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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004
Left image
Right image
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e : interocular distance (eye base) ON
v : viewing distance .e
S : light line pitch
D : distance between light lines and pixels
P : pixel width
Figure 1. Principle of parallax barrier autostereoscope.
Wa =
3. AUTOSTEREOSCOPIC EFFECT
3.1 3D Viewing Zone
The principle of the above autostereoscopic technology implies
that a viewer can only acquire stereoscopic effect in certain
locations and range, which is hereafter referred as viewing
zones (Son et al, 2003). This will be studied geometrically as
shown below.
The 3D geometry of viewing zones for a general
autostereoscopic display panel is depicted in Figure 2, where
the origin of the coordinate (x, y, z) is located at the central
point of the monitor, W and H are respectively the width and
height of the monitor. The lights emerging from both the left
and right images cross cach other and illustrate multiple
viewing zones that are shaped to different volumetric diamond
structures. The optimum viewing zones with horizontal parallax
are located along the nominal viewing line parallel with x-axis
and at the viewing distance v away from the display plane. For
an autostereoscopic system, the value of v has been optimized
according to the pitch of the barrier or the lenticular. In general,
the number of the optimum viewing zones, N, is limited by We,
where e is the eye base. Therefore, the n optimum viewing
zones located left or right alternately from the center (0,0,v)
could be denoted by n = +1, + 2,..+ N/2 . Each diamond-type
viewing zone can be regarded as the combination of two
triangular pyramids which are referred as front pyramid and
rear pyramid. For convenience, in Figure 3 we draw the
projection of the viewing geometry on the xz-plane and show
the projection of the pyramids as front triangle and rear triangle,
respectively.
In Figure 3 the light from (W/2, 0, 0) to (0, 0, v) is denoted by
R, and each light from (W/2, 0, 0) to (ne, 0, v) is denoted by R,
Similarly the light from (-W/2, 0, 0) to (0, 0, v) is represented
by L, and each light from (-W/2, 0, 0) to (ne, 0, v) is
represented by L,. Because the ideal width of the viewing zone
under 2D projection is the average eye base, viewers can move
their heads freely inside each viewing zone. Consequently, it is
necessary to estimate the volume of each 3D diamond shape as
the movement boundary for operators implementing the
photogrammetric practices.
Figure. 2. 3D viewing zones for an autostereoscopic display
Monitor ) >
Rcar triangle —- Front triangle
if d | R n-1 Ly
AN ENS i (n-1)e ne
Ro I jb RaL; R,-1 Ra La L.
Z
Figure 3. Projection of the viewing geometry on xz-plane with
front triangle and rear triangle in viewing zone.
Based on the 3D coordinate system shown in Figure 2 and its
xz-projection shown in Figure 3, we can address the range of
viewing zone and the movement boundary for viewers. Let h,
represent the distance between the pixel and x-axis on xy-plane
at z=0 and A, denote the distance between operator's eyes and
x-axis on xy-plane at z=v . For the front triangle, the
coordinates of triangle points (n-/)e, ne and /n are defined by
the following coordinate pairs
((n-1)e, h,, v),
(ne, h,, v),
We(2n —1) Wh, + eh p Wv
1
2IW +e)’ We We th
Based on this, we can calculate the volume of front pyramid as
WevH /(6W -- 6e) and the area of front triangle as
Wev/(2W +2e) .
points (n-1)e, ne and 7, are
((n-1)e, h,, v),
(ne, he, V),
We(2n-1) Wh,-eh, w
XW-e)' W-e 'W-e
The volume of rear triangular pyramid is WevH /(6W — 6e) and
Similarly, the coordinates of rear triangle
)- (2)
