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E
i
positions. Given that vision axes are not necessarily orthogonal to the observed
images area (ROI), the viewing of these images induces trapezoidal distortion if we
don't take into account this slanted viewing during the shooting. This has an im-
mediate consequence in order to achieve depth perception. If the trapezoidal distor-
tions are not similar for the two images seen by a spectator, the stereoscopic match-
ing by the brain is more delicate, or even impossible. This reduces or cancels the
depth perception. This constraint, well-known in stereoscopy, is called the “epipolar
constraint”.
Solutions (also called toe-in camera model) of convergent systems have been pro-
posed [19, 20], but such convergent devices manifest the constraint presented above.
So, unless a systematic trapezoidal correction of images is performed beforehand
(which might not be desirable as it loads down the processing line and produces a
qualitative deterioration of the images) such devices do not afford to produce a qual-
itative 3D content. As demonstrated by [14, 21], we must use devices with shooting
pyramids sharing a common rectangular base (off-axis camera model) and with tops
arranged on a line parallel to the rows of this common base in the scene. For example
Dodgson
et al.
use this shooting layout for their time-multiplexed autostereoscopic
camera system [22].
Thus, aiming axes are necessarily convergent at the center of the common base
and the tops of the shooting pyramids must lie on
m
lines parallel to the rows of
the common base. Figure 3(a) shows a perspective representation of such a shooting
geometry. This figure defines the layout of the capture areas (
CA
i
), and the cen-
ters (
C
i
) and specifies a set of parameters describing the whole shooting geometry
completely. Figures 3(b) and
3(c) show top and full-face representations of this
geometry, respectively.
The shooting geometry analysis is expressed using a shooting global reference
frame
R
=(
CP
,
X
,
Y
,
Z
≡
×
Y
) centered at the desired convergence point
CP
(which is also the center of the common base
CB
of the scene) and oriented in
such a way that the first two vectors of the reference frame are parallel to the main
directions of the common base
CB
of the scene and so, parallel to the main direc-
tions of the capture areas. The physical size of
CB
is
Wb
and
Hb
. Furthermore, the
first axis is supposed to be parallel to the rows of the capture areas and the second
axis is supposed to be parallel to the columns of these areas.
The
n
X
m
pyramids, representative of a shooting layout, according to the princi-
ples explained before to resolve the known issue, are specified by:
×
•
an optical axis of
Z
direction,
•
optical centers
C
i
(
i.e.
: principal points) aligned on one or more (
m
) line(s) par-
allel to the rows of the common base (so on
X
direction) and
•
rectangular capture areas
CA
i
.
These capture areas must be orthogonal to
Z
, so parallel between them and parallel
to
CB
and to centers lines (which are defined by their distances from
CB
,
D
i
2
along
Z
,
P
i
2
along
Y
and
c
i
along
X
). These capture areas are also placed at distances
f
i
along
Z
,
β
i
along
Y
and
α
i
along
X
from their respective optical center
C
i
.Their
