Download Aggressive region growing for speckle reduction in ultrasound images

Pattern Recognition Letters 24 (2003) 677–691
www.elsevier.com/locate/patrec
Aggressive region growing for speckle reduction
in ultrasound images
Yan Chen a, Ruming Yin b, Patrick Flynn
c,*
,
Shira Broschat
d
a
Siemens Medical Imaging, Issaquah, WA 98127, USA
Maxim Integrated Products, Portland, OR 97124, USA
c
Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN 46556, USA
d
School of Electrical Engineering and Computer Science, Washington State University, P.O. Box 642752,
Pullman, WA 99164-2752, USA
b
Abstract
Speckle appears in all conventional medical B-mode ultrasonic images and can be an undesirable property since it
may mask small but diagnostically significant features. In this paper, an adaptive filtering algorithm is proposed for
speckle reduction. It selects a filtering region size using an appropriately estimated homogeneity value for region
growth. Homogeneous regions are processed with an arithmetic mean filter. Edge pixels are filtered using a nonlinear
median filter. The performance of the proposed technique is compared to two other methods––the adaptive weighted
median filter and the homogeneous region growing mean filter. Results of processed images show that the method
proposed reduces speckle noise and preserves edge details effectively.
Ó 2002 Elsevier Science B.V. All rights reserved.
Keywords: Speckle; Adaptive filtering; Ultrasound imaging; Region growing
1. Introduction
Speckle in ultrasound imagery results directly
from the use of a coherent transducer and occurs
when structure in the object is on a scale too small
to be resolved by the imaging system (Burckhaardt,
1978). It is an interference phenomenon––small
scatterers cause constructive and destructive phase
interference at the receiving array. Speckle can be
an undesirable property since it may mask small
but diagnostically significant features.
*
Corresponding author.
E-mail address: fl[email protected] (P. Flynn).
An examination of the literature reveals a
number of interesting speckle suppression techniques as well as analyses of speckle formation.
The value of the median filter in suppression of
impulsive noise has long been recognized. Pitas
and Venetsanopoulos (1992) published a seminal
survey on the use of order statistics (such as the
median) in image filtering.
Dutt and Greenleaf (1996) highlighted the effect
of logarithmic compression on speckle visibility,
and their analysis suggested a normalized variance
as an estimable speckle strength statistic. This
statistic motivated the development of a tunable
unsharp masking filter for speckle suppression.
Kofidis et al. (1996) proposed a content-based
0167-8655/03/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved.
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Y. Chen et al. / Pattern Recognition Letters 24 (2003) 677–691
technique for speckle suppression. The input
image is segmented into homogeneous regions using
a learning vector quantizer for unsupervised segmentation. An order statistic filter with optimal
mean-squared error properties is tuned to each
image segment and applied to remove speckle
contamination.
Hao et al. (1999) proposed a multiscale denoising technique for B-scan images. The original
image is decomposed into a low-frequency component and a high-frequency component using an
adaptive median filter. Each component undergoes
a hierarchical wavelet transform, and selected coefficients in the transform domain are thresholded
adaptively. Inverse wavelet transformations and
summing of results produce an output image with
suppressed speckle content.
In a previous paper (Chen et al., 1996), we
discussed the statistics of speckle and proposed
general methods for speckle reduction prior to
image formation. Recently, much interest has focused on post-formation image filtering (Bamber
and Daft, 1986; Bernstein, 1987; Fong et al., 1989;
Kotropoulos and Pitas, 1992; Loupas et al., 1989)
and in this paper we propose an improved method
of this type. Two advantages of post-formation
image processing are its applicability to existing
images and its ease of implementation on generalpurpose computers. The increasing power of digital
signal processing chips and parallel computation
already allow some image processing algorithms
of this sort to be executed in real time.
Median filtering (a standard post-filtering
technique) is often effective for speckle reduction.
It uses the median intensity in a suitably sized and
shaped region Wij surrounding the pixel ði; jÞ of
interest as the output pixel value; hence it eliminates any impulsive artifacts with an area (in pixels) less than half the region size kWij k. Since the
amount of smoothing performed by the median
filter is influenced only by the region size, the
median filter removes some high frequency signals.
This results in blurring at edges. Furthermore,
when a speckle artifact is larger (in pixels) than
1=2kWij k, it remains in the output image after filtering.
Adaptive filtering techniques have been developed for feature detection in ultrasonic images
(Bamber and Daft, 1986; Bernstein, 1987). As with
median filtering, most of these techniques generate
the filter output at each pixel from the properties
of the data samples observed through a fixedsize region Wij (typically rectangular) containing
the pixel of interest. The adaptive weighted median
filter (AWMF) (Loupas et al., 1989) is an enhanced
median filter. The weighted median of a region
Wij ’s pixels is defined as the median of an extended
sequence formed by replicating pixels in Wij by
an amount calculated from their distance to ði; jÞ
and an estimate of the local image homogeneity
hij . The use of pixel replication in the AWMF
technique eliminates the requirement that speckle
artifacts be smaller than half the region size as is
required for pure median filtering.
An alternative or supplemental approach for
improving speckle suppression is to expand the
local processing region as much as possible, allowing non-speckle pixels to dominate speckle
pixels in population. Koo and Park (1991) proposed a technique called the homogeneous region
growing mean filter (HRGMF). Their technique
requires a pre-specified, image-dependent constant
homogeneity h0 as a threshold value. The local
homogeneity hij is estimated initially within an
estimation window Wij of default size containing
ði; jÞ; the ratio of pixel sample variance to pixel
mean in the window is a typical estimator. If
hij < h0 , the region is assumed to lie completely
within a homogeneous background and is expanded; otherwise, the region is contracted. After
the maximal-sized homogeneous region is obtained by means of this procedure, the output pixel
value is set to the mean intensity of the region.
Karaman et al. (1995) modified the HRGMF
method to use ‘‘appropriately’’ shaped and sized
local filtering kernels Wij . Their method estimates
image homogeneity hij in an 11 11 neighborhood
of ði; jÞ and uses it to form a connected local filtering kernel Wij for speckle suppression. The filter
output is the mean or the median of intensities in
Wij .
We investigated the methods described above
through implementation and analysis. We found
the quality of the AWMF technique’s output to
be sensitive to the values of its empirically selected
parameters, especially when the region is small. In
Y. Chen et al. / Pattern Recognition Letters 24 (2003) 677–691
the HGRMF technique, the expansion of regions
is often blocked prematurely by speckle. Furthermore, the HGRMF technique uses a constant
homogeneity threshold, but statistical tests show
that homogeneity depends on the size of the region
as well as on image depth. In Karaman’s modification, the homogeneity is measured using a fixed
region size. A small region size does not guarantee
selection of a connected region, and a large region
size may cause the region to grow too large and
blur object edges.
In this paper, we propose a new region growing
method, called aggressive region growing filtering
(ARGF), for ultrasound speckle reduction. As in
many speckle reduction techniques, it constructs a
filtering region Wij at each pixel ði; jÞ and the output pixel at ði; jÞ is computed from this region. The
distinctive elements of the proposed technique are
as follows:
(1) An adaptive homogeneity threshold h0;ij ,
rather than a constant threshold h0 , is used
to determine an appropriate shape and size
for the region Wij . The adaptive homogeneity
threshold is based on the statistics of expected
local image homogeneity.
(2) An aggressive region growing method is used
to avoid premature blockage of the filtering region growth due to speckle.
(3) The filtering regions are recycled for neighboring pixels when possible, avoiding a initialization step in homogeneous regions. This
reduces computation time.
(4) Once the final filtering region is determined at
ði; jÞ, one of two filters is used to compute the
output pixel value. A trimmed arithmetic mean
filter is used to filter regions judged to be
homogeneous to preserve contrast, but a simple median filter is used for heterogeneous
regions that are assumed to contain resolvable
edges.
In Section 2, the aggressive region growing
filtering technique is described. It is applied to
tissue-mimicking phantom images and to real tissue images. Results are compared with two other
speckle suppression methods in Section 3. The
pooled signal-to-noise ratio (SNR) and contrast-
679
to-noise ratio (CNR) are used to evaluate the results of the three methods.
2. Aggressive region growing filtering
Recent interest in B-mode ultrasound image
analysis has focused on post-formation image
filtering techniques that are applied to envelopedetected ultrasound images. Several adaptive (region-based) techniques have been developed for
speckle noise suppression, but there are no systematic rules to determine the appropriate region
size for each pixel in a given B-mode image. The
size of a region appropriate for one local region
may not be appropriate for other parts of the
image. For example, we might prefer a large region
to smooth speckle and a small region to preserve
object edges. Choosing a correct region size is
critical for high quality output since it involves a
tradeoff between speckle removal and boundary
detection.
Before we discuss the details of the proposed
aggressive region growing filtering method, we
introduce some notation and definitions. Let X ¼
½xij , i ¼ 1; . . . ; Nr , j ¼ 1; . . . ; Nc be the input image
containing Nr rows and Nc columns with intensity
value xij at pixel ði; jÞ. A region W of X is a connected subset of X. We will often use the notation
Wij to identify a local region associated with ði; jÞ.
Two sample statistics, the arithmetic mean l^W and
the variance r^2W of image intensities, are frequently
computed within a region and are given by
l^W ¼
1 X
xij
kW k ði;jÞ2W
and
r^2W ¼
1 X
2
ðxij l^W Þ ;
kW k ði;jÞ2W
where kW k denotes the cardinality of W (i.e., the
number of pixels in W).
The statistics of homogeneity can be examined
to find an expected homogeneity value for an image region of a given size not containing an object
edge. These homogeneity values are used as criteria in a two-step process which first identifies a
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Fig. 1. Diagram of the aggressive region growing method.
minimal homogeneous region containing the pixel
of interest and then expands that region (up to a
pre-specified maximum size) while satisfying the
homogeneity criterion. The size of the output region identifies the specific local filtering procedure
to be used to produce the value of the output pixel.
The resulting region shape depends on the region
growing method. ARGF uses a simple fourdirection growing method whose result is a rectangular shape.
Fig. 1 shows a diagram of the proposed ARGF
method. The details of the approach are presented
below.
2.1. Homogeneity model
The statistics of ultrasonic speckle have been
studied for many years. In uniformly spatially
distributed speckle regions, the amplitude of fully
developed speckle has been determined to follow a
Rayleigh distribution with the mean proportional
to the standard deviation (Burckhaardt, 1978).
However, logarithmic compression of the echo
amplitude data is widely used in clinical ultrasound scanners. Other nonlinear signal processing
may also be employed inside scanners. These
procedures may change the statistics of speckle
features, and a robust homogeneity-based technique must take such gray-scale transformations
into account.
Figs. 2 and 3 show the gray-level histograms for
a uniform speckle phantom and two homogeneous
regions (highlighted rectangles) in a real human
neck image. Both histograms show a Gaussianshaped rather than a Rayleigh-shaped distribution. Thus, the linear relation between the
standard deviation and the mean does not seem to
exist. In such cases, Loupas et al. (1989) suggested
that the local mean might be proportional to the
local variance rather than to the standard deviation. We tested this linearity hypothesis using
Pearson’s product-moment correlation coefficient
(Winkler and Hays, 1975) for which perfect linearity yields the values þ1 (positive slope) or )1
(negative slope) and nonlinearity yields zero. The
local mean and the local variance were measured
at different locations on uniform speckle regions
using an 11 11 rectangular region. We thus obtained a pair of sample populations M ¼ f^
li ; i ¼
1; . . . ; ng and S ¼ f^
r2i ; i ¼ 1; . . . ; ng. The product–
moment correlation coefficient between the local
mean and the variance is given by
Pn
ð^
l l^M Þð^
r2i l^S Þ
cM;S ¼ i¼1 i
;
n^
rM r^S
where the n pairs of values fð^
l2i ; r^2i Þg represent a
sample of size n from the two sample populations
M and S, and f^
lM g, f^
lS g, f^
rM g and f^
rS g represent
the sample means and the sample standard deviations of M and S, respectively. In our tests, the
resulting correlation coefficient value was found to
exceed 0.9, so for our test data we can assume that
the mean and the variance have a linear relationship.
The linear relation between the mean and the
variance ensures that speckle specifications of these
images fit the signal-dependent noise model proposed by Loupas et al. (1989):
pffiffiffi
y ¼ x þ n x:
Here y is the observed signal, x is the true signal, and n is the speckle noise. In a homogeneous
speckle region, we assume that the underlying
signal x is constant. Thus, from the signal model
we obtain r2 ¼ xr2n , where r2 and r2n are the variance of the observed signal y and the variance of
Y. Chen et al. / Pattern Recognition Letters 24 (2003) 677–691
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Fig. 2. The uniform speckle phantom image. (a) The original image, (b) gray-level histogram.
Fig. 3. (a) The selected homogeneous regions, (b) the gray-level histogram of region A, (c) gray-level histogram of region B.
the noise n, respectively. If the arithmetic mean l
of the output signal is used as the expectation of x,
then r2n ¼ r2 l. In such a way, the ratio r2 =l can be
used to describe the baseline noise level in a
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Y. Chen et al. / Pattern Recognition Letters 24 (2003) 677–691
homogeneous region, and we define its sample estimate at a pixel ði; jÞ as the local homogeneity hij :
r^2ij
ð1Þ
hij ¼ :
l^ij
We use hij in a decision procedure to determine
whether a local region (a filtering region containing a pixel of interest) is homogeneous. Obviously,
any method using hij to discriminate the speckle
features can only be used successfully in ultrasonic
images when the linear relationship between the
mean and the variance is confirmed.
