Cryptography Reference
In-Depth Information
background region of a video sequence often contains several moving objects.
Therefore, rather than explicitly estimating the values of all pixels as one
distribution, we prefer to estimate the value of a pixel as a mixture of Gaus-
sians [19, 20, 21]. In [19], the probability that an observed pixel will have an
intensity value x
t
at time t is estimated by K Gaussian distributions defined
as follows:
K
ω
l,t
(2π)
1/2
e
−
2
(x
t
−µ
l
)
T
Σ
−1
l
(x
t
−µ
l
)
,
P (x
t
)=
(9.1)
l=1
where ω
l,t
is the weight of the l
th
distribution of pixel x
t
s mixture model;
µ
l
is the mean of the l
th
distribution; and Σ
l
is its covariance matrix, where
Σ
l
= σ
l
I, σ
l
is the standard deviation of the l
th
distribution, and I is an
identity matrix. To update the model, each new pixel is checked to see it
matches the existing Gaussian distributions. To adjust the weight of each
distribution, the weight ω
l,t
is updated by:
ω
l,t
=(1−α)+α(M
l,t
),
(9.2)
where α is the learning rate that controls the speed of the learning; M is a
Boolean value indicating whether or not a match is found. The definition of
M is as follows: M
l,t
= 1 when a match is confirmed on the l
th
distribution
at time t; otherwise, M
l,t
=0.
The parameters µ and σ can be updated as follows:
µ
l,t
=(1−β)µ
l,t−1
+ βx
t
,
(9.3)
σ
l,t
=(1−β)σ
l,t−1
+ β(x
t
−µ
l,t
)
T
(x
t
−µ
l,t
),
(9.4)
where β = αP (x
t
µ
l,t−1
,σ
l,t−1
). In each frame, pixels far away from the back-
ground distributions are recognized as foreground. A connectivity algorithm
is then applied to identify possible objects in motion. It is widely recognized
that an overly segmented result may break the detected objects into pieces.
Therefore, morphological operations must be applied to fix the completeness
of foreground objects. A detected foreground object is considered as a blob and
characterized by its position and color distribution to support the subsequent
tracking process. Fig. 9.2 illustrates the process of background estimation and
foreground segmentation. Fig. 9.2(a) is the original video frame with a moving
subject. After background estimation, an estimated background is shown in
Fig. 9.2(b). The foreground pixels obtained after applying background sub-
traction are shown in Fig. 9.2(c), in which noise, caused by wavering tree
branches, for example, can be filtered out by morphological operations. In the
meantime, blobs with high connectivity can be separated from the background
and detected as foreground objects as shown in Fig. 9.2(d).
