Image Processing Reference
In-Depth Information
in detail in a paper by Lee [4]. An alternative approach based on geometrical optics
results in a reasonable approximation of the 2-D PSF as a circle of unit area with a
radius R. The PSF is given by
1
p
R
2
x
2
þ
y
2
R
2
h
(
x, y
) ¼
(
2
:
6
)
0
otherwise
In this equation, R is the blur radius and is given by
f
2
2F
j
L
L
0
j
R
¼
(
2
:
7
)
LL
0
where
f is the focal length of the lens
F is the f number of the lens that is the focal length divided by diameter of the
lens aperture
L
0
is the distance at which the lens has been focused
L is the distance from the object to the lens
2.2.2 P
OINT
S
PREAD
F
UNCTION OF
M
OTION
B
LUR
Another example of a linear imaging system is the motion blur resulting from camera
motion or object motion. Consider an object with uniform motion in the horizontal
direction characterized by a constant speed v. During the exposure time T, a point on
the object moves by a distance x
0
¼
vT. Thus, the 2-D PSF is a line of length x
0
,thatis,
1
x
0
d(
y
)
0
x
x
0
h
(
x, y
) ¼
(
2
:
8
)
0
otherwise
Consequently, the image g
(
x, y
)
, which is moving with a speed
of v in the horizontal direction, is found by the following equation:
of an object
f
(
x, y
)
x
0
ð
1
x
0
g
(
x, y
) ¼
f
(
x, y
)
*
h
(
x, y
) ¼
f
(
x
l
, y
)dl
(
:
)
2
9
0
where * stands for convolution. Using a change of variable
l ¼
vt, we can rewrite
the above integral as
T
ð
1
T
g
(
x, y
) ¼
f
(
x
vt, y
)d
t
(
2
:
10
)
0
The above equation can be generalized for any type of motion as
ð
T
1
T
g
(
x, y
) ¼
f
(
x
x
0
(
t
)
, y
y
0
(
t
))d
t
(
2
:
11
)
0
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