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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5835_Библиотеки_им_академика_М_И_Перельмана.pdf
Chen et al. [20] proposed an autocorrelation coefficient to analyze the texture
information. However, there was a fundamental weakness with texture-based strat-
egies. The settings of US machine parameters had to be fixed for acquiring ultra-
sound images. If the ultrasound parameter setting subsequently changed, CAD
performance became very unstable [21]. Moreover, a CAD system trained with
images from one US machine needs to be trained again for a different US machine
because the new machine will have different image resolution and image quality.
Hence, Chen et al. [21] proposed nearly setting-independent features based on shape
information. Their system was very robust and powerful: The statistical data using a
receiver operating characteristic (ROC) curve were all greater than 0.95. Chang et
al. [22] also used six shape features in their analysis: factor, roundness, aspect ratio,
convexity, solidity, and extent.
Note that all of the mentioned strategies were used on 2-D ultrasound images.
Recently, 3-D US [23] has shown promising signs of overcoming the limitations of
traditional 2-D US and allowing physicians to view the anatomy in three dimensions
interactively, instead of assembling the sectional images in their minds. Chen et al.
[16, 24, 25] proposed a 3-D US texture features autocorrelation matrix and run dif-
ference matrix. However, as pointed earlier, the preceding texture-based CAD
approach is highly machine dependent and utilizes these machine settings all of the
time.
Shape is also an important visual feature for an image. Shape representation
seeks primarily effective and important shape features based on either shape bound-
ary information or a boundary joined with interior points [26]. Thus, our chapter
adapts a methodology based on geometric deformable models such as a level set,
which has the ability to extract the topology of shapes of breast tumors. In the level
set paradigm, tracking of the evolution of contours and surfaces is solved using
numerical methods. The efficacy of this scheme has been demonstrated with numeri-
cal experiments on some synthesized images and some low-contrast medical images
[27, 28]. Recently, the medical shape extraction approach in medical images has
been dominated by the level set framework of Suri et al. [29–31].
In this chapter, we propose a CAD system based ona combination of twostages:
capturing the topology of a shape, thus preserving its irregularity, and then statisti-
cally quantifying regular and irregular shapes accurately. The chapter examines the
use of CAD for improving the diagnostic accuracy of breast lesion detection in 3-D
breast ultrasound. Further, it helps to characterize breast lesions into benign and
malignant lesions, which is clinically useful information for breast radiologists. Our
CAD algorithm for detection of breast lesions uses a level set framework and our
classification strategy uses a perceptual shape analysis. In addition, beam angle sta-
tistics [32, 33] is utilized for shape quantification of lesions, because this approach
handles the concavities and convexities of lesions.
The database consists of 134 pathology-proven 3-D breast ultrasound cases
including 70 benign and 64 malignant breast tumors. All of them are applied to our
proposed CAD method to analyze the classification of breast lesions. For the simi-
larity measurement on the 3-D acquisition method, the similarity values for benign
and malignant lesions are 1,733 ± 759 and 4,081 ± 1,683, respectively. These values
are statistically significant because the p-value is smaller than 0.001 (by Student’s
t-test). To compare system performance, the proposed framework is also applied to
144 Breast Lesion Classification Using 3-D Ultrasound
2-D ultrasound images, called the 2-D acquisition method. Inthis method, each 2-D
image is obtained by selecting the middle slice from 3-D data. The system accuracy,
sensitivity, specificity, positive predictive value, and negative predictive value are
85.07% (114 of 134), 87.50% (56 of 64), 82.86% (58 of 70), 82.35% (56 of 68),
and 87.88% (58 of 66), respectively, for the 2-D acquisition method; 83.58% (112
of 134), 93.75% (60 of 64), 74.29% (52 of 70), 76.92% (60 of 78), and 92.86%
(52 of 56), respectively, for the 3-D acquisition method. The ROC area indexes are
0.915 and 0.934, respectively, for 2-D and 3-D acquisition methods. In our experi-
ments, the proposed CAD system is suitable for both the 2-D and 3-D acquisition
methods.
