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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