Graphics Reference
In-Depth Information
2
Traditional Kernel-Based Tracker
The kernel-based tracker describes the target model with
m
-bins histogram features.
Let
x
and
{x
ii
be the pixel location centered at
q
=
{
uu
q
be the norma-
=
1...
n
=
1...
m
lized target model. The sub-feature
q
in this model can be computed as:
n
(
) ( )
qc
=
K
xx
−
ʴ
b
x
−
u
(1)
u
q
h
i
0
i
i
=
1
()
c
is a normalizing constant and
K
x
where
is the kernel function with band-
h
width of
h
, which will be discussed later.
ʴ
is the Kronecker delta function and
()
b
x
i
is the feature mapping function from the color of location
x
i
to the histogram
bins.
It calculates the sub-features of target candidate
p
(y)
=
{
p
(y)}
centered at
u
u
=
1...
m
y in the same way,
n
(
) ( )
p
(y)
=
c
K
x
−
y
ʴ
b
x
−
u
(2)
u
py
h
i
i
i
=
1
where
p
c
is a normalizing constant. Then Bhattacharyya coefficient is utilized to
calculate the similarity between target model and candidate,
[
]
m
ˁ
(y)
≡
ˁ
pq
(y),
=
p
(y)
⇅
q
(3)
u
u
u
=
1
Expanded around y using the first-order Taylor series and integrated with for-
mula (2), the former equation can be approximated as
c
m
m
1
py
ˁ
(y)
≈
p
(y )
⇅
q
+
ˉ
(x )
K
(y
−
x )
(4)
u
0
u
i
h
i
2
2
u
=
1
u
=
1
where
m
()
ˉ
(x )
=
qp
(y )
ʴ
b
x
−
u
(5)
i
u
u
0
i
u
=
1
Then the mean shift algorithm is utilized to optimize the equation (4) and the kernel
is then recursively moves from the current location
y
y
ac-
to the new location
0
cording to the following iteration:
n
(
) ( )
h
G
G
xy
−
ˉ
ˉ
xx
h
i
0
i
i
y
=
i
=
1
(6)
1
n
(
) ( )
h
xy
−
x
h
i
0
i
i
=
1
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