Section 6.2 reviews the level set segmentation framework. The proposed archi-
tecture for the CAD system is described in Section 6.3. In Section 6.4, the experi-
mental protocol will be used to evaluate the performance of the CAD system. Some
special issues will be discussed in Section 6.5. Finally, a conclusion is drawn and
future works discussed in Section 6.6.
6.2 Level Set Segmentation Method
The level set segmentation technique is capable of capturing the topology of shapes
in medical images [27, 34]. This technique supports recovery of arbitrarily complex
shapes, such as corners and protrusions, and automatically handles topological
changes such as merging and splitting. Recently, a large number of implementations
for computer vision and medical imaging based on this basic concept have been
published [22, 23, 27–29, 35–37].
6.2.1 Basic Level Set Theory
As a starting point and motivation for the level set approach, consider a closed
curve moving in a plane. Let C(0) be a smooth and closed initial curve in Euclidean
plane ᑬ
2
, and let C(t) be the family of curves that is generated by the movement of
initial curve C(0) along the direction of its normal vector after time t. The main idea
of the level set approach is to represent the front C(t) as the level set {φ = 0} of a func-
tion φ. Thus, given a moving closed hypersurface C(t), that is, C(t = 0):[0, ∞)→ ᑬ
N
,
we hope to produce a formulation for the motion of a hypersurface propagating
along its normal direction with speed F, where F can be a function of various argu-
ments, such as curvature or normal direction. Let φ(x, t = 0), where x is a point in
ᑬ
N
, be defined by (x, t = 0) =±d is the signed distance from x to C(t = 0), and a plus
(minus) sign is chosen if the point x is outside (inside) the initial front.
The goal is to produce an equation for the evolving function φ(x, t), which con-
tains the embedded motion of C(t) as the level set {φ = 0}. Let x(t), t ∈ [0, ∞) be the
path of a point on the propagating front, that is, x(t = 0) is a point on the initial front
C(t = 0). Because the evolving function φ is always zero on the propagating front
C(t),
(x, x(t), t) = 0. By the chain rule [27],
φφ
tx
i
N
i
i
t
x+=
=
∑
1
0
(6.1)
6.2 Level Set Segmentation Method 145
where
x
i
t
is the ith component of x at time t, and N is the number of components.
Because
(
)
(
)
()
()
φ φφφ φ
x
i
i
N
xxx x
N
i
t
N
ttt t
xxxxx
Ft
=
∑
=
=
1
123
123
,,,, , ,,,KK
x
∇φ
(6.2)
where F(x(t)) is the speed function with the front for all components of x at time t.
Combining (6.1) and (6.2), the final curve evolution equation is given as:
()
∂φ
∂
κφ
t
F=∇
(6.3)
where φ is the level set function and F(κ) is the speed with which the front (or
zero-level curve) propagates. This fundamental equation describes the time evolu-
tion of the level set function φ in such a way that the zero-level curve of this evolving
function is always identified with the propagating interface [29]. The preceding
equation is also called a Eulerian Hamilton-Jacobi equation [29, 34]. Equation (6.3)
for 2-D and 3-D cases can be generalized as follows:
()
()
∂φ
∂
φ
∂φ
∂
φ
κ
κ
t
Fxy
t
Fxyz
=∇
=∇
,
,,
and
(6.4)
where (x, y) and (x, y, z) are the points on the propagation directions, and F
κ
(x, y)
and F
κ
(x, y, z ) are curvature-dependent speed functions in 2-D and 3-D, respectively
[29]. The evolution of the front in the normal direction with speed F is the zero-level
curve at time t of the function φ(x, y, t), as shown in Figure 6.1.
