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()
()
where
. The procedure ends when the iteration time is up to a preset
threshold or the distance between two consecutive results (stopping criterion) is under
another preset threshold.
The tracker chooses Epanechnikov kernel as kernel function, which assigns a big-
ger weight to the locations nearer by the center of the target. The assigned weights
make the probability density function smoother and enhance the robustness of the
tracker. However, it excludes the background information which is important to track-
ing task. Some subsequent works are centralized on this problem, but almost all the
ameliorations are to correct the model features by suppressing the background infor-
mation.
G
x
=−
K
′
x
h
h
3
The Proposed Dual-Kernel Tracker
In this paper, we take the advantage of background information in a different way.
Two kernels are designed to respectively focus on the foreground and background.
The tracker based on these two kernels obtains a higher precision and reveals the
robustness to the background change and clutter.
Unlike the kernel-based tracker, we choose Gaussian kernel as the kernel functions
and describe them as follows:
2
1x
()
K
fg
x
=
c
exp
−
(7)
h
fg
2h
ʻ
⇅
( )
()
()
bg
fg
fg
K
x
=
c
max
K
−
K
x
(8)
h
bg
h
h
()
()
fg
bg
where
K
x
is foreground kernel and
K
x
is background kernel.
c
and
h
h
fg
( )
()
fg
K
.
The bandwidth h here is the window size of an enlarged region which contains both
foreground and background.
fg
c
are the normalization constants.
max
K
is the maximum value of
x
bg
h
h
is the ratio of the target size to the enlarged size.
These two parameters are utilized as follows:
ʻ
2
2
x1
=
x
y
+
(9)
ʻ
⇅
h
ʻ
h
h
x
y
where x
.
With these two kernels, we obtain a new iteration formula as follows:
=
( ,
xy
)
and h(,
=
hh
)
x
y
fg
bg
y
=⇅
ʸ
y
+⇅
ʸ
y
(10)
1
1
1
2
1
where
y
fg
and
y
bg
are obtained from formula (6) respectively with foreground
kernel and background kernel.
ʸ
and
ʸ
are the weights calculated by
1
2
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