IEEE Geoscience and Remote Sensing Magazine - March 2022 - 137

sizes in the scale pool are first cropped. Having extracted
the feature of the resized image patches ,, ,,zz z
SAMF tracker can determine the optimal scale si
" ss
the following optimization problem:
().
argmsiax rz
si
f
12 sk, the
by solving
(28)
Moreover, the location of the peak value can be used to
estimate the new location of the object. Thus, the SAMF
tracker achieves both location and scale prediction at the
same time.
Remark 6: Taking into account that the new samples
extracted in each frame have different scales, the SAMF
tracker first converts the sample bilinear interpolation to
the same size and then uses the same linear-interpolation
template update strategy as the KCF tracker, that is, (12)
and (26).
DSST AND FDSST TRACKERS
The scaling pool algorithm given in the SAMF tracker [83]
coped with the scale variations, but its operation speed
and robustness left room for further improvement. Danelljan
et al. made an innovative contribution to the scaleestimation
algorithm.
In [84], the training regression equation adopted the
ridge regression in the KCF tracker [39], i.e., (18), and applied
a linear kernel, i.e., (25). Their solution is
t
w = D
xx I
c xy
/ k)
k=1
tt
tt
c )
9
.
9
k +m N
Then, the core idea of the DSST tracker in [84] is to train
two filters, namely, a translation wtrans
w .scale When a new frame arrives, the translation filter is
first used to search for the new object's location; then, the
samples of the different scales [, ,, ]
zz z
ss
f
12 sk are extracted
near the new center. The samples in various scales are used
for the scale filter to predict the proper scale. Then, the translation
filter uses the samples centered at the predicted location
for training, while the scale filter utilizes the samples
in different scales that were centered at the predicted scale
for training. Such a scale-evaluation method combines both
robustness and speed.
Remark 7: In the implemented code, the translation
filter adopts the promoted 2D results of (29), where the
training samples and filter in a certain feature channel are
2D. Differently, the DSST tracker pulls the 2D matrices
into a 1D vector to train the 1D scale filter, adopting (29)
directly. Such a strategy greatly boosts the processing speed
of the DSST tracker. Another reason that the DSST tracker
achieves fast scale estimation is that the scale filter crops
the patches about the size of the object, which is relatively
small, making feature extraction more efficient.
Based on the DSST tracker, Danelljan et al. further
proposed a faster version, called the fDSST tracker [79],
which improves tracker performance while obtaining an
MARCH 2022 IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE
(29)
even higher tracking speed. The strategy can be summarized
into three points. First, the fDSST tracker uses subgrid
interpolation to reduce the size of training samples
and search samples. Second, the fDSST tracker performs
principal component analysis (PCA) on the features of the
sample (similar to the PCA of the CN in the CN tracker
[87]) to achieve feature dimensionality reduction. Finally,
the scale filter is compressed by reducing the total number
of features to the number of features after PCA dimensionality
reduction, which greatly reduces redundant information.
Under these three acceleration strategies, an fDSST
tracker can expand its search region to obtain a better
tracking performance.
FEATURE REPRESENTATION
For the sake of better robustness and favorable discriminative
ability of the trackers, it is of vital importance to learn
sufficient and effective object features. The trackers that introduced
this part [87]-[89] put forward a variety of new
methods to learn and effectively utilize the expressive features,
thus promoting DCF algorithms to a new level.
CN TRACKER
The CN tracker [87], which was proposed by Danelljan
et al., put forward an innovative color feature based on the
CSK tracker [86], which is another powerful handcrafted
feature. Further, the CN tracker also settled the multichannel
training problem.
The color attribute [76], also known as the CN, directly
and a scale filter
denotes the 11 color language labels defined by human beings.
The CN feature first maps the value of each channel in a
red-green-blue image to the 11-dimensional CNs' probability,
which, when summed up, equals one. Then, the 11-dimensional
color space is mapped to the 10-dimensional orthogonal
basis subspace; thus, dimension reduction and normalization
are achieved at the same time (the CN tracker).
However, there is a linear relationship between the computational
complexity of the CSK tracker and the number
of dimensions of the feature used. To lessen the amount of
calculation cost and to guarantee high speed, the CN tracker
further proposed low-dimensional adaptive color attributes,
where PCA is performed on 10-dimensional features
to select the two dimensions with the most information
(the analysis results of each frame are adaptive), that is, the
CN_2 tracker.
Except for proposing the color feature, another improvement
in the CN tracker [87] is that it considers the information
in the previous frames in their training progress, i.e.,
T
()
T
E // ^hiz*ww ,
f 11
=- m+
==
f d
D
f
c
c
xy
f
c
2
2
/ wf
c=1
2
2
n
D
(30)
where ·f denotes the values in the fth frame, e.g., fi indicates
the weight for the fth frame. We assume that the training
sample is a single-feature channel, i.e.,
solution for the filter parameter T
x RN 1# . The
!
a in the Tth frame is
137
IEEE Geoscience and Remote Sensing Magazine - March 2022

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