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1
Image Processing
:
4. Optical Flow
Aleix M. Martinez
aleix@ece.osuedu
Motion estimation
•
Optical flow is used to compute the motion of the
pixels of an image sequence. It provides a dense
(point to point) pixel correspondance.
•
Correspondence problem
: determine where the
pixels of an image at time
t
are in the image at
time
t+1
.
•
Large number of applications.
Two
important
definitions
•
Motion field:
“the 2
D projection of a 3D
motion onto the image plane.”
•
Optical flow:
“the apparent motion of the
brightness pattern in an image sequence.”
The method of
The method of
Horn and Schunck
•
This is the most fundamental optical flow algorithm.
•
As you will see, it has several
important
flaws that
makes its use inappropriate in a large number of
applications.
•
Most of the other algorithms proposed to date are
based on the formulation advanced by Horn and
Schunck.
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•
If the brightness is assumed to be constant from
frame to frame, then the motion associated to
each pixel
(x,y)
of an image
I
can be modeled as:
This is known as the
data conservation
constraint
.
•
The 1
st
order Taylor expansion
)
,
,
(
)
,
,
(
t
t
t
v
y
t
u
x
I
z
y
x
I
0
t
y
x
I
v
I
u
I
R
t
y
x
D
dxdy
I
v
I
u
I
E
2
)
(
)
,
,
(
)
,
,
(
t
t
t
v
y
t
u
x
I
z
y
x
I
t
I
t
y
I
y
x
I
x
t
y
x
I
t
y
x
I
)
,
,
(
)
,
,
(
0
t
0
t
I
y
I
dt
dy
x
I
dt
dx
0
dt
dI
,
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 Fall '10
 Martinez
 Image processing

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