Digital Signal Processing Reference
In-Depth Information
Prob{
S
(
u
)=
s
k
|
d
n
}=
Prob{ ( )
Su
=
s
and
Su
(
)
=
s
;
α
=
1,
, }
n
k
α
k
. (4)
α
Prob{ (
Su
)
=
s
;
α
=
1,
, }
n
α
k
α
where the denominator of (4) is the probability of conditional data event and can be
inferred by (3); the numerator is the probability of occurrences of the conditional data
event and
u
being the state
s
k
at the same time. The numerator can be obtained by the
ratio denoted by
c
k
(
d
n
)/
N
n
, where
c
k
(
d
n
) is the number of those replicates, among the
c
(
d
n
) previous ones, associated to a central value
S
(
u
) equal to
s
k
. The conditional
probability can be defined as:
cd
()
.
(5)
Prob{ ( )
Su
=
s Su
|
(
)
=
s
;
α
=
1,
, }
n
≈
k
n
k
α
k
cd
()
α
n
Based on (5), the state of
u
can be drawn using Monte Carlo methodology. Because
(5) adopts the idea of probability method, the drawn states of
u
are random, which can
reflect prior probability models existing in the training image.
(a) (b)
Fig. 1.
Data templates.(a)a 2D data template;(b)a 3D data template
(a) (b) (c)
Fig. 2.
Procedure of a data event captured by a 5 ×5 template. (a) a 5×5 data template;(b) a
15×15 training image;(c)a data event
(a) (b)
Fig. 3.
Data events captured by the data templates displayed in Fig.1. (a) captured by a 2D data
template;(b) captured by a 3D data template.
