Digital Signal Processing Reference
In-Depth Information
( specifically, for outdoor environment, shadow pixels falling on neutral surfaces tend
to be more blueish ) are also exploited. Finally, the texture features are characterized
by the distribution of local edge directions. If the textures of a small region centered
at a candidate pixel are correlated to the background reference, the pixel is classified
as shadow. We continue the paper as follows. In Section 2, we describe the method
for detecting foreground pixels first, and then present the method for removing shad-
ows. Experimental results are presented in Section 3, and our conclusions are drawn in
Section 4.
2
Detecting Moving Objects and Shadows
2.1
Moving Foreground Detection
The first step of the proposed algorithm is change detection, which calculates the change
mask by thresholding the difference image
D
=
{d
k
(
p
)
}
, with
d
k
(
p
)=
I
k
(
p
)
−
I
k−
1
(
p
)
of two consecutive
input frames. Under the hypothesis that no change occurred at position
,where
I
k
(
p
)
and
I
k−
1
(
p
)
are the image values at pixel
p
, i.e., the null
hypothesis
H
0
, the corresponding difference follows a Gaussian distribution with mean
zero and variance
σ
2
which is equal to twice the variance of the camera noise. To make
the detection more reliable, the decision to be taken should not be based on
d
k
(
p
)
p
only.
Instead , we evaluate a normalized square sum of the frame differences [9]:
d
k
(
p
)
σ
2
Δ
k
(
p
)=
(1)
p
∈W
(
p
)
where
W
(
p
)
is a window of observation centered at position
p
.
is performed to assess whether the
null hypothesis can be accepted or not. Under the null hypothesis, the normalized square
sum
A significance test [9] on the distribution of
Δ
is known to obey a
χ
2
distribution with
N
w
degrees of freedom, where
N
w
denotes the number of pixels within the window
W
(
p
)
Δ
k
(
p
)
in our
experiments. Coupling the threshold
t
s
to the rate of false alarms associated with the test
is reasonable and feasible. Given an acceptable false alarm rate
α
,
t
s
can be determined
using
which is of size
3
×
3
α
=Pr(Δ
k
(
p
)
>t
s
|H
0
)
(2)
In the following steps, the background images will serve as the references for the sub-
sequent assessment. So, a reliable background information is needed. In this work, fol-
lowing the approach of [10], we use a stationary map, the value in which indicates that
the corresponding pixel keeps stationary for how many consecutive frames, to record
the history of frame difference mask. Specifically, for pixels labeled as 'changed' in the
difference mask, the corresponding value in the stationary map is cleared to zero. For
these labeled as 'unchanged', the corresponding value is increased by one [10]. If the
value in the stationary map exceeds a predefined threshold, the background is updated
in a causal low-pass filtering manner as depicted as follows:
B
k
(
p
)=
ηB
k−
1
(
p
)+(1
− η
)
I
k
(
p
)
(3)
