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( )
ʸ
=⇅
c
ˁ
p
fg
1
y,
fg
q
fg
(11)
1
1
( )
bg
bg
bg
ʸ
=⇅
c
ˁ
p
1
y,
q
(12)
2
2
( )
where
q
fg
is the foreground model and
q
bg
is the background model.
p
fg
y
fg
is
( )
y
fg
and
bg
bg
y
bg
.
the foreground candidate at
p
y
is the background candidate at
c
and
c
are utilized to normalize
ʸ
and
ʸ
.
1
2
denotes the appearance variation of foreground which may due to
the illumination or background change. For this condition, the tracking result from
background kernel plays an important role. On the contrary, a smaller
A smaller
ʸ
1
denotes a
distinct change of background and meanwhile the foreground is more reliable.
The background kernel also plays an important role in correcting model drift. We
utilize the following formula to updating the background model
ʸ
2
( )
bg
bg
bg
p
1
y+
2
q
bg
q
=⇅
c
(13)
where
c
is a normalization constant. We update the background model each iteration
to adaptive the background change while relatively restrict the foreground model
renew. The reason is that the background may change most of the time but the fore-
ground is relatively constant. It should be noted that a suitable updating strategy of
foreground model can largely suppress the model drift problem. However, it is
beyond the discussing in this paper. We refer to some relative works [11, 12] to this
problem.
4
Experimental Results
We evaluate the tracking performance of the proposed dual-kernel tracker (DKT), the
kernel-based tracker (KBT) [1], and the KBT based on background contrasting (BC-
KBT) [8]. For all the trackers, we select a three times bigger region around the target
as background. The upper limit of mean shift iterations is set at 15 and the stopping
criterion threshold is set at 0.1. Of particular note, we set the tracking window as
fixed for all the trackers although the targets decreased in size.
Figure 1 shows the tracking results of an airplane taking off from the runway. In
the video clip, the background changes acutely several times, which affects the track-
ing results of KBT and BC-KBT. Both KBT and BC-KBT lost the target in frame of
150 and 250, while the proposed DKT estimated the target position with acceptable
precision.
Figure 2 shows the tracking results of a more challenging video sequence. A lot
of background clutters appear in the latter part of the sequence, which greatly increas-
es the tracking difficulty. Along with the target shrinking its size, the surrounding
backgrounds changed severely, and both KBT and BC-KBT are cheated by the back-
ground clutters.
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