2.2. Adaptive homogeneity criterion
Non-textured regions have a smaller value of hij ,
while hij is higher in regions containing edges. If we
use the homogeneity values of regions containing
uniform speckle as a decision threshold h0 , we can,
in principle, classify image regions as homogeneous
or non-homogeneous by comparing their homogeneities hij –h0 . If hij < h0 , the region tested is
considered to be homogeneous and should be
smoothed; otherwise, it contains a resolvable edge
and should be preserved. However, speckle features
are affected by many factors, including the local
mean level, image depth, and measurement region
size. Since the homogeneity criterion h0 describes
speckle features, it is also affected by these factors.
In such cases, an adaptive or adjustable criterion is
preferred. We use the ultrasound images of both the
uniform speckle phantom and real human neck to
develop and test relationships between homogeneity hij and these factors. The results are used to
construct an adaptive homogeneity criterion.
2.2.1. Region size
In the HRGMF method, a fixed value h0 is
chosen for the homogeneity threshold. A region
with homogeneity below h0 is considered to be
homogeneous; otherwise it is assumed to contain
an edge. Statistical tests on both phantom images
and real object images show that homogeneity
depends on the region size used to form the estimate. Thus, we propose using an adjustable homogeneity criterion based on local statistics.
Homogeneity is measured at different locations
in uniform speckle regions using different region
sizes. Fig. 4 shows the experimentally determined
relationship between homogeneity and region size.
The values plotted in (a) are the sample means of
the measurements, and the corresponding sample
deviations are plotted in (b). Examination of the
homogeneity h versus region size suggests the parameterized model:
h0 ¼
akwk
;
b þ kwk
ð2Þ
Fig. 4. The nonlinear relation between h and region size kW k (a), and between the standard deviation of h and kW k (b), the uniform
speckle phantom image (solid curve) and the real neck image (dotted curves for two test regions).
Y. Chen et al. / Pattern Recognition Letters 24 (2003) 677–691
where a and b are parameters with values that are
estimated empirically, and kwk is the region size.
While homogeneity h increases as the region size
grows larger, its standard deviation decreases.
Therefore, the following parameterized model for
the standard deviation r0 is proposed:
r0 ¼ c þ kedkW k ;
ð3Þ
where c and k are parameters with values that are
estimated empirically. The model parameters are
obtained via nonlinear regression based on observed homogeneity measurements.
We conducted homogeneity estimation experiments using three different phantom images. The
goal of these experiments was to identify an appropriate parameterized model for homogeneity
as a function of region size. To gain confidence in
the model, a statistical hypothesis test was applied
to two sets of homogeneity estimates obtained
from different locations of the test region. The
image was tiled twice with r c rectangles. In the
first tiling, the upper left corner of the ‘‘first’’
rectangle was located in the upper left corner of
the image. The second tiling was a displacement
(by r=2 pixels vertically and r=2 pixels horizontally) of the first tiling. Rectangles that fell partially outside the image were ignored. Using this
procedure, we generated two sets of homogeneity
estimates for each testing region size. The t-test
was applied to the two sets to test a null hy-
683
pothesis that the homogeneity estimates in each
set were drawn from the same distribution. This
t-test accepted the null hypothesis at the 99%
significance level for all images at region sizes
between 50 and 200 pixels. This implies that there
is no systematic effect of region placement on the
homogeneity estimates.
2.2.2. Local mean
The homogeneities of small regions within a
uniform speckle area may depend on their local
means. The relationship between the homogeneity
hij and the local mean l^Wij (Fig. 4(a)) was measured
for a uniform speckle phantom image using different region sizes. Since the frequency of pixels at
gray levels of 100–160 is high (Fig. 3(b)) and this
range of gray levels exhibits good linearity, the
linear model
hij ¼ a þ b^
lWij
was used for parameter estimation using a least
squares regression algorithm. The resulting slope b^
of the linear model was about 0.01. Since this
value is small, we neglect the effect of the local
mean level and consider homogeneity hij to be
constant in areas of uniform speckle.
2.2.3. Image depth
Fig. 5 shows estimates of hij versus region size
at different depths (vertical positions) in the image.
Fig. 5. The dependency of hij on local mean (a) and on image depth (b).
