Biomedical Engineering Reference
In-Depth Information
By normalizing each coefficient with the sum of all
(1115) a filter that preserves the scale of the image is
obtained.
Goshtasby and Turner
[38]
reported that smoothing
with a Gaussian filter reduced noise and helped in
thresholding of the endocardial surfaces on cardiac MR
images.
Preprocessing with
extremum sharpening
combined
with median filtering has proven to be useful in
segmenting microscopic images of blood cells
[14, 65]
.In
this method, a minimum and maximum are calculated
within an
N
by
N
window around each pixel (
x
,
y
). The
value of the extremum operator is simply whichever of
the two extrema is the closest to the value at pixel (
x
,
y
).
When the pixel (
x
,
y
) has a value exactly midway be-
tween minimum and maximum, the operator takes the
value of the pixel. The appropriate window size for the
extremum sharpening has to be commensurate with
the width of the image edges.
The extremum sharpening is usually followed by
median filtering, which smoothes out the slightly ragged
contours left by the sharpening operation. The standard
procedure suggested in
[65]
for segmenting cells was:
9
9 median filter (noise removal), 3
3 extremum
sharpening, and finally 5
5 median filter, followed by
thresholding based on threshold determined from the
histogram.
The median and Gaussian smoothing, as well as ex-
tremum sharpening, ''improve'' image histograms by
producing images with strongly bimodal histograms.
Additional techniques for making histogram valleys
deeper are discussed in Weszka
et al.
[127]
.
A more elaborate approach used for specific types of
images is provided by
adaptive filtering
techniques where
the parameters of the algorithm are modified locally
based on the pixel's neighborhood
[51, 68]
. If, for ex-
ample, the neighborhood has relatively constant in-
tensity, we can assume that we are within an object with
constant features and we can apply an isotropic
smoothing operation to this pixel to reduce the noise
level. If an edge has been detected in the neighborhood,
we could still apply some smoothing, but only along the
edge. Adaptive filtering combines an efficient noise re-
duction and an ability to preserve and even enhance the
edges of image structures. Westin used adaptive filtering
successfully for the thresholding of bones on CT images
[126]
.
pixels (called seeds) that belong to the structure of in-
terest. Seeds can be chosen by an operator, or provided
by an automatic seed finding procedure. In the next step
neighboring pixels are examined one at a time and added
to the growing region, if they are sufficiently similar
based on a uniformity test (also called a homogeneity
criterion). The procedure continues until no more pixels
can be added. The object is then represented by all pixels
that have been accepted during the growing procedure
[1, 6, 36, 77, 85, 96, 102, 104, 107, 113, 116]
.
One example of the uniformity test is comparing the
difference between the pixel intensity value and the
mean intensity value over a region. If the difference is
less than a predefined value, for example, two standard
deviations of the intensity across the region, the pixel is
included in the region; otherwise, it is defined as an edge
pixel. The results of region growing depend strongly on
the selection of the homogeneity criterion. If it is not
properly chosen, the regions leak out into adjoining areas
or merge with regions that do not belong to the object of
interest. Another problem of region growing is that dif-
ferent starting points may not grow into identical regions.
The advantage of region growing is that it is capable of
correctly segmenting regions that have the same prop-
erties and are spatially separated. Another advantage is
that it generates connected regions.
Instead of region merging, it is possible to start with
some initial segmentation and subdivide the regions that
do not satisfy a given uniformity test. This technique is
called
splitting
[41, 96, 107]
. A combination of
splitting
and merging
adds together the advantages of both
approaches
[6, 84, 133]
.
Various approaches to region growing segmentation
have been described by Zucker
[133]
. Excellent reviews
of region growing techniques were done by Fu and Mui
[30]
, Haralick and Shapiro
[41]
, and Rosenfeld and
Kak
[96]
.
An interesting modification of region growing tech-
nique called
hill climbing
was proposed by Bankman
et al.
for detecting microcalcifications in mammograms
[8]
.
The technique is based on the fact that in a given image
f
(
x
,
y
), the edge of a microcalcification to be segmented is
a closed contour around a known pixel (
x
0
,
y
0
), the local
intensity maximum. For each pixel, a slope value
s
(
x
,
y
)is
defined as
sðx; yÞ¼
fðx
0
; y
0
Þfðx; yÞ
dðx
0
; y
0
; x; yÞ
;
(6.4.4)
6.4.3 Region growing
where
d
(
x
0
,
y
0
,
x
,
y
) is the Euclidean distance between
the local maximum pixel and pixel (
x
,
y
).
In the first step, the object's edge points are identified
by radial line search emanating from the local maximum.
The line search is applied in 16 equally spaced directions
originating from the pixel (
x
0
,
y
0
), and for each direction,
Whereas thresholding focuses on the difference of pixel
intensities, the region growing method looks for groups
of pixels with similar intensities. Region growing, also
called region merging, starts with a pixel or a group of