6.2.2 Summary of Level Set Theory
Level set theory can be used for image segmentation by using image-based features
such as mean intensity, gradient, and edges in the governing differential equation. In
a typical approach, a contour is initialized by a user and is then evolved until it fits
the topology of an anatomic structure in the image [27].
There are challenges associated with using the level set framework by itself on
the raw images. This is because the propagation of the fronts can sometimes lead to
bleeding of the fronts due to noise structures present in the images [38]. One way to
handle this is by removing the noisy structures and then enhancing the structures to
be segmented. The combined effect of these two processes will assist the level set
front propagations to recognize the edges of the structures, thereby bringing the
speed close to zero at the structure edges. Keeping this in mind, we have developed
our breast lesion identification chain. Once successful identification of breast lesions
has occurred, our mission is to quantify the segmented shape and then classify it into
breast lesion type to yield an image with clinical utility. Thus, combining such steps
for breast radiologists is like developing a system for CAD.
146 Breast Lesion Classification Using 3-D Ultrasound
6.3 Proposed Architecture for the CAD System
The architecture for the breast CAD system is shown in Figure 6.2. The input to the
system consists of 3-D breast slices acquired using a 3-D acquisition method. The
main component of the system architecture consists of segmentation of the breast
lesions, the dependent engine that finds the shapes of different breast lesions.
Besides the main engine, there are components in the architecture that provide sta-
bility to the segmentation engine. This is the preprocessing subsystem for removing
the system noise or acquisition noise, hence a diffusion filter, named after the
method it uses. The final component of the system is the shape analysis subsystem.
This subsystem accepts the silhouettes of the breast lesions and helps in quantifying
the shapes and classifying the shapes. Because this subsystem uses statistics derived
from the contours and their angular relationships, one block in Figure 6.2 is labeled
“Beam Angle Statistics.” In the following sections, we will present the blocks of the
system architecture in detail.
6.3 Proposed Architecture for the CAD System 147
(a)
(b)
φ(,, )xyt
1
φ(,, )xyt
2
Ct()
1
Ct()
2
Ct()
2
Figure 6.1 Level set methodology and curve evolution. (a) The evolving level set function and
(b) the zero-level set value of the surface.
Data
acquisition
Diagnosis
result
Similarity
comparison
Beam angles
statistics
Sigmoid
filter
Anisotropic
diffusion filter
Preprocessing
Shape descriptor
Contour
extraction
Level set
Segmentation
Figure 6.2 System architecture.
6.3.1 Data Acquisition
For the study in this chapter, the 3-D ultrasoundbreast images were acquired using a
Voluson 730 (General Electric, USA) scanner with a Voluson small part transducer
S-VNW5-10. The transducer with a linear array of crystal elements has the follow-
ing specifications: 5- to 10-MHz scan frequency, 40-mm scan width, and 20° to 30°
sweep angles. A set of 2-D ultrasound images was obtained by the slow tilt move-
ment of a sectorial mechanical transducer. After completing the scanning process
(about 10 seconds per case), the 3-D US image was obtained by reconstructing these
2-D US images. This scanning process of acquiring the successive 2-D US images at
regular angular intervals arranges the set of2-D image planes in a fanlike geometry.
6.3.2 Preprocessing Subsystem Architecture
6.3.2.1 Anisotropic Diffusion Filtering
To improve image quality, the speckle noise in ultrasound images must be reduced.
Although conventional lowpass filtering and linear diffusion can be used to reduce
speckle, the edge information may be blurred simultaneously. The anisotropic diffu-
sion filtering cannot only reduce the speckle noise on the ultrasound image, but can
also preserve the edge information [39]. It also satisfies the fundamental require-
ments discussed earlier. Consider the anisotropic diffusion equation
()
()
IcxytI
t
=∇div , ,
(6.5)
where div is the divergence operator, c(x, y, t) = f(|| I(x, y, t)||) is the diffusion coeffi-
cient, (x, y) is spatial position, and t is an artificial time parameter. The anisotropic
diffusion equation uses the diffusion coefficient that is selected locally as a function
of the magnitude gradient of the intensity function in the image for estimating the
image structure. This function is selected to satisfy f(z) → 0 when z →∞so that dif-
fusion processing is stopped across the edges. Therefore, the speckle noise within a
homogeneous region can be blurred and the region boundary can be preserved.
