Information Technology Reference
In-Depth Information
⎡
⎤
W
w
i
⎣
H
h
i
⎦
I
i
u
i
|
R
CSu
i
|
r
=
−
∀
i
(4)
1
Remarking that
f
i
Wb
=
D
i
2
w
i
and
f
i
Hb
=
D
i
2
h
i
,
u
i
is expressed in reference frame
r
as:
⎡
X
+
Z
Wb
⎤
c
i
D
i
2
⎣
Y
Hb
⎦
D
i
2
Z
+
D
i
2
Z
P
i
2
D
i
2
u
i
|
r
=
∀
i
(5)
−
0
By this time, and assuming
U
was visible on both images
l
i
and
i
, we notice that
u
l
i
and
u
i
lie on the same row of the ROI. This fulfills the epipolar constraint and thus
permits stereoscopic reconstruction of
u
=[
x
i
,
y
i
,
z
i
]
t
r
from
E
l
i
and
E
i
according to:
z
i
z
i
+
d
i
2
u
l
i
u
i
=
b
i
2
x
,
which yields
z
i
and
(6)
E
i
u
=
z
i
+
d
i
2
d
i
2
E
i
u
i
,
which then gives
x
i
,
y
i
(7)
Thus, after some calculus, the relation between the 3D coordinates of the scene
points and those of their images perceived by a viewer may be characterized under
homogeneous coordinates by:
⎡
⎣
⎤
⎦
∗
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
μ
i
γ
i
0
x
i
y
i
z
i
1
X
Y
Z
1
ρμ
i
δ
i
0
a
i
=
k
i
2
(8)
1
0
00
k
i
2
(ε
i
−
1)
d
i
2
ε
i
The above equation can be seen as the analytic distortion model for observer posi-
tion i which matches the stereoscopic transformation matrix given in [12]. As such
this model clearly exhibits the whole set of distortions to be expected in any multi-
scopic 3D experience, whatever the number of views implied or the very nature of
these images (real or virtual). It shows too that these distortions are somehow inde-
pendent from one another and may vary for each observer position i. The following
detailed analysis of this model and its further inversion will offer a novel multiscopic
shooting layout design scheme acting from freely chosen distortion effects and for
any specified multiscopic rendering device.
The above model exhibits some new parameters quantifying independent dis-
tortion effects. Those parameters may be analytically expressed from geometrical
parameters of both shooting and rendering multiscopic devices. Their relations to
geometrical parameters and impact on distortion effects are now presented:
•
k
i
2
control(s) the global enlarging factor(s),
d
i
2
D
i
2
k
i
2
=
(9)
