Biomedical Engineering Reference
In-Depth Information
information is enhanced while retaining the context in-
formation of the original image. This is accomplished in
one step by convolving the original image with the kernel
after adding one to its central coefficient. Edge enhance-
ment appears to provide greater contrast than the original
imagery when diagnosing pathologies.
Edges can be enhanced with several edge operators
other than those just mentioned and illustrated.
6.3.4.4 Local-area histogram
equalization
A remarkably effective method of image enhancement is
local-area histogram equalization, obtained with a modi-
fication of the pixel operation defined in Section 6.3.3.3.
Local-area histogram equalization applies the concepts of
whole-image histogram equalization to small, overlapping
local areas of the image
[7,11]
. It is a nonlinear operation
and can significantly increase the observability of subtle
features in the image. The method formulated as shown
next is applied at each pixel (
m,n
) of the input image.
h
LA
ðm; nÞðiÞ¼
X
Figure 6.3-8 Output image obtained when local-area histogram
equalization was applied to the image in
Fig. 6.3-2a
. Note that the
local-area histogram equalization produces very high contrast
images, emphasizing detail that may otherwise be imperceptible.
This type of enhancement is computationally very intensive and it
may be useful only for discovery purposes to determine if any
evidence of a feature exists.
6.3.5 Operations with multiple
images
K
X
L
d
ðfðm þ l; n þ kÞiÞ;
k¼K
l ¼L
i ¼
0
;
1
;
.
P
1
This section outlines two enhancement methods that
require more than one image of the same scene. In both
methods, the images have to be registered and their dy-
namic ranges have to be comparable to provide a viable
outcome.
j
ð
2
K þ
1
Þ
$
ð
2
L þ
1
Þ
X
1
H
LA
ðm; nÞðjÞ¼
h
LA
ðm; nÞðiÞ;
i ¼
0
j ¼
0
;
1
;
.
P
1
6.3.5.1 Noise suppression by image
averaging
gðm; nÞ¼ðP
1
Þ
$
H
LA
ðm; nÞðfðm; nÞÞ
where
h
LA
(
m, n
)(
i
) is the local-area histogram,
H
LA
(
m,
n
)(
j
) is the local-area cumulative histogram, and
g
(
m, n
)
is the output image.
Figure 6.3-8
shows the output image
obtained by enhancing the image in
Fig. 6.3-2a
with local-
area histogram equalization using
K ¼ L ¼
15 or a
31
31 kernel size.
Local-area histogram equalization is a computationally
intensive enhancement technique. The computational
complexity of the algorithm goes up as the square of the
size of the kernel. It should be noted that since the
transformation that is applied to the image depends on
the local neighborhood only, each pixel is transformed in
a unique way. This results in higher visibility for hidden
details spanning very few pixels in relation to the size of
the full image. A significant limitation of this method is
that the mapping between the input and output images
is nonlinear and highly nonmonotonic. This means that it
is inappropriate to make quantitative measurements of
pixel intensity on the output image, as the same gray level
may be transformed one way in one part of the image and
a completely different way in another part.
Noise suppression using image averaging relies on three
basic assumptions: (1) that a relatively large number of
input images are available, (2) that each input image has
been corrupted by the same type of additive noise, and
(3) that the additive noise is random with zero mean
value and independent of the image. When these as-
sumptions hold, it may be advantageous to acquire
multiple images with the specific purpose of using image
averaging
[1]
since with this approach even severely
corrupted images can be significantly enhanced. Each of
the noisy images
a
i
,(
m
,
n
) can be represented by
a
i
ðm; nÞ¼fðm; nÞþd
i
ðm; nÞ;
where
f
(
m
,
n
) is the underlying noise-free image, and
d
i
(
m, n
) is the additive noise in that image. If a total of
Q
images are available, the averaged image is
Q
Q
X
gðm; nÞ¼
1
a
i
ðm; nÞ
i ¼
1