6.3.2.2 Image Enhancement Via Sigmoid Mapping
In a breast ultrasound image, different tissues have different intensities, and the
intensity values of malignant and benign tumors tend to be mostly low [40]. For
accurate segmentation of the tumor region, we enhance the tumor boundary by
mapping the intensities based on a sigmoid intensity transform. The sigmoid trans-
form is a nonlinear mapping that maps a specific intensity range into a new intensity
range with a very smooth and continuous transition. This mapping can focus atten-
tion on a specific set of intensity values and progressively decrease the values outside
the range. We will focus on the tumor regions and fade out the other regions. The
following equation represents the sigmoid intensity transformation:
()
~
max
min min
II I
e
I=−
+
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
+
−
−
⎛
⎝
⎜
⎞
⎠
⎟
1
1
1 β
α
(6.6)
148 Breast Lesion Classification Using 3-D Ultrasound
where I and
~
I
are the intensity of the input and output pixels; I
max
and I
min
are the
maximum and minimum values of the input image;
is the width of the input inten-
sity range; and
defines the intensity around which the range is centered. The values
of (α, β) =(8, 60)for theparameters are often adopted in the experiments. However,
the parameters are not the same in each case; they can be slightly adjusted. The
results for different lesion cases obtained via an anisotropic diffusion filter and sig-
moid function are shown in Figure 6.3. Note that this enhancement acts as a
clamper or stopper when using the level set framework.
6.3.3 Segmentation Subsystem Based on the Level Set Framework
In the level set framework, the fundamental Eikonal equation, (6.3), describes the
time evolution of the level set function Φ in such a way that the zero-level curve of
this evolving function is always identified with the propagating interface [29]. The
speed function here has two components, the gradient speed and curvature speed
function. The gradient speed function helps the deformable level set to clamp near
the irregularity of the breast lesion. Thus, the gradient information plays an impor-
tant role in making sure that the best boundaries are determined, thus preserving the
true lesion of the breast.
To improve the performance of the level set, the gradient speed function is pad-
ded with two additive steps, which are actually hidden in the process. First, partial
differential equation (PDE) diffusion is adopted for smoothing the images and pre-
serving the edges of the breast lesions [31]. Second, the enhancement of the lesions is
done by using the sigmoid function, which acts like a stopper in the level set frame-
work. Note carefully that the sigmoid function is more like a region-based stopper
because the sigmoid function really enhances those edges which are truly corre-
6.3 Proposed Architecture for the CAD System 149
(b)
(a)
Figure 6.3 The preprocessing results of image enhancement using anisotropic diffusion filtering
and sigmoid filtering. (a) and (b) are the benign and malignant cases, respectively. In each case,
the first image is original input, the second image has been processed with an anisotropic diffusion
filter (t = 5), and the last image has been enhanced by sigmoid filtering (α = 8, β = 60).
sponding to the breast lesion in the ultrasound image. The stopper is the critical
function for making the level set framework work and preventing bleeding of the
propagating front.
Note that ultrasound images have high speckle and noise in them. Thus level set
work would be likely to give misleading, irregular results if it were to be run on the
raw images or images without enhancement processing. Note that the implementa-
tions are done using the PDE for surface propagation and evolution [29, 31]. The
implementations are done in the narrow band and the initial curve is placed inside
the breast lesion. Because the capture range of the level set is large, it immediately
clamps to the lesion shape and its irregularity. The irregularity of the lesion is pre-
served in the level set framework as the topology of the lesion is extracted. The out-
put of the level set segmentation engine leads to the extracted boundary and its (x, y)
locations of the breast lesion.
