Graphics Reference
In-Depth Information
H
I
3
×
3
H
0
3
×
1
Q
=
0
3
×
1
0
How can
H
be recovered once
Q
is estimated?
6.21 While the Rodrigues formula in Equation (
6.58
) tells us how to generate
R
i
given
r
i
, we also need to know the inverse operation. Show that:
R
i
r
i
=
r
i
(6.83)
(
r
i
)
=
(
)
−
2cos
trace
R
1
(6.84)
)
2 sinc
(
r
i
)
r
i
=
(
R
32
−
R
23
,
R
13
−
R
31
,
R
21
−
R
12
(6.85)
That is, Equation (
6.83
) shows that
r
i
is an eigenvector of
R
i
corresponding
to a unit eigenvalue, which tells us its direction. The correct magnitude
can be determined from Equations (
6.84
)-(
6.85
) using a two-argument
arctangent function.
r
i
6.22
Show that solving Equation (
6.72
) is equivalent to solving a series of
n
inde-
pendent 3
3 systems, where
n
is the number of scene points in the bundle
adjustment problem.
×
