Image Processing Reference
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 )
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
g ( x, y ) ¼
f ( x x 0 ( t )
, y y 0 ( t ))d t
where g ( x, y )
is the output image.
a. Show that the OTF of the system is
e j (v x x 0 ( t )þv y y 0 ( t )) d t
H (v x ,
v y ) ¼
b. Suppose that the image undergoes motion in the x-direction only, at the rate
of x 0 ( t ) ¼
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.
Find the Fourier transform of a line oriented at an angle
as shown in