We ran our system-based segmentation strategy with and without the prepro-
cessing block to understand the importance of our sigmoid stopper to the level set
framework. In thefirst scenario,we ranthe software architecture without the prepro-
cessing block, thatis, without the so-called “stopper,” as shown in Figure 6.4 (middle
columns). Then we ran our complete system consisting of the PDE diffusion–based
noise smoother and sigmoid-based stopper followed by level set–based propagation,
as seen in Figure 6.4 (last column). Note carefully, that due to large speckle noise in
the ultrasound breast slices, the results from the first scenario lead not only to inaccu-
rate results butare likely to bleed over more iterations. In contrast, with the smoother
and stopper, system performance is not only robust, but accurate.
150 Breast Lesion Classification Using 3-D Ultrasound
(b)
(a)
Figure 6.4 The segmentation results with and without the preprocessing block in the CAD archi
-
tecture. (a) and (b) are the benign and malignant cases, respectively. In each case, the first image
is the raw image; the second image has had the level set without the PDE smoother and sigmoid
enhancer run on it; and the last image has been processed by the proposed level set-based frame
-
work with the PDE smoother and sigmoid enhancer.
6.3.4 Beam Angle Statistics
The classification of lesions is the main goal of this research. The classification crite-
ria are based on the shapes of the breast lesion, which in turn depends on how well
we statistically compute the measure of irregularity of the breast lesions. Thus, we
need a measure that can define the description of the silhouette of the breast lesions.
One such method is to use a shape description, given the silhouette, represented as a
discrete set of contour points. One must ascertain that this descriptor has properties
such as invariance to scale, rotation and translation, and a low sensitivity to noise.
Once such descriptor was developed previously [32, 33] using the statistics taken
around the points, but represented by the neighborhood angles of the ordered set of
points. The authors termed this strategy beam angle statistics (BAS) because the
angles computed were formed with the help of segments resembling beams. The
idea of BAS originates from the concept of curvature of the contour. Due to the
nature of breast lesions, however, the fluctuations of the contours are so rough that
the curvature method for BAS computation is not justified. We thus implemented a
constrained method, where BAS was computed on a limited set of contour points
around the Kth point on the contour. We call this method K-curvature BAS
statistics.
Before we define the K-curvature method, we first define mathematically the
curvature function, represented by k(t), where t represents the arc length
parameterization. This curvature function virtually represents how much a curve
bends at each point at the shape boundary and is mathematically defined by the
variant of the slope s(t) along the arc length t.If(x(t), y(t)) represents the curve k(t),
then the slope (angle) of the curve is represented as:
()
()
()
st
dy t
dx t
=
−
tan
1
(6.7)
The curvature function is nothing but the derivative of the slope, which can be
mathematically given as follows [41]:
()
()
() () () ()
() ()
(
)
kt
ds t
dt
xtyt ytx t
xt yt
==
′′′−′ ′′
′+′
22
32
(6.8)
where
′
x
is the first-order differentiation and
′′
x
is the second-order differentiation;
the same definitions are applied to
′
y
and
′′
y
.
Because the fluctuations on the boundary have an extreme influence on the cur-
vature function, we introduce smoothing to prevent noise in the slope function by
the K-slope method [32, 33].The K-slopeat a boundarypoint is defined by theslope
of a line that points with its Kth right neighbor or left neighbor. Hence, the K-curva-
ture at a boundary point is defined by the difference between the K-slope values of
its Kth right neighbor and left neighbor. However, a good value for parameter K is
difficult to choose. A single K-value would not capture an accurate curvature for all
varieties of shapes. This problem can be solved when the K-curvature function is
considered to be the output of a stochastic process [32, 33].
