Image Processing Reference

In-Depth Information

x

y

FIGURE 2.64

2.5
Consider a linear, shift-invariant image degradation system with a PSF

h
(
x, y
) ¼
e
2
[j
x
jþj
y
j]
. Suppose the input to the system is an image consisting of

one line as shown in Figure 2.64. What is the output image g
(
x, y
)

?

2.6
Suppose that an image f
(
x, y
)

be

the time-varying components of motion in the x-andy-directions, respectively.

The total exposure at any point of the recording medium (e.g.,

undergoes planer motion, and let x
0
(
t
)

and y
0
(
t
)

film) is obtained

by integrating the instantaneous exposure over the time interval during which

the shutter is open. Then, if T is the duration of exposure, we have

ð

T

1

T

g
(
x, y
) ¼

f
(
x
x
0
(
t
)

, y
y
0
(
t
))d
t

0

where g
(
x, y
)

is the output image.

a. Show that the OTF of the system is

ð

T

1

T

e
j
(v
x
x
0
(
t
)þv
y
y
0
(
t
))
d
t

H
(v
x
,

v
y
) ¼

0

b. Suppose that the image undergoes motion in the x-direction only, at the rate

of x
0
(
t
) ¼

0

:

5at
2
. Sketch the resulting MTF.

2.7
A PSF has no spatial frequencies greater than 400 cycles

=

mm. What values

would you assign to the sampling interval

D
x and the DFT length so as to obtain

samples of the MTF in which aliasing is negligible and samples are spaced no

further than 5 cycles

=

mm apart? The DFT length must be a power of 2.

2.8

Find the Fourier transform of a line oriented at an angle

u

as shown in

Figure 2.65.

Search WWH ::

Custom Search