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Y. Chen et al. / Pattern Recognition Letters 24 (2003) 677–691
Each contour represents a range of depths as noted. Clearly, the relationship between homogeneity
and depth is nonlinear, but no specific relationship
could be found. We used a simple method to remove the effects of image depth in our tests: we
split the test image into four parts and applied
statistical tests to each part. Four corresponding
sets of parameters were obtained for the homogeneity model. At each pixel, the ARGF procedure
used one of these different sets of parameters depending on its depth in the image.
2.2.4. Homogeneity criterion
The tests of homogeneity dependency described
above suggest an improved homogeneity criterion:
use the homogeneity model (Eqs. (2) and (3)) to
obtain an adaptive homogeneity criterion. In this
criterion, h0;kW k;d and r0;kW k;d describe the statistical
specifications of homogeneous regions and are
adaptively determined based on the current region’s size and depth in the image. Whether or not
a new region is homogeneous is determined by
comparing its homogeneity hij to this adaptive
homogeneity criterion. If its homogeneity hij
is below h0;kW k;d þ r0;kW k;d , the region is assumed to
be homogeneous. In summary, the new region is
assumed to be homogeneous only if it satisfies
hij < h0;kW k;d þ r0;kW k;d :
While homogeneity models were found to be
appropriate for all images, the model parameters
did vary from image to image; thus, an independent estimation procedure for each new imaging
configuration is recommended. In our tests, the
statistics of speckle are obtained from the uniform
speckle phantom image. The real image would be
taken under the same system setup, i.e., using the
same scanner, frequency, and resolution.
2.3. The aggressive region growing filtering technique
The objective of the ARGF algorithm is to find
one of the following at each pixel:
(a) A maximal-sized homogeneous region to which
simple linear filters can be applied.
(b) A non-homogeneous region containing resolvable object edges that can be processed by
nonlinear filters to preserve edge details.
The ARGF procedure constructs a homogeneous filtering region whose size is adjusted, by
shrinking and growing, to be of maximal size but
below a pre-specified upper limit. This construction has three phases: selection of a (possibly nonhomogeneous) seed region, contraction of this seed
region until it is homogeneous, and expansion of
this homogeneous region until either it no longer
satisfies the homogeneity criterion or its size exceeds a pre-specified size threshold. The algorithm
is summarized as follows:
For each pixel ði; jÞ:
1. Define an initial seed region Wij to be of size
11 11 and centered at ði; jÞ.
2. Region contraction
a. Calculate the homogeneity hij of Wij .
b. Calculate the homogeneity threshold parameters h0;kW k;d and r0;kW k;d corresponding to
the current Wij and depth d in the image.
c. While ðhij > h0;kW k;d þ r0;kW k;d Þ and kWij k >
Smin , shrink the region and go to Step 2.a.
3. Region growing
a. Calculate the homogeneity hij of the current
region;
b. Update the homogeneity criterion h0;kW k;d
and r0;kW k;d corresponding to the current
Wij and depth d in the image.
c. While ðhij 6 h0;kW k;d þ r0;kW k;d Þ, hij changes by
less than r0;kW k;d , and kW k < Smax , expand
the region and go to Step 3.a.
4. Filtering
a. If kW k > w0 , the value of the output pixel at
ði; jÞ is the trimmed arithmetic mean of the
pixels in Wij .
b. If kW k 6 w0 , the value of the output pixel at
ði; jÞ is the median of the pixels in Wij .
2.3.1. Seed window size
The initial seed region Wij is 11 11 pixels
in size and centered at ði; jÞ. In our experiment, a
size of 7 7 is considered minimal (hence, Smin ¼
49), since speckle artifacts can sometimes exceed
this size, causing an incorrect classification of a
Y. Chen et al. / Pattern Recognition Letters 24 (2003) 677–691
seed region inside a speckle artifact as homogeneous.
2.3.2. Region contraction
The initial seed region Wij is contracted by removing its outermost rows and columns (hence,
the first contraction operation returns the 9 9
region centered at ði; jÞ, and contraction is repeated until the homogeneity hij agrees with the
estimate h0 predicted by Eq. (2) to within a tolerance t0 predicted by Eq. (3). If the contraction
procedure fails to find a homogeneous region before the size shrinks to the minimal threshold value
Smin , a pixel is assumed to be an edge, a 3 3
median filter is applied to preserve edge details,
and processing continues at Step 1 with the next
pixel.
685
That is, we replace those zi in the tails of the sorted
list by the median of the zi . The homogeneity estimate hij is obtained from Z 0 .
