Stereoscopic depth rendition

Stereoscopic depth rendition specifies how the depth of a three-dimensional object is encoded in a stereoscopic reconstruction. It needs attention to ensure a realistic depiction of the three-dimensionality of viewed scenes and is a specific instance of the more general task of 3D rendering of objects in two-dimensional displays.

Depth in stereograms

A stereogram consists of a pair of two-dimensional frames, one for each eye. Common to both are the widths and heights of objects; their depth is encoded in the differences between right and left eye views. The geometric relationship between an object's third dimension and these position differences is presented below and depends on the location of the stereo-camera lenses and the observer's eyes. Other factors, however, contribute to the depth seen in a stereoscopic view and whether it corresponds to that in the actual object; the act of viewing a stereoscopic display often alters observers' three-dimensional perception.

Stereoscopic reconstruction

The right and left eyes' panels in a stereoscopic reconstruction are created by projection from the principal points of the twin recording camera. The geometrical situation is most clearly understood by analyzing how the screens are generated when a small cubical element of side length dx = dy = dz is photographed from a distance z with a twin camera whose lenses are a distance a apart.

In the left eye panel of the stereogram the distance AB is the representation of the front face of the cube, in the right eye panel, there is in addition BC, the representation of the cube's depth, i.e., the intercept on the screen of the rays from the cameras' principal points to the back of the cube. This interval computes to the first order to

d

z

∗

a

z

{\displaystyle dz*{\frac {a}{z}}}

.