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C2
V8
V(1) V(2) V(3) V9
V4
V7
R SR(V(x,y))
V3
V(4) V(x,y) V(5) V1
V(x,y)
V2
V5
Vn-1
V(6) V(7) V(8) V6
Vn
C1
(a) (b)
Figure 3. The ViBe-based method: (a) the eight neighbor domain; and (b) the background model of ViBe.

3.2. Adaptive updating mechanism for ViBe method
When the background of the video is established, the next step is to detect the moving objects. The basic
discrimination mechanism for the general ViBe method is as follows: for each pixel in the new frame of the
video, a sphere ( ( , )) of radius centered on the value ( , ) of the pixel is defined (see Figure 3b).
Then, the pixel of the new frame can be determined as the background or foreground by [44] :

{
1, Ψ{ ( ( , )) ∩ ( , )} ≤
1( , ) = (5)
0, Ψ{ ( ( , )) ∩ ( , )} >
wherefunction Ψ{ ( ( , ))∩ ( , )} meansthecardinalityofthesetintersectionofthesphere ( ( , ))
and the collection of ( , ). is a threshold. If 1( , ) = 1, it means the pixel point ( , ) belongs to
foreground. Otherwise, it means the pixel point ( , ) belongs to background.

Thelaststepistorandomlyupdatethebackgroundmodelwitheachnewframe. Becauseofthestrongstatistical
correlation between a pixel and its neighboring pixel, when a pixel is detected as the background pixel, it has
a probability of 1/ to update model sample set (where is called update rate). Meanwhile, it also has the
probability of 1/ to update the background model of neighboring pixels.

FromthediscriminationmechanismoftheoriginalViBealgorithminFigure3a,b, wecanseethatthedetection
radius and the update rate are two very important parameters. In general, the detection radius should be
larger and the update rate should be smaller in the dynamic background, to make more pixels be classified
as background, and vice versa. However, in the general ViBe algorithm, the values of the parameters and
are predefined by the designers, which reduce the adaptivity of the ViBe algorithm. Because the value of the
eight neighboring pixels difference between the background and the current frame is the factor that can reflect
the complex degree of background, it is used to determine the values of the detection radius and the update
rate adaptively. Namely,
{
0 · (1 + ), > 0
= (6)
0 · (1 − ), ≤ 0

{
0 · (1 − ), > 0
= (7)
0 · (1 + ), ≤ 0
where 0 and 0 are the initial values of the detection radius and the update rate ; 0 is a threshold; and
is a parameter to judge the change of the current scenario, which is calculated by

∑
+1 ( , )
= (8)