Biomedical Engineering Reference
In-Depth Information
Figure 6.3-3 (a) Original image where gray levels are not uniformly distributed. Many image details are not well visualized in this image
because of the low contrast. (b) Histogram of the original image in (a). Note the nonuniformity of the histogram. (c) Cumulative histogram
of the original image in (a). (d) Histogram-equalized image. Contrast is enhanced so that subtle changes in intensity are more readily
observable. This may allow earlier detection of pathological structures. (e) Histogram of the enhanced image in (d). Note that the dis-
tribution of intensity counts that are greater than the mean value have been distributed over a larger gray level range. (f) Cumulative
histogram of the enhanced image in (d). (g) Original brain MRI image (courtesy of Dr. Christos Dzavatzikos, Johns Hopkins Radiology
Department). (h) through (l) same steps as above for brain image.
A simple and readily available procedure for re-
distribution of the pixels in the image is based on the
normalized cumulative histogram, defined as
HðjÞ¼
M
$
N
X
Figure 6.3-3a
presents an original dental image where
the gray levels are not uniformly distributed, while the
associated histogram and cumulative histogram are
shown in
Figs 6.3-3b
and
6.3-3c
, respectively. The
cumulative histogram is then used to map the gray levels
of the input images to the output image shown in
Fig. 6.3-3d
.
Figure 6.3-3e
presents the histogram of
Fig. 6.3-3d
, and
Fig. 6.3-3f
shows the corresponding
cumulative histogram.
Figure 6.3-3f
should ideally be
a straight line from (0,0) to (
P
1,
P
1), but in fact
only approximates this line to the extent possible given
the initial distribution of gray levels.
Figure 6.3-3g
j
hðiÞ; j ¼
0
;
1
;
.
; P
1
:
The normalized cumulative histogram can be used as
a mapping between the original gray levels in the image
and the new gray levels required for enhancement. The
enhanced image
g
(
m, n
) will have a maximally uniform
histogram if it is defined as
gðm; nÞ¼ðP
1
Þ
i ¼
0
$
Hðfðm; nÞÞ:
