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Basics of depth perception
Benefits of 3D images
Are 3D images comfortable
Ability to see in 3D
Transparent shapes in 3D

Basics of depth perception
The diagram below was first described by Helmholtz (1867)(1) and describes the basic geometry of binocular vision. It is helpful in thinking about how perception of stereoscopic images works, to a first approximation.

The helmholtz equation of stereo image perception.

The two eyes are on the left and are viewing a pair of corresponding points on the screen plane on the right. The corresponding points, represented in red and green, are fused by the brain to be perceived as a single point in depth, in this case at a distance behind the display plane. The physical disparity on the screen plane is d, the inter-occular separation is E and the viewing distance if  Z. A simple equation derived from Helmholtz's work relating these variables and describing how perceived depth, pd, varies in a stereoscopic image is: 

= Z / ( (E/d) - 1 )

From this we can say that:

1) the larger their viewing distance, Z, the more perceived depth the viewer sees.
2) the more screen disparity, d, the more perceived depth the viewer sees.
3) the smaller their eye separation, E, the more perceived depth the viewer sees.

These statements have a number of consequences that make stereoscopic images fundamentally different from 2D images.

Portability - stereoscopic images are not straightforward to move between different 3D displays.
Images designed to work on projection screens will not usually work on desktop 3D displays and vice-versa because the different viewing distance can radically change the depth representation in the image.
Also an image that works well on a small display may not work on a larger display viewed from the same distance, because the disparity scales up and as a consequence the perceived depth effect can become excessive.

Children - because children have smaller eye separation they will tend to see more depth in a stereoscopic image than adults, this can mean images designed by adults are not comfortable for children to view. And conversely an image designed by a child might appear much flatter to an adult. Even within adults there is a significant range of inter-occular separation, Dodgson (2003).

(1) Page 330 onwards in Volume III, in the section entitled Laws of Stereoscopic Projection.

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