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noisy and unstable. To address this problem, in this work we adopt an alternative
long-term motion estimation approach using background extraction and subtrac-
tion, given that most surveillance CCVT systems are based on fixed views. More
precisely, we utilise a Gaussian mixture background model of [24]:
)=
∑
i
α
i
g
(
f
(
x
,
y
)
,
θ
i
,
x
,
y
,
σ
i
,
x
,
y
)
,
(
,
b
x
y
(1)
where
x
,
y
is the location of each pixel,
(
θ
i
,
x
,
y
,
σ
i
,
x
,
y
)
are the model parameters of
each individual Gaussian component
g
,and
f
t
(
is the local pixel intensity. Once
the parameters are estimated, the likelihood of one frame
f
x
,
y
)
at time
t
with re-
spect to the background model is computed as the probability distance given by
(
x
,
y
)
)=
∑
i
α
i
ex p
2
1
2
(
f
t
(
x
,
y
)
−
θ
i
,
x
,
y
)
(
,
−
v
x
y
(2)
σ
y
2
i
,
x
,
This type of motion information is very effective at highlighting changes in motion
of every pixel in the scene. However, this is also an undesirable property since the
noisy motion caused by lighting changes is inevitably augmented. See Fig. 8 (b) as
an example. To suppress the noisy motion caused by lighting changes, we further
take spatial motion contrast into consideration in the Gaussian mixture model as
follows:
)=
∑
i
α
i
ex p
2
1
2
(
f
t
(
x
,
y
)
−
θ
)
i
,
x
,
y
(
,
−
v
x
y
(3)
σ
s
In the background model of Eq.(2),
σ
i
,
x
,
y
is the estimated strength of the motion of
each pixel at
σ
i
,
x
,
y
. Examples of motion
extraction using this model are shown in Fig. 8 (b) and (c), where in (b) motion was
estimated using the Gaussian mixture background model without considering spatial
motion contrast whilst in (c), it was taken into account. This demonstrates clearly
the effectiveness of utilising the spatial motion contrast measure given by Eq.(3) for
removing motion noise as compared to existing Gaussian mixture models.
(
x
,
y
)
, we calculate
σ
s
in Eq.(3) as the mean of
2.3
Spatial Motion Descriptor
Base on the background modeling described in Sec. 2.2, we can estimate a mo-
tion confidence measure of each hypothesis created by the static detector. Next is to
construct a robust hypothesis descriptor based on the motion information. Inspired
by the success of SIFT descriptor [16], we propose a multi-level spatial pyramid
descriptor by directly utilising the motion confidence calculated from Eq.(3) to ef-
fectively describe the motion region of the hypothesis. The descriptor extraction
procedure consists of the following steps:
1. Creating a codebook of confidence measure. Because the confidence
v
(
x
,
y
)
is
in principle a probability with
v
∈
[
0
,
1
]
, we can create
C
bins of the value with
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