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set, inspired from Chan and Vese approach [2], where topological changes are
naturally handled.
3.1 Motion Estimation by Optical Flow
Recently, many motion estimation techniques were developed. Although, Block
matching technique is the most used techniques and it have promising results
motion estimation especially with improvement techniques [8], we have used the
optical flow which had given us good results.
In our system, we use gradient-based optical flow algorithm proposed by Horn
and Schunck [1]. similar to T. Macan and S. Loncaric [11],we have integrated the
algorithm in multi-grid technique where the image is decomposed into Gaussian
pyramid-set of the reduced images. The calculation starts at a coarser scale of
the image decomposition, and the results are propagated to finer scales.
Let us suppose that the intensity of the image at a time t and position (x,
y) is given by I (x, y, t). The assumption on brightness constancy is made that
the total derivative of brightness function is zero which results the following
equation:
∂I
∂x
dx
dt
+
∂I
∂y
dy
dt
+
∂I
∂t
=0
or I
x,i
u
i
+
I
y,i
v
i
+
I
t,i
=0
(1)
This equation is named 'Brightness Change Constraint Equation'. Where u and v
are components of optical flow in horizontal and vertical directions, respectively,
and
I
x
,
I
y
and
I
t
are partial derivatives of I with respect to x, y and t respectively.
Horn and Schunck added additional smoothness constraint because the equation
(1) is insucient to compute both components of optical flow. They minimized
weighted sum of smoothness term and brightness constraint term:
2
+
2
)
dx
(
I
x
u
+
I
y
v
+
It
)
2
+
λ
(
∇
u
∇
v
(2)
Ω
Minimization and discretization of equation (2) results in two equations for each
image point where vector values
u
i
and
v
i
are optical flow variables to be de-
termined. To solve this system of differential equations, we use the iterative
Gauss-Seidel relaxation method.
3.2 Our Moving Object Segmentation Model
In our case, taking into consideration the motion information obtained by calcu-
lating the optical flow, we propose the following descriptors for the segmentation
of mobile objects in a video surveillance dataset:
k
in
(
x, Ω
in
)=
λ
2
|
SV
g
(
x
)
−
c
1
(
Ω
in
)
|
2
(3)
k
out
(
x, Ω
out
)=
λ
|
SV
g
(
x
)
−
c
2
(
Ω
out
)
|
k
b
(
x
)=
μ
With
c
1
is the average of the region
Ω
in
,
c
2
is the average of the region
Ω
out
,
μ
and
λ
constants positive. SVg(x) is the image obtained after a threshold of the
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