6.3 Proposed Architecture for the CAD System 151
Let the shape boundary presented by the ordered set of points be given as B =
{f(1), ..., f(N
b
)}, where
() () ()
()
fi xi yi i N
b
==,,,1 K
(6.9)
where N
b
is the number of boundary points. The beams are the lines connecting the
reference point with the remains of the points on the boundary, as shown in Figure
6.5(a). For each point f(i), the beams of f(i) are defined by the set of vectors
()
(){}
Bfi V V i N j N
ij ij b b
===
+−
,,,,,,for 1 1 2KK
(6.10)
where V
i j
and V
i–j
are the forward and backward vectors of f(i) connecting to f(i + j)
and f(i − j). The slope of each beam is computed as
S
y
x
lN
V
il
il
b
il+
==±
−
+
+
tan , , ,
1
12
Δ
Δ
K
(6.11)
Therefore, the beam angle θ
K
(i) of point f(i) between the forward and backward
vectors is calculated as:
()
()
θ
KVV
is s
il il
=−
−+
(6.12)
An example of the beam angle when l equals 4 is shown in Figure 6.5(b).
The angle between each couple of beams is taken as the random variable at each
boundary point. For this purpose, BAS may offer a compact descriptor for a shape
representation by the mth moment θ
m
(i) of the random variable θ
K
(i), which is
defined as:
()
⎣⎦
()
()
Ei P im
m
K
m
KK
K
θθθ==
∑
0123,, ,,K
(6.13)
where E is the expected value, and P
K
(θ
K
(i)) is estimated by the histogram of θ
K
(i)at
each boundary point f(i). Then, each boundary point f(i) is represented as a vector
Γ(i), whose elements are the moments of the beam angles as:
() ()
⎣⎦
()
⎣⎦
()
⎣⎦
⎣⎦
Γ i E iE iE i= θθ θ
123
,,,K
(6.14)
152 Breast Lesion Classification Using 3-D Ultrasound
fi()
fi()
fi(4)−
θ ()i
fi(4)−
fi(4)−
fi(4)+
4
(a) (b)
Figure 6.5 (a) The beams of point f(i) and (b) the beam angle of 4-curvature at point f(i).
Thus, a contour can be represented by plotting the moments of the θ
K
(i)’s for all
boundary points.
The different order moments of BAS for a shape boundary are illustrated in
Figure 6.6. The boundary of a breast lesion after level set segmentation is shown in
Figure 6.6(a), and we can observe that the variation of the boundary in the dotted-
line range is huge. The corresponding BAS for different order moments are also
shown in dotted-line range in Figure 6.6(b–d). Generally, the amplitude of a curve
will become bigger in a higher-order moment of BAS, so that a higher-order
moment can be sufficient for representing most variation of shape boundary. In this
example, the variations of the lesion’s boundary can be clearly observed and ana-
lyzed on the fifth-order moment of BAS. Therefore, the fifth-order moment of BAS
is used in our experiments, and the other reason for using a higher-order moment
will be shown in the following section.
6.3.5 Similarity Between Shapes: A Classification Strategy
For breast ultrasound images, there are several distinguishable properties between
benign masses and malignant masses [42]. Most benign masses are generally well
circumscribed, compact, and roughly elliptical; malignant masses usually have an
irregular semblance, blurred boundary, and are surrounded by a radiating pattern
of linear spicules. However, the irregular situations must still be considered because
some lesions may have the opposite characteristics.
To solve this problem, the idea is to use a best-fit ellipse to cover the segmented
lesion. For most benign tumors with round and well-circumscribed features, the
segmented lesion could be covered by its corresponding best-fit ellipse. If the differ-
ence between the segmented tumor and its best-fit ellipse is small, the tumor should
be benign undoubtedly, and vice versa.
6.3 Proposed Architecture for the CAD System 153
(d)
(c)
(b)
(a)
N
N
N
Figure 6.6 Different order moments of beam angle statistics: (a) the shape boundary, (b) first-
order moment, (c) third-order moment, and (d) fifth-order moment. The variations of the lesion
boundary can be clearly observed and analyzed on higher-order moment of BAS. Note: N is the
number of boundary points.