Game Development Reference
In-Depth Information
A general diagram of the HMM classifier is shown in Figure 23. The recognizer
consists of
M
different HMMs corresponding to the modeled gesture classes. In
our case,
M=7
as it can be seen in Table 2. We use first order left-to-right models
consisting of a varying number (for each one of the HMMs) of internal states
G
k, j
that
have been identified through the learning process. For example, the third HMM,
which recognizes low speed on
hand
lift,
consists of only three states
G
3,1
,
G
3,2
and
G
3,3
. More complex gesture classes, like the
hand clapping,
require as
much as eight states to be efficiently modeled by the corresponding HMM. Some
characteristics of our HMM implementation are presented below.
•
The output probability for any state
G
k, j
(
k
corresponds to the
id
of the
HMM while
j
refers to the
id
of the state within a particular HMM) is
obtained by a continuous probability density function (pdf). This choice has
been made in order to decrease the amount of training data. In the discrete
case, the size of the code book should be large enough to reduce quantiza-
tion error and, therefore, a large amount of training data is needed to
estimate the output probability. One problem with the continuous pdf is the
proper selection of the initial values of density's parameters so as to avoid
convergence in a local minimum.
•
The output pdf of state
G
k, j
is approximated using a multivariate normal
distibution model, i.e.:
1
T
−
1
exp{
−
(
O
−
)
C
(
O
−
)}
i
k
,
j
k
,
j
i
k
,
j
2
b
(
O
)
=
k
,
j
i
(1)
K
1
(
2
π
)
2
⋅
C
2
k
,
j
µ
k, j
is the mean vector
of state
G
k, j
,
C
k, j
is the respective covariance matrix and
K
is the number
of components in
O
i
(in our case
K
=6). Initial values for
where
O
i
is
i-th
observation (input feature vector),
µ
k, j
and
C
k, j
were
obtained off-line by using statistical means. Re-estimation is executed using
a variant of the Baum-Welch procedure to account for vectors (such as
µ
k, j
)
and matrices (such as
C
k, j
).
•
Transition probabilities
a
k,mn
between states
G
k, m
and
G
k, n
are computed by
using the cumulative probability of
b
k,m
(
O
i
) gives the estimation of the
transition probability, i.e.,
k
Φ
. Note that, since the HMM is
assumed to operate in a left-to-right mode,
a
k,mn
=0,
n<m
,
a
k,mn
=1-
a
k,mn
at all
times.
a
= 1
−
(
)
k
,
mn
,
m
i
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