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(a)
5 10 5
0
5
10
15
(b)
(c)
Fig. 2.2 Demonstration of the equivalence of the kernel-projected value whether moving the
camera or moving the kernel: (a) a static kernel and the signal at the goal; (b) a static kernel
and a shifted signal; and (c) a shifted kernel and the signal at the goal
V =(ξ ξ 0 ) T P ˙
ξ
ξ ξ 0 ) T P ∂ξ
=(
x x
(2.6)
K ( w + x ( t ))
ξ ξ 0 ) T P
=(
I 0 ( w
,
0 ) d w
u
.
x
I
Jacobian
J
After reversing the change of coordinates, (2.6) can be written as
ξ ξ 0 ) T P
0 ) d w u
K ( w )
V =(
I 0 ( w
x ( t )
,
x
I
x ( t )) d w u
ξ ξ 0 ) T P
(2.7)
K ( w )
=(
I ( w
,
.
x
I
 
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