Biomedical Engineering Reference
In-Depth Information
Figure 6.3-9 Filtering with the Butterworth filter. (a) Fourier transform of MRI image in (e); the five circles correspond to the
b
values
75, 90, 95, 99, and 99.5%. (b) Fourier transform of low-pass filter with
b
¼ 90% which provides the output image in (f). (c) Band-pass filter
with band
b
¼ 75% to
b
¼ 90% whose output is in (g). (d) High-pass filter with
b
¼ 95%, which yields the image in (h). (Courtesy of
Dr. Patricia Murphy, Johns Hopkins University Applied Physics Laboratory.)
determines the amount of retained image power. The
percentage of total power that the retained power con-
stitutes is given by
b
¼
P
ðu;vÞ
˛
S
jFðu; vÞj
2
that form 5% of the image power.
Figure 6.3-9c
shows
a band-pass filter formed by the conjunction of a low-pass
filter at 95% and a high-pass filter at 75%, while the
output image of this band-pass filter is in
Fig. 6.3-9g
.
P
c
ðu;vÞ
jFðu; vÞj
2
100
and is used generally to guide the selection of the cutoff
threshold. In
Fig. 6.3-9a
, circles with radii
r
b
that cor-
respond to five different b values are shown on the
Fourier transform of an original MRI image in
Fig. 6.3-9e
.
The
u ¼ v ¼
0 point of the transform is in the center of
the image in
Fig. 6.3-9a
. The Butterworth low-pass filter
obtained by setting
D
T
equal to
r
b
for b
¼
90%, with
c ¼
1
and
n ¼
1, is shown in
Fig. 6.3-9b
where bright points
indicate high values of the function. The corresponding
filtered image in
Fig. 6.3-9f
shows the effects of
smoothing. A high-pass Butterworth filter with
D
T
set
at the 95% level is shown in
Fig. 6.3-9d
, and its output in
Fig. 6.3-9h
highlights the highest frequency components
6.3.7 Concluding remarks
This chapter has focused on fundamental enhancement
techniques used on medical and dental images. These
techniques have been effective in many applications and
are commonly used in practice. Typically, the techniques
presented in this chapter form a first line of algorithms in
attempts to enhance image information. After these al-
gorithms have been applied and adjusted for best out-
come, additional image enhancement may be required to
improve image quality further. Computationally more
intensive algorithms may then be considered to take
advantage of context-based and object-based information
in the image.
