Image Processing Reference
In-Depth Information
Fig. 13.9. The images registered by the
left
and
right
camera system shown in Fig. 13.4
Finally, we put together (13.76) and (13.83):
T
L
M
I
[
I
,
0
]
p
=
0
T
R
M
I
M
E
p
=
0
(13.84)
to obtain:
A
=
T
L
M
I
[
I
,
0
]
T
R
M
I
M
E
.
Ap
=
0
,
with
(13.85)
Equation (13.85) can be solved for
p
by minimizing
Ap
2
=
p
T
A
T
Ap
(13.86)
The found
p
is now in the left camera coordinate system and solves a 4D linear
symmetry direction estimation problem. Accordingly,
p
is given by the least eigen-
vector of
A
T
A
. An analogous solution and interpretation in terms of direction in a
4D space can evidently also be made for Eq. (13.72). We summarize our findings as
the following two lemmas.
Lemma 13.8.
Given the intrinsic matrices
M
I
,
M
I
and the extrinsic matrices,
M
E
=[
R
L
,
t
L
]
,
M
E
=[
R
R
,
t
R
]
(13.87)
of two cameras, the stereo extrinsic matrix yields
