Biomedical Engineering Reference
In-Depth Information
Figure 6.4-3 An example of the sensitivity of the threshold level
selection. (A) Cross-sectional intensity profile of a light object on
a dark background with three thresholding levels T l, T2, and T3,
and three other levels generated by adding a small value DT;
(B) a hypothetical plot of the area (A) or perimeter (P) versus
thresholding level T.
when prior
information on object
locations is not
available.
A related technique that evaluates multiple thresholds
is based on an estimate of the gradient magnitude around
the segmented object edge
[16]
. The average gradient
magnitude is given by
Figure 6.4-2 An example of global thresholding. (A) Original
image, (B) histogram of image A, (C) result of thresholding with T ¼
127, (D) outlines of the white cells after applying a 3 3 Laplacian
to the image shown in C.
DT PðTÞ
DA
¼
PðTÞ
G ¼
lim
D
T
/0
HðTÞ
;
(6.4.2)
where
H
(
T
) is the histogram function. The threshold
that maximizes the average boundary gradient is selected.
If an image contains more than two types of regions, it
may still be possible to segment it by applying several
individual thresholds
[96]
, or by using a multithresholding
technique
[86]
. With the increasing number of regions,
the histogram modes are more difficult to distinguish,
and threshold selection becomes more difficult.
Global thresholding is computationally simple and
fast. It works well on images that contain objects with
uniform intensity values on a contrasting background.
However, it fails if there is a low contrast between
the object and the background, if the image is noisy, or if
the background intensity varies significantly across the
image.
intensities in the circular regions around selected pixels,
the threshold is calculated automatically and it corre-
sponds to the least number of misclassified pixels be-
tween two distributions. The result of the thresholding
operation is displayed as a contour map and super-
imposed on the original image. If needed, the operator
can manually modify any part of the border. The same
technique was also applied to extract lymph nodes from
CT images and was found to be very sensitive to user
positioning of interior and exterior points
[95]
. Some of
the threshold selection techniques are discussed in Refs.
[25, 96, 127]
.
In many applications appropriate segmentation is
obtained when the area or perimeter of the objects is
minimally sensitive to small variations of the selected
threshold level.
Figure 6.4-3
A shows the intensity profile
of an object that is brighter than background, and three
threshold levels for segmentation:
T
1,
T
2, and
T
3. A
small variation
DT
in the lowest threshold level will cause
a significant change in the area or perimeter of the seg-
mented object. The same is true for the highest threshold
level. However, a change of
DT
in the middle level will
have minimal effect on the area or perimeter of the
object. The object area
A
(
T
) and perimeter
P
(
T
) are
functions of the threshold
T
that often exhibit the trend
shown in
Fig. 6.4-3
B. Therefore, the threshold level that
minimizes either
dA
(
T
)/
dT
or
dP
(
T
)/
dT
is often a good
choice, especially in the absence of operator guidance and
6.4.2.2 Local (adaptive) thresholding
In many applications, a global threshold cannot be found
from a histogram or a single threshold cannot give good
segmentation results over an entire image. For example,
when the background is not constant and the contrast of
objects varies across the image, thresholding may work
well in one part of the image, but may produce un-
satisfactory results in other areas. If the background
variations can be described by some known function of
position in the image, one could attempt to correct it by
using gray level correction techniques, after which
a single threshold should work for the entire image.
