Biomedical Engineering Reference
In-Depth Information
Another solution is to apply
local (adaptive) thresholding
[6, 9, 18, 25, 41, 63, 80, 127]
.
Local thresholds can be determined by (1) splitting an
image into subimages and calculating thresholds for each
subimage, or (2) examining the image intensities in the
neighborhood of each pixel. In the former method
[18]
,
an image is first divided into rectangular overlapping
subimages and the histograms are calculated for each
subimage. The subimages used should be large enough to
include both object and background pixels. If a subimage
has a bimodal histogram, then the minimum between the
histogram peaks should determine a local threshold. If
a histogram is unimodal, the threshold can be assigned by
interpolation from the local thresholds found for nearby
subimages. In the final step, a second interpolation is
necessary to find the correct thresholds at each pixel.
In the latter method, a threshold can be selected using
the mean value of the local intensity distribution.
Sometimes other statistics can be used, such as mean
plus standard deviation, mean of the maximum and
minimum values
[16, 25]
, or statistics based on local
intensity gradient magnitude
[25, 62]
.
Modifications of the above two methods can be found
in Refs.
[30, 41, 80, 96]
. In general, local thresholding is
computationally more expensive than global thresh-
olding. It is very useful for segmenting objects from
a varying background, and also for extraction of regions
that are very small and sparse.
Figure 6.4-4 Median filtering as a preprocessing step for
thresholding; (A) original autoradiography image, (B) result of a 7 7
median filter, (C) result of a 9 9 median filter. Corresponding
image histograms are shown on the right.
sharpens the peaks on the image histogram (
Figs 6.4-4
B
and C) and allows selection of thresholds for image
segmentation.
A common smoothing filter is the
Gaussian filter,
where for each pixel [
i, j
], the convolution mask co-
efficients
g
[
i, j
] are based on a Gaussian function:
g½i; j¼
exp
ði
2
þ j
2
Þ
2s
2
6.4.2.3 Image preprocessing
and thresholding
Many medical images may contain low-contrast, fuzzy
contours. The histogram modes corresponding to the
different types of regions in an image may often overlap
and, therefore, segmentation by thresholding becomes
difficult. Image preprocessing techniques can sometimes
help to improve the shape of the image histogram, for
example by making it more strongly bimodal. One of the
techniques is image
smoothing
by using the
mean
(
aver-
age
)or
median
filter discussed in Chapter 6.3
[53, 65,
96, 99]
. The mean filter replaces the value of each pixel
by the average of all pixel values in a local neighborhood
(usually an
N
by
N
window, where
N ¼
3, 5, 7, etc.). In
the median filter, the value of each pixel is replaced by
the median value calculated in a local neighborhood.
Median smoothing, unlike the mean filter, does not blur
the edges of regions larger than the window used while
smoothing out small textural variations.
Figure 6.4-4
il-
lustrates results of preprocessing on an autoradiography
image using a median filter with 7
7 and 9
9 win-
dows.
Figure 6.4-4
A shows the original image and its
histogram, which is unimodal and, therefore, precludes
selection of an appropriate threshold. Median filtering
;
(6.4.3)
where s is the spread parameter (standard deviation)
that defines the degree of Gaussian smoothing: Larger
s implies a wider Gaussian filter and a greater amount
of smoothing. The Gaussian filter can be approximated
in digital images by an
N
by
N
convolution mask. A 7
7
Gaussian mask with s
2
¼
2
[52]
is obtained with the
coefficients of the following matrix:
1470741
412263326124
726557155267
10 33 71 91 71 33 10
726557155267
412263326124
1470741
