Image Processing Reference
In-Depth Information
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
10
20 30
Spatial frequency, cycles/°
40
50
FIGURE 2.4
MTF of the HVS.
final example, we consider the MTF of the HVS. The measurement on
human subjects has con
As a
rmed that the MTF of the HVS can be approximated by the
empirical function given by [3,5],
b
e
vr
q
v
¼MTF(v
r
) ¼
A
aþ
v
r
v
0
v
0
MTF(v
x
,
v
y
) ¼MTF
2
x
þv
2
y
(
2
:
29
)
In image processing applications, the following parameter values have been
used: A
¼
2
:
6,
a ¼
0
:
0192,
v
0
¼
8
:
772 cycles
=
degree and
b ¼
1
:
1. The plot of
MTF is shown in Figure 2.4.
The MTF of LSI discrete systems (such as a digital printer) can be measured
using DFT concepts. In a discrete system, a sampled input (an image described as
pixels) results in an output (printed image) that is the convolution of the input with
the system PSF (in this case resulting from the inef
ciencies of the development
process). Using linear system theory concepts, the MTF of the system can be
measured by applying a sampled sinusoid with a certain frequency to the system
and measuring its output. The ratio of the output to input modulation gives the MTF
at that particular frequency and orientation. The main problem with this approach is
that even for a given orientation, many such measurements are needed before a
good approximation to the MTF curve can be constructed. An approach that is based
on square-wave analysis is more ef
cient. Since the harmonics of a square wave
contain signi
cant energy at high frequencies, a single measurement can determine
several MTF points. To
find the MTF of such a linear system, an input level is
chosen and a square wave with two amplitudes near that input level is constructed.
The number of pixels contained in each cycle of the square wave (which de
nes the
fundamental frequency or the
first harmonic of the wave) would depend on the
resolution needed for the MTF measurement. In practice, several square waves with
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