IEEE Geoscience and Remote Sensing Magazine - March 2022 - 143

V
,
==
E
c
c
E
E wG wyTf
f
^h // " * JG ,
11
==
rn
++
T
c
T
c
2
2
m
f
c
/
wG~9
1
2
F
,
where the previous samples in the fth frame xf
by Gaussian means n weight fi is substituted by ,f
f ,
2
2
(58)
are replaced
r and
the number of total frames T is reduced to V.
Finally, in the ECO algorithm, the filter model is updated
every five frames instead of frame by frame. Thus, the
ECO tracker achieved both more favorable performance
and amazing speed.
CONTEXT-AWARE CF TRACKERS
Although the spatial punishment in the SRDCF tracker
[90] can repress background noises, it utilizes a fixed global
punishment, that is, artificially reducing the weight of the
filter periphery to suppress the background response. As a
means of improving the discriminative ability of the filter,
learning background information, especially, can usually
achieve a better effect. Aiming to learn context information,
Mueller et al. proposed the context-aware CF (CACF)
tracker [96].
In the CACF tracker, during the training stage, the authors
changed the original ridge regression formula (3) to
D
w
=- +
=
E^h // c
c
c 1
wx yw
==1
c
k
2
c
*
D
+m / / c
i=1
1
region, and xi
wx ,
*
i
c
2
2
2
2
m1
c
(59)
where x0 denotes the training samples from the object
represents the samples from the context
around the object region.
Remark 14: Innovatively, to obtain a structure similar to
the ridge regression equation, the authors further derive the
deformation of the main formula as
D
* rr
1
E wx ywc
c
=- m+
==
// (60) //hx w
1
cc
c
2
2
where xc
r
1
1
and yr can be expressed as
V
rr
R
xc== ,
h
T
S
S
S
SS
x0
c
m
m
2 1
h
2
x
x
k
c
c
X
W
W
W
WW
y
T
S
S
S
SS
N
X
W
W
W
WW
2
2
,
E^ww .
t tt
h
=- m+
)
l ^ cc
xc
9
y
2
2
c==1
c
By applying a partial derivative, a closed solution to (64)
can be obtained:
R y V
N
(61)
where 0 RN ! N denotes a zero vector. The solution to (60)
can be obtained:
w =t c
xx ++00 12
)
tt mm /tt
cc
99
9
ttc
xy
)
k
xx
i
c
i=1
The experiments have shown that trackers with the
context-aware algorithm in the CACF tracker, i.e., the
MARCH 2022 IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE
EXPERIMENTAL EVALUATION AND ANALYSIS
This section presents the experimental results and analysis,
divided into five sections. The " Implementation
143
)
i
c
.
(62)
t c)
w =
tt
t
x
c ^
ll
l
y 9 t ) cx ^
h9 xc
h
h+m
.
xx
x
) ^
cc
c
(65)
Remark 16: As this result was derived without any theorems
or restrictions, it is theoretically possible to predict
any affine transform of x, e.g., translation (the KTC tracker),
scale change (the KSC tracker), and rotation (the KRC
tracker), and apply any kernel function.
t c
2
2
D
D
2
2
Staple_CA and SAMF_CA trackers, can be more robust when
compared with the original tracker in most scenes.
Remark 15: Although the CACF tracker [96] can make
the filter learn the background information near the object's
bounding box, it has an obvious shortcoming: the
background information learned by the CACF tracker is
the four fixed background boxes in the relative position
around the object, which is not enough for the tracker to
tackle complex scenes.
KCC TRACKER
The kernel trick used in the KCF tracker [39] can map samples
x to a high-dimensional space for division and thus
has a relatively good shielding effect on noise and distractors.
However, there are two obvious limitations in the
KCF tracker: 1) due to the application of (9), the training
samples must be circulant; and 2) the kernel function used,
k ,xxl
is also required to have the same weight for each pixel
in the samples.
In the KCC tracker [85], Wang et al. unearthed the huge
potential of the kernel method, which not only eliminates
the two limitations in the KCF tracker but also further expands
the kernel method to the calculation of changes such
as scale and rotation (not just translation), and proved to be
more robust than the scaling pool in the SAMF tracker [83]
and the scale filter in the DSST tracker [84].
In [85], the authors first defined a kernel vector
6 hh@ where xi
l =^hx z
llf^^zxk
zx1
,, ,, ,
denotes any affine transform
of x, which is not a limited translation. l (·) is the kernel
function, the same as k. Then, the kernel cross correlator
(response output) is defined as
D
t / ^h
t
= lxc
c =1
c
rz .w9 t c)
(63)
Based on this definition, the KCC tracker proposed their
training regression equation as
D
D
(64)
IEEE Geoscience and Remote Sensing Magazine - March 2022

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