In effect the two procedures above allow the
region to expand over a modest amount of speckle.
The amount of tolerance for speckle in the region
is controlled by a in the clamping of pixel intensities. For pragmatic reasons (primarily computation time), we specify an upper limit Smax on the
region size. Fig. 6 shows situations arising from
different locations of the pixel of interest. The
black rectangles denote the result of the contraction procedure, and the white rectangles denote
the final regions that are contracted, grown, and
finally blocked by nearby objects.
2.3.3. Aggressive region growing
The contraction procedure described above
yields a small homogeneous region Wij containing
the pixel under consideration. The next step is to
find the maximum homogeneous region around
the pixel by growing the region. An aggressive
region procedure is used as follows:
A systematic region growing method expands
the region one side at a time is used. The direction
of expansion cycles clockwise through the four
compass directions (i.e., north, south, east, west),
and the first side to be expanded is the north side.
The expansion employs an initial ‘‘step size’’ of 5
(the current side of expansion grows outward by
five pixels at each step). After this procedure terminates, it is repeated with a ‘‘step size’’ of 1. As
in the shrinking procedure, the estimated and
predicted homogeneities are compared after each
expansion to determine whether region expansion
should continue.
Next, pixel intensities are clamped. Let
Z ¼ fz1 ; . . . ; zn g be the sorted array of pixel intensities in the region Wij being examined. For a
specified trimming factor a (conveniently specified
as a percentage between 0 and 50), a set Z 0 ¼
fz01 ; . . . ; z0n g is formed, where
2.3.4. Optimization (reuse of existing homogeneous
regions)
At each pixel ði; jÞ, calculation of the homogeneity hij is needed in the region contraction procedure prior to region growing. This can consume
a significant amount of time for large seed regions.
Thus, we developed an optimization of the basic
procedure to reuse previously obtained homogeneous regions and save computation time.
When the maximal-sized homogeneous region
for a pixel ði; jÞ is obtained, its neighboring pixels
ði 1; j 1Þ are likely to be in this homogeneous
region as well. Hence, the region contraction
procedure of the ARGF method for the new pixel
can be avoided. For example, a homogeneous region Wiðjþ1Þ used for the region growing procedure
of the new pixel can be constructed directly from
the homogeneous region obtained earlier for its
neighbor Wij . Therefore, ARGF skips its region
shrinking procedure and starts with the region
growing procedure at each pixel after the leftmost
in each row. The homogeneous region for the
growing procedure of the new pixel ði; j þ 1Þ is
constructed as a maximal-sized square region
within the resulting homogeneous region of its
neighbor and is centered at the new pixel. The
reuse of existing filtering regions saves considerable computation time.
z0i ¼ zn=2
zi
zn=2
2.3.5. Filtering
Koo and Park (1991) assumed that the intensity
variance of speckle noise is small and that after
if 1 6 i 6 na
if na < i < nð1 aÞ;
if nð1 aÞ 6 i 6 n:
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Y. Chen et al. / Pattern Recognition Letters 24 (2003) 677–691
Fig. 6. Illustration of region growing: (a) phantom image, (b) close-up of a region in the phantom image.
region growing, a substantial homogeneous region
is available. An arithmetic mean filter might seem
appropriate in such cases since it works well on a
homogeneous region in the presence of several
types of noise. It is well known that an arithmetic
mean filter will remove noise that has a zero-mean
Gaussian distribution. Although the histogram of
a uniform speckle region typically shows a Gaussian distribution, the histograms of small homogeneous regions sometimes have a skewed shape. In
such cases, a mean filter will decrease the image
contrast and a mode filter is preferred. To avoid
the difficulty of determining the mode of a small
population, Davies (1988) proposed the iterative
truncated median filter to approximate a mode
filter. This filter bisects the original distribution
using the median value and gives the new median
of the truncated distribution as the output. The
method can be used for many distributions.
The distribution for ultrasound images shows a
unimodal shape that is close to a Gaussian distribution. In this case, the replacement of the median
with the mean in Davies’ filter will not change its
output significantly but will reduce its computa-
tional cost. The new output is the average of those
points with intensities within one standard deviation of the mean of the original distribution.
