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The resulting
K
strong clusters can discriminate
K
types of facial expressions.
The algorithm to construct strong clusters is shown in Algorithm 2.
Algorithm 2.
Construction of the strong clusters
Input:
The
number
of
strong
clusters
K
(note
that
this
is
the
same
as
the
num-
ber
of
weak
clusters
in
a
set
of
weak
clusters)
and
the
weak
cluster
sets
{
C
1
,
1
,...,
C
1
,
K
},...,{
C
8
,
1
,...,
C
8
,
K
}
.
Procedure:
1: Compute the similarity matrix
S
from Equation (3).
⎛
⎝
⎞
⎠
s
1
,
1
s
1
,
2
···
s
1
,
N
s
2
,
1
s
2
,
2
···
s
2
,
N
. .
.
.
.
.
s
N
,
1
s
N
,
2
···
s
N
,
N
S
=
(3)
where
s
i
,
j
is the number of weak clusters that contain both frame images
x
i
and
x
j
.There-
fore, 0
8.
S
is symmetric because
s
i
,
j
=
s
j
,
i
.
2: Generate
N
initial sets of strong clusters
G
1
,...,
≤
s
i
,
j
≤
G
N
such that
G
i
=
{
x
i
}
.
3:
N
.
4: Integrate
G
j
∗
ν
←
(
G
i
∗
←
G
i
∗
∪
G
j
∗
)
. The subscripts
i
∗
and
j
∗
(
i
∗
<
j
∗
)
are deter-
into
G
i
∗
mined so that Γ
in Equation (4) is maximized.
1
|
G
i
∗
||
G
j
∗
|
∑
a
∈
G
i
∗
∑
Γ
=
s
ab
(4)
b
∈
G
j
∗
5: Renumber the subscripts of the strong cluster sets to be
G
1
,...,
G
ν
−
1
.
6: ν
←
ν
−
1.
7: If ν
>
K
then return to step 4. Otherwise, finish the clustering and output the strong
clusters
G
1
,...,
G
K
. Note that our method judge that the same facial expression appears
in the frame images
x
i
and
x
j
if they are classified into the same strong cluster.
5
Emotional Scene Detection
The emotional scenes are detected from a video according to the result of the facial
expression recognition for each frame image. An emotional scene with a certain
facial expression is determined by using the frame images in the corresponding
strong cluster.
At the first step of the emotional scene detection, each frame image in the strong
cluster is regarded as a single emotional scene. Then, neighboring emotional scenes
are integrated into a single emotional scene. The integration process is repeated until
no more emotional scenes can be integrated.
The resulting emotional scenes are regarded as the emotional scenes for the
strong cluster. As a result, a total of
K
sets of emotional scenes can be detected
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