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from
K
strong clusters. The algorithm to detect the emotional scenes is shown in
Algorithm 3.
Algorithm 3.
Emotional scene detection
Notations:
E
i
:The
i
-th emotional scene in which the facial expression
c
appears.
first
(
E
i
)
: The frame number of the beginning frame in
E
i
.
last
(
E
i
)
: The frame number of the ending frame in
E
i
.
E
i
)
: The length of
E
i
. It is equivalent to
last
E
i
)
−
E
i
)
−
length
(
(
first
(
1.
#
int
(
E
i
)
: The number of emotional scenes integrated into
E
i
.
#
nonemo
: The number of nonemotional frames in
E
i
. Note that a nonemotional
frame means that the facial expression appears in that frame is different from
c
.
dist
(
E
i
,
E
j
)
: The distance between
E
i
E
i
)
(
and
E
j
(
i
<
j
)
. It is equivalent to
first
(
E
j
)
−
last
(
E
i
)
−
1.
Initialize:
For each frame image classified into the facial expression
c
, initialize according
to Equation (5):
first
(
E
i
)=
last
(
E
i
)=
c
i
,
#
int
(
E
i
)=
0
,
#
nonemo
(
E
i
)=
0
,
length
(
E
i
)=
1
,
(
1
≤
i
≤
M
c
)
(5)
where,
c
i
is the frame number of the
i
-th emotional frame in the video.
M
c
is the number
of emotional frames. An emotional frame is the frame classified into
c
. That is, each
emotional scene consists of a single emotional frame.
Procedure:
1: Find
i
∗
in accordance with Equation (6):
i
∗
=
argmin
i
dist
(
E
i
,
E
i
+
1
)
E
i
)
−
E
i
)
length
(
#
nonemo
(
s
.
t
.
dist
(
E
i
,
E
i
+
1
)
≤
#
int
(
E
i
)+
1
length
(
E
i
+
1
)
−
#
nonemo
(
E
i
+
1
)
#
int
(
E
i
+
1
)+
1
∧
dist
(
E
i
,
E
i
+
1
)
≤
(6)
2: If there is no
i
∗
that satisfies Equation (6), finish the procedure and output current emo-
tional scenes. Otherwise, proceed to step 3.
3: Integrate
E
i
∗
+
1
into
E
i
∗
by updating
E
i
∗
as follows:
last
(
E
i
∗
)
←
last
(
E
i
∗
+
1
)
,
#
int
(
E
i
∗
)
←
#
int
(
E
i
∗
)+
1
,
#
nonemo
(
E
i
∗
)
←
#
nonemo
(
E
i
∗
)+
first
(
E
i
∗
+
1
)
−
last
(
E
i
∗
)
−
1
Note that
length
(
E
i
∗
)
is also updated due to the update of
last
(
E
i
∗
)
.
4: Delete
E
i
∗
+
1
and renumber the subscripts of
E
i
so that the emotional scenes become
E
i
,...,
E
c
M
c
−
1
.
5:
M
c
←
M
c
−
1 and return to step 1.
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