A formal description of this trimmed mean filter
follows. Let Wij be the current filtering region and
ð^
lWij ; r^Wij Þ be the sample mean and standard deviation of Wij . The original region Wij is trimmed to
construct the new pixel set Pij :
Pij ¼ fxkl jðk; lÞ 2 Wij \ jxkl l^Wij j < r^Wij g:
The output pixel value at ði; jÞ is the mean value of
the set Pij :
1 X
yij ¼
xkl :
kPij k xkl 2P
For distributions that are symmetric about the
mean, the output of this filter is identical to that
of the regular arithmetic mean filter. If a skewed
distribution is present, the output is biased toward
the mode of the distribution and so it preserves the
image contrast.
In the ARGF method, the trimmed mean filter
is applied in the homogeneous region following the
region growing procedure. Pixels in a non-homo-
Y. Chen et al. / Pattern Recognition Letters 24 (2003) 677–691
geneous region are assumed to contain resolvable
edges and are processed by a small median filter
(3 3 in our tests) to preserve edge details.
3. Experimental results
The proposed speckle reduction method was
applied to B-mode ultrasound images of phantoms
and real objects. The test images were obtained
using two different system configurations: a linear
687
probe operating at 8.0 MHz and a curved probe
operating at 3.5 MHz. The phantom image is a
real ultrasound image from a tissue-mimicking
phantom that was constructed with voids to model
cysts and lesions. Figs. 7(a) and 8(a) are the two
phantom images using the linear probe and the
curved probe, respectively. Fig. 9(a) shows a real
ultrasound image of a human neck using the linear
probe. It consists of vessels and an air-filled organ.
For comparison, two other methods (the AWMF
and the HRGMF) were also applied to each test
Fig. 7. Speckle reduction comparison for a lesion phantom image: (a) original image, (b) result of AWMF, (c) result of HRGMF,
(d) result of ARGF.
688
Y. Chen et al. / Pattern Recognition Letters 24 (2003) 677–691
Fig. 8. Speckle reduction comparison for a lesion phantom image: (a) original image, (b) result of AWMF, (c) result of HRGMF,
(d) result of ARGF.
image. All images presented in this section were
printed using a linear gray scale without any
compression.
following equation for a pixel ðk; lÞ in the neighborhood of ði; jÞ:
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
2
wkl ¼ round w0 c ði kÞ þ ðj lÞ ;
3.1. Adaptive weighted median filter
The AWMF (Loupas et al., 1989) is obtained
from the median filter through the introduction of
integer weight coefficients that control the replication of the corresponding pixels’ values in the
median procedure. The output computed at pixel
location ði; jÞ is the median of an extended input
set formed by replicating each pixel xkl in an appropriately defined neighborhood of ði; jÞ a total
of wkl times; the wkl are integer-valued weights and
are adjusted on the basis of local region statistics.
We used an isotropic weight model given by the
where w0 is a pre-specified weight assigned to the
center pixel ði; jÞ in the region, round½ is a roundto-nearest integer function, c is a scaling constant,
and hij is the homogeneity estimate for the neighborhood of pixel ði; jÞ (Eq. (1)). The performance
of the AWMF method depends on the filtering
region size and its parameter selections. In our
tests, a 9 9 region with w0 ¼ 10 and c ¼ 0:25 was
used. Figs. 7(b) and 8(b) depict the results of the
AWMF method applied to the phantom images.
Fig. 9(b) shows the result of the AWMF method
applied to the real neck image.
Y. Chen et al. / Pattern Recognition Letters 24 (2003) 677–691
689
Fig. 9. Speckle reduction results for a real human neck image: (a) original image, (b) result of AWMF, (c) result of HRGMF, (d) result
of ARGF.
3.2. Homogeneous region growing mean filtering
As discussed in the introduction, the HRGMF
method uses a constant homogeneity value as a
criterion in its region growing procedure. This
value is obtained from measurements using an
appropriate region size. To ensure that the growth
procedure finds a larger homogeneous region, we
used a 20 20 region size to find this criterion
value. Since it is not known how large the homogeneous region will be at the pixel of interest before the growing procedure is invoked, the choice
of the ‘‘appropriate’’ region size involves a tradeoff
between the region growing and its quality. A
small size results in a small homogeneity criterion
that may stop the region growing too early. A
large size may result in an over-grown homogeneous region. Figs. 7(c) and 8(c) depict the results
of the HRGMF method applied to the phantom
images. Fig. 9(c) shows the result of the HRGMF
method applied to the real neck image.
3.3. Aggressive region growing filtering
In the region contracting and growing procedures of the ARGF method, two models, Eqs. (2)
and (3), are used to adjust adaptively the homogeneity criterion corresponding to its region size.
