
SIS (Single Image Stereograms) . Thisiscurrentlythemostcommontype. The
picture consists of (slightly modified) tiles. This type of dot stereogram is somewhat
more complex to generate, but the basic algorithm is the same.
SIRTS (Single Image Random Text Stereograms) . Thistypeisidenticalto
SIRDS but uses ASCII characters instead of dots. The resulting stereogram has low
resolution.
A dot stereogram is easier to perceive in three dimensions if it is printed on pa-
per rather than displayed on a screen. Here are two simple methods for viewing this
interesting type of stereoscopic image.
In the pull-back method , hold the picture close to and in front of your face. Imagine
that you are looking straight ahead, right through the picture. When your eyes relax and