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where
L
1
is the number of I- and P-frames in a GOP,
L
2
is the size of the sliding
window used in LPF, and
A
is the ratio between the average frame distances of
two sliding windows.
D
TWAM
(
by
low-pass filtering, and scales the filtered signal by the ratio between the two sliding
windows. By setting
L
2
to the number of I- and P-frames in a GOP as discussed
previously,
D
TWAM
(
n
)
reduces the noise in the frame distance
D
(
n
)
n
)
can be simplified and written in a recursive format:
D
TWAM
(
n
)=
A
(
D
(
n
)
,
L
)
∗
F
(
D
(
n
)
,
L
)
(7.6)
p
2
(
n
,
L
)
=
(7.7)
∗
(
,
)
L
q
n
L
where
p
(
n
,
L
)=
p
(
n
−
1
,
L
)+
D
(
n
)
−
D
(
n
−
L
)
(7.8)
q
(
n
,
L
)=
q
(
n
−
1
,
L
)+
D
(
n
−
L
)
−
D
(
n
−
2
L
)
(7.9)
This can be implemented with a circular buffer of length 2
L
, which involves only
two additions, two subtractions, two multiplications and one division once the
current frame distance
D
is obtained. Conventional methods such as thresholding
can be applied to locate the scene changes in
D
TWAM
(
(
n
)
n
)
.
7.2.3
Demonstration
Two MPEG-1 video files obtained from [
189
] are selected to demonstrate the effect
of TWAM. Although the files are MPEG-1 encoded, the algorithm can be adjusted to
accommodate MPEG-2, Motion-JPEG, and H.263 video data. Figures
7.1
a and
7.2
a
show the unprocessed frame distance plots, and Figs.
7.1
b and
7.2
b show the TWAM
version of video files
V
1
and
V
2
respectively.
V
1
has 14 sharp and dissolve transitions,
and the transitional regions are marked by the plot with an offset of 1.8 in the
vertical direction. Figure
7.1
b shows a peak near frame 0, which is caused by the
initialization of the circular buffer and is ignored during thresholding. Transitions 1,
6, 8, 13, and 14 are dissolve transitions, and it can be seen in Fig.
7.1
b that TWAM
leads to an increase in frame distance for all of them. In particular, the peak of
transition 6 is increased from 0.23 to 0.42. This transition involves two shots that
are similar in content, and the transition could not be detected by the conventional
method. The magnitudes of five sharp transitions are reduced after TWAM, but
they remain as local maxima and can still be detected. Although some of the
non-transitional regions are amplified by TWAM, it is possible to detect all 14
transitions with no false alarms using a threshold value between 0.3 and 0.42.
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