Image Processing Reference
In-Depth Information
where x
0
(
t
)
are the equations for motion in the x- and y-directions, respect-
ively. For example, for uniform motion in both x- and y-directions x
0
(
t
) ¼
v
x
t and
y
0
(
t
) ¼
v
y
t. If there is acceleration in the x-direction, then x
0
(
t
) ¼
and y
0
(
t
)
5at
2
0
:
þ
v
x
t, where
a is acceleration in the x-direction.
2.2.3 P
OINT
S
PREAD
F
UNCTION OF
H
UMAN
V
ISUAL
S
YSTEM
The third example of an LSI imaging system is the HVS. The optics of the eye, that
is, the cornea, the pupil, and the lens, constitute a blur type (low-pass) PSF, while the
rod and cone detectors
inhibitory response constitute a sharpening type (high-pass)
linear system. The actual PSF of the eye is the cascade of these two PSFs [3,5].
Finally, the PSF of a printing system consisting of a scanner, printer, and display
device is the convolution of the PSFs of the three imaging subsystems. This will be
described in detail in Chapter 3.
'
2.3 OPTICAL AND MODULATION TRANSFER FUNCTIONS
The optical transfer function (OTF) of an imaging system is defined as the 2-D
Fourier transform of its 2-D PSF and is given by the following integral
1
1
h
(
x, y
)
e
j
(v
x
x
þv
y
y
)
d
x
d
y
H
(v
x
,
v
y
) ¼
(
2
:
12
)
1
1
Either the OTF or the PSF completely characterizes an LSI imaging system. The
OTF of an imaging system is a complex quantity and consists of magnitude and
phase. The modulus of the OTF normalized to a value of 1 at zero frequency is
referred to as the modulation transfer function (MTF), that is,
H
(v
x
,
v
y
)
M
(v
x
,
v
y
) ¼
(
2
:
13
)
H
(
0, 0
)
As an example, consider uniformmotion in the x-direction; theOTF is one-dimensional
(1-D) since there is no motion in the y-direction. This 1-D OTF is given by
2
v
x
x
0
2
x
0
ð
j
v
x
x
0
¼
sin
v
x
x
0
e
j
v
x
x
0
1
x
0
1
e
j
v
x
x
0
e
j
v
x
x
OTF(v
x
) ¼
d
x
¼
(
2
:
14
)
2
0
The corresponding MTF is
2
v
x
x
0
2
¼
sin
v
x
x
0
MTF(v
x
) ¼
OTF(v
x
)
OTF(
(
2
:
15
)
)
0
Figure 2.2 shows MTF of uniform motion in the x-direction.
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