Chapter 2 Principles of Stereoscopic Depth Perception and ...

2.4. Stereoscopic video production
plane defined by Y=0. It is largest at the corners of the image. Vertical parallax
causes what is known as keystone distortion, a depth plane curvature
which makes objects at the corner of the stereoscopic image appear further
away than objects at the centre of the image (Woods et al. 1993). When
properly calibrated, the parallel camera set-up does not produce vertical
disparities, and as a consequence no keystone distortion will occur.
With the stereoscopic formulae discussed here it is possible to determine
precisely the amount of disparity captured in the filming process, translating
real-world object space (X,Y,Z) into CCD 9 (or camera plane) coordinates
(x l ,y l ) and (x r ,y l ). When stereoscopic images are presented on a
display, the CCD coordinates need to be transformed into screen coordinates.
This is achieved by multiplying the CCD coordinates by the screen
magnification factor M, which is the ratio of the horizontal screen width to
the camera sensor width 10 . The subsequent perception of the image space
by the viewer is dependent on a number of viewing factors, with which
we will conclude this chapter.
Stereoscopic viewing factors
Figure 2.13 illustrates the viewing parameters that play a role in the perception
of stereoscopic images. The disparities presented to the observer
are a function of (i) the screen parallax (P), which is the horizontal linear
distance between common (homologous) points on the display surface, (ii)
the distance of the observer to the screen (V), and (iii) the observer’s eye
separation (E), also known as interocular or inter-pupillary distance (IPD).
Variations in IPD for adult males range from 5.77 cm to 6.96 cm, with a median
of 6.32 cm (Woodson 1981). Although usually 6.5 cm is taken as the
average IPD, it is advisable to produce and display stereoscopic video in
such a way that people with smaller eye separations can still comfortably
fuse the stereoscopic scene.
As is illustrated in Figure 2.13, the observed depth Z i of an image point
projected with screen parallax P is equal to the sum of the distance between
the observer and the screen, V, and an offset term, Z m . Through the
use of similar triangles we obtain the following equation:
P
¢
E
(2.14)
Z m V £ Z m 9 Charge Coupled Device - the camera imaging sensor
10 In fact, the screen parallax values are of opposite sign to the CCD disparity values as
the projection onto the camera’s image plane occurs in mirror image through the lens
79