The model parameters are obtained using nonlinear regression on the homogeneity measurements
of the uniform speckle phantom image. As described in Section 2, the parameters are used for
the processing of other ultrasound images obtained using the same system configuration. To
consider the effect of depth, the image is divided
into parts, and model parameters are estimated for
each part. Table 1 contains the model parameters
corresponding to the upper part of the uniform
690
Y. Chen et al. / Pattern Recognition Letters 24 (2003) 677–691
Table 1
The parameters of the homogeneity models for the phantom
images
Fig. 7
Fig. 8
A
B
C
D
K
3.25
1.63
19.4
19.67
0.4
0.27
0.004
0.004
0.9
0.41
speckle phantom images (Figs. 7(a) and 8(a)). The
upper size limit for the homogeneous region in
region growing is 700. Fig. 7(d) and Fig. 8(b) show
the results of the ARGF method applied to these
phantom images. Fig. 9(d) shows the result of the
ARGF method applied to the real neck image.
3.4. Comparisons and evaluation
Comparisons of the results for both the lesion
phantom image and the human neck image demonstrate the value of the ARGF technique.
Speckle is smoothed and point targets and cysts
are clearer than in the original image. A good
image processing technique should reduce speckle
noise while preserving interesting features. The
general method for evaluating image quality is
based on the SNR. The usual SNR is calculated
from the gray-level mean divided by the standard
deviation:
l
SNR0 ¼ :
r
However, this value will vary with the location and
size of the region. Thus, to evaluate the overall
noise factor of one image, we use the pooled SNR
of a group of predefined regions determined to be
homogeneous. The pooled signal to noise ratio is
given by
SNRp ¼
l^p
;
r^p
where l^p and r^p are sample estimates of the pooled
mean and pooled standard deviation calculated as
follows:
Pm
nk l^k
l^p ¼ k¼1
N
Pm
r^2p ¼
k¼1
½ðnk 1Þ^
r2k þ nk l^k N l^2p
:
N m
Here, m is the number of regions, l^k and r^2k are the
sample mean and variance of the
Pmkth region, whose
size (in pixels) is nk , and N ¼ k¼1 nk .
In ultrasonic imaging, we want to improve the
SNR of both an object and its background while,
at the same time, increasing the contrast between
the two. Thus, we define two figures of merit for
the statistical features of an object and its background: the pooled SNR and the pooled CNR:
SNR ¼
ð1=2Þð^
l1 þ l^2 Þ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
r^1 þ r^22
j^
l1 l^2 j
CNR ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
;
r^21 þ r^22
where l^1 and r^21 are the pooled mean and pooled
variance of the object, and l^2 and r^22 are the
pooled mean and pooled variance of the background.
Comparisons of the SNR and CNR for both
the original and processed images can be performed under the same conditions. The pooled
regions can be defined either quantitatively or
qualitatively. Chen et al. (1996) described a quantitative procedure that uses edge detection to find a
lesion or cyst. However, for practical ultrasound
images with lower contrast and high noise, edge
detection often fails and a qualitative approach is
preferred. For this work, the pooled regions were
defined qualitatively, and the results for the SNR
and CNR for the three images are given in Table 2.
These agree with the visual gray scale results presented in Figs. 7–9, which show that the ARGF
Table 2
SNR and CNR measurements
Image
Algorithm
SNR
CNR
Fig.
Fig.
Fig.
Fig.
Fig.
Fig.
Fig.
Fig.
Fig.
Fig.
Fig.
Fig.
Unprocessed figure
AWMF
HRGMF
ARGF
Unprocessed figure
AWMF
HRGMF
ARGF
Unprocessed image
AWMF
HRGMF
ARGF
2.92
3.64
3.74
3.89
5.08
6.44
6.12
6.53
3.52
4.43
4.83
4.99
0.62
0.76
0.78
0.81
2.27
2.63
2.62
2.74
2.09
2.61
2.80
2.84
7(a)
7(b)
7(c)
7(d)
8(a)
8(b)
8(c)
8(d)
9(a)
9(b)
9(c)
9(d)
Y. Chen et al. / Pattern Recognition Letters 24 (2003) 677–691
technique outperforms both the AWMF and
HRGMF techniques.
4. Conclusions
In this paper we presented an ultrasound
speckle reduction method called aggressive region
growing filtering (ARGF), which was found to give
better results than other region growing methods.
It was shown that the ARGF method improves
both the CNR and SNR for phantom and real
images of cysts, lesions, and vessel areas.
To save computing time, we limit the maximum
region size and use a trimmed mean filter for large
homogeneous regions. This does not change the
CNR significantly, but it reduces computation by
at least 60%.
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