Database Reference
In-Depth Information
ʾ
t
(
represents the Bayesian probability of being the state
S
i
at time
t
and state
S
j
at time
t
i
,
j
)
1, given the model and the observation sequence. Equation (
11.23
) can
also be written in the form of the forward and backward variables, as:
+
u
t
+
1
)=
ʱ
t
(
i
)
a
ij
b
j
(
)
ʲ
t
+
1
(
j
)
(
,
ʾ
i
j
(11.24)
t
P
(
Tr
|
ʻ
)
where
ʲ
t
are the forward and backward variables, respectively. These
variables can be solved inductively. The numerator term in Eq. (
11.24
)isjust
P
ʱ
t
and
(
q
t
=
S
i
,
q
t
+
1
=
S
j
|
Tr
,
ʻ
)
and the division by
P
(
Tr
|
ʻ
)
gives the desired probability
measure. If
is defined as the Bayesian probability of being in state
S
i
at time
t
,
given the observation sequence and the model,
ʳ
t
(
i
)
ʳ
t
(
i
)
can be related to
ʾ
t
(
i
,
j
)
by
summing over
j
, giving:
N
S
j
)=
∑
ʳ
t
(
i
1
ʾ
t
(
i
,
j
)
(11.25)
=
Using the above formulas, we can devise a method for re-estimation of the
parameters of an HMM. A set of re-estimations from
¯
A
B
ʻ
=(
A
,
B
,
ˀ
)
to
ʻ
=(
,
,
ˀ
)
¯
are:
T
−
1
t
=
1
ʾ
t
(
i
,
j
)
a
ij
=
∑
(11.26)
T
−
1
t
=
1
ʳ
t
(
i
)
∑
v
k
}
ʳ
t
(
i
)
b
i
=
∑
u
t
=
t
∈{
t
|
(11.27)
t
ʳ
t
(
i
)
∑
=
1
ˀ
=
ʳ
¯
(
i
)
(11.28)
1
¯
and repeat
the calculation of these equations, we then can improve the probability of
Tr
being
observed from the model until some limiting point is reached.
Based on Eqs. (
11.25
)-(
11.28
), if we iteratively use
ʻ
in place of
ʻ
11.7.4
Experimental Result
The HDM05 database is one of the very useful sources for testing motion analysis,
synthesis and classification algorithms [
356
]. The proposed algorithm was applied
to the HDM05 database, which contains several hours of motion capture data,
including various walking and kicking motions, cartwheels, jumping jacks, grabbing
and depositing motions, squatting motions, and so on. Table
11.7
shows the
description of the HDM05 database. This mocap data was recorded by the optical
marker-based Vicon system, shown in Fig.
11.12
. A number of well-specified
motion sequences were executed several times and performed by five actors.
The recorded data was manually cut out to obtain suitable motion clips, which
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