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m
3
4
5
1
2
6
(a)
(b)
(c)
Fig. 1.5
Epipolar lines (white) on a sample image: (a) between
v
1
and
v
2
; (b) between
v
1
and
c
; and (c) between
v
2
and
c
from Section 1.3.1 the subscript of
v
refers herein to the camera number), the four
homogeneous matrices encoding the relative pose between the virtual views. Finally,
let
D
[1]
and
D
[2]
denote the reflection transformations about the two mirrors, written
c
1
c
1
in
. We are now ready to introduce the following proposition, which establishes
a link between
H
R
and
H
v
[2]
c
1
.
2
v
[1]
2
Proposition 1.4 (Multiple cameras mirroring).
The following equation holds true:
H
v
[2]
D
[1]
D
[2]
=
H
−
1
R
2
v
[1]
2
H
R
(1.13)
c
1
c
1
Proof.
From (1.12) we have that
c
1
=
H
v
[2]
D
[1]
c
1
D
[2]
1
v
[1]
1
.
(1.14)
Pre-multiplying and post-multiplying (1.14) by
H
−
1
R
and
H
R
, respectively, we obtain
H
v
[2]
D
[1]
c
1
D
[2]
H
−
1
R
H
R
=
H
−
1
R
1
v
[1]
1
c
1
H
R
.
(1.15)
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