Digital Signal Processing Reference
In-Depth Information
decomposition. The experimental results show that the proposed technique is effective
in real AAR data via multi-scale low rank and sparse decomposition.
2
Drogue Detection via Ms-Lrsd
2.1
Object Detection Based on Lrsd
For the drogue image sequences
{
f f f
acquired by the camera on the probe, our
purpose is to differentiate drogue from the image sequence, in which
T
denotes
number of frames, and the size of each image
f
t
is
m
}
1
,,,
T
n
. And the image at
t-
th frame
can be decomposed into background
b
t
and object
d
t
, that is
f
t
=b
t
+d
t
. The object
d
t
is
the expected drogue at
t-
th frame. If the image pixels at
t-
th frame are stacked as a
column vector
×
ë û
, then the decomposition of
image sequences for moving object detection can be represented as
F
=
B
+
D
,
where
( )
, let
é
ù
FFFF
´
1
,,, R
mn T
T
F
=
vec f
=
Î
i
i
are
background term and object term, respectively. Here we discuss the intrinsic
properties of background and object for decomposition [12]. Firstly, we assume that
the videos are captured with no turbulence.
The background term
B
: The ideal background of each image in image sequences
should be almost the same. So the linear correlations of background term are strong.
That means the background term
B
should be a low rank matrix. The moving objects
term
D
: The number of pixels occupied by the moving objects, which is drogue, is
usually small compared to the total number of pixels in each image. It is a reasonable
assumption for most realistic surveillance videos. Therefore, the foreground moving
objects can be captured by restricting the number of nonzero entries, expressed as
zero norm constraints. The combination with the above constraints on background
term
B
and moving objects term
D
for decomposition of
F
is performed by solving the
following low rank and sparse optimization, which can be described as [12, 13]
é
( )
( )
ù
R
mn T
´
and
()
( )
B
=
vec b
1
,,
vec b
Î
D
=
vec d
1
,
,
vec d
∈
R
mn T
×
ë
û
T
T
(
)
()
(1)
min
rank
B
+
λ
D
,
s t F
. .
=
B
+
D
0
BD
where
λ
is the weighting parameter,
⋅
denotes zero
norm. The moving object
D
can be obtained by solving the above formula.
()
denotes the rank of matrix,
rank
⋅
0
2.2
Multi-Scale Lrsd for Drogue Detection
We can see that the drogue has complete structure information from the figure 2. In
order to overcome the influence of non-structure information, caused by atmospheric
or aircrafts, we use a multi-scale method for moving objects detection, the objection
are detected by fusion the multi-scale detection results via low rank and sparse
decomposition. We use stationary wavelet transform (SWT) for images sequences
decomposition. The SWT algorithm inserts
21
-
j
zeroes between the filter
coefficients at the resolution level
j
. The size of each wavelet sub-band equals to the
size of the input image. Each image
f
t
can be decomposed into four parts at scale
j
:
