Phương pháp chẩn đoán hình ảnh (Phần 4)

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3

Texture and
Morphological Analysis
of Ultrasound Images of
the Carotid Plaque for
the Assessment of Stroke
Christodoulos I. Christodoulou,
Constantinos S. Pattichis, Efthyvoulos Kyriacou,
Marios S. Pattichis, Marios Pantziaris, and
Andrew Nicolaides

CONTENTS
3.1

3.2
3.3

Introduction
3.1.1 Ultrasound Vascular Imaging
3.1.2 Previous Work on the Characterization of Carotid Plaque
Materials
The Carotid Plaque Multifeature, Multiclassifier System
3.3.1 Image Acquisition and Standardization
3.3.2 Plaque Identification and Segmentation
3.3.3 Feature Extraction
3.3.3.1 Statistical Features (SF)
3.3.3.2 Spatial Gray-Level-Dependence Matrices
(SGLDM)

3.3.3.3 Gray-Level Difference Statistics (GLDS)
3.3.3.4 Neighborhood Gray-Tone-Difference Matrix
(NGTDM)
3.3.3.5 Statistical-Feature Matrix (SFM)
3.3.3.6 Laws’s Texture Energy Measures (TEM)
3.3.3.7 Fractal Dimension Texture Analysis (FDTA)
3.3.3.8 Fourier Power Spectrum (FPS)
3.3.3.9 Shape Parameters
3.3.3.10 Morphological Features

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3.3.4
3.3.5

3.3.6

Feature Selection
Plaque Classification
3.3.5.1 Classification with the SOM Classifier
3.3.5.2 Classification with the KNN Classifier
Classifier Combiner
3.3.6.1 Majority Voting

3.3.6.2 Weighted Averaging Based on a Confidence
Measure

3.4

Results
3.4.1 Feature Extraction and Selection
3.4.2 Classification Results of the SOM Classifiers
3.4.3 Classification Results of the KNN Classifiers
3.4.4 Results of the Classifier Combiner
3.4.5 The Proposed System
3.4.5.1 Training of the System
3.4.5.2 Classification of a New Plaque
3.5 Discussion
3.5.1 Feature Extraction and Selection
3.5.2 Plaque Classification
3.5.3 Classifier Combiner
3.6 Conclusions and Future Work
Appendix 3.1 Texture-Feature-Extraction Algorithms
Acknowledgment
References

3.1 INTRODUCTION
There is evidence that carotid endarterectomy in patients with asymptomatic carotid
stenosis will reduce the incidence of stroke [1]. The current practice is to operate
on patients based on the degree of internal carotid artery stenosis of 70 to 99% as
shown in X-ray angiography [2]. However, a large number of patients may be
operated on unnecessarily. Therefore, it is necessary to identify patients at high risk,
who will be considered for carotid endarterectomy, and patients at low risk, who
will be spared from an unnecessary, expensive, and often dangerous operation. There

are indications that the morphology of atherosclerotic carotid plaques, obtained by
high-resolution ultrasound imaging, has prognostic implications. Smooth surface,
echogenicity, and a homogeneous texture are characteristics of stable plaques,
whereas irregular surface, echolucency, and a heterogeneous texture are characteristics of potentially unstable plaques [3–6].
The objective of the work described in this chapter was to develop a computeraided system based on a neural network and statistical pattern recognition techniques
that will facilitate the automated characterization of atherosclerotic carotid plaques,
recorded from high-resolution ultrasound images (duplex scanning and color flow
imaging), using texture and morphological features extracted from the plaque
images. The developed system should be able to automatically classify a plaque into
(a) symptomatic (because it is associated with ipsilateral hemispheric symptoms)
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and (b) asymptomatic (because it is not associated with ipsilateral hemispheric
events).
As shown in this chapter, it is possible to identify a group of patients at risk of
stroke based on texture features extracted from high-resolution ultrasound images of
carotid plaques. The computer-aided classification of carotid plaques will contribute
toward a more standardized and accurate methodology for the assessment of carotid
plaques. This will greatly enhance the significance of noninvasive cerebrovascular
tests in the identification of patients at risk of stroke. It is anticipated that the system
will also contribute toward the advancement of the quality of life and efficiency of
health care.
An introduction to ultrasound vascular imaging is presented in Subsection 3.1.1,

followed by a brief survey of previous work on the characterization of carotid plaque.
In Section 3.2, the materials used to train and evaluate the system are described. In
Section 3.3, the modules of the multifeature, multiclassifier carotid-plaque classification system are presented. Image acquisition and standardization are covered in
Subsection 3.3.1, and the plaque identification and segmentation module is described
in Subsection 3.3.2. Subsections 3.3.3 and 3.3.4 outline, respectively, the feature
extraction and feature selection. The plaque-classification module with its associated
calculations of confidence measures is presented in Subsection 3.3.5, and the classifier combiner is described in Subsection 3.3.6. In the following Sections 3.4 and
3.5 the results are presented and discussed, and the conclusions are given in Section
3.6. Finally, in the appendix at the end of the chapter, the implementation details
are given for the algorithms used to extract texture features.

3.1.1 ULTRASOUND VASCULAR IMAGING
The use of ultrasound in vascular imaging became very popular because of its ability
to visualize body tissue and vessels in a noninvasive and harmless way and to
visualize in real time the arterial lumen and wall, something that is not possible with
any other imaging technique. B-mode ultrasound imaging can be used to visualize
arteries repeatedly from the same subject to monitor the development of atherosclerosis. Monitoring of the arterial characteristics like the vessel lumen diameter, the
intima media thickness (IMT) of the near and far wall, and the morphology of
atherosclerotic plaque are very important in assessing the severity of atherosclerosis
and evaluating its progression [7].
The arterial wall changes that can be easily detected with ultrasound are the end
result of all risk factors (exogenous, endogenous, and genetic), known and unknown,
and are better predictors of risk than any combination of conventional risk factors.
Extracranial atherosclerotic disease, known also as atherosclerotic disease of the
carotid bifurcation, has two main clinical manifestations: (a) asymptomatic bruits
and (b) cerebrovascular syndromes such as amaurosis fugax, transient ischemic
attacks (TIA), or stroke, which are often the result of plaque erosion or rupture, with
subsequent thrombosis producing occlusion or embolization [8, 9].
Carotid plaque is defined as a localized thickening involving the intima and
media in the bulb, internal carotid, external carotid, or common femoral arteries

(Figure 3.1). Recent studies involving angiography, high-resolution ultrasound,
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10:30:00

RT PROX ICA
(a)

7R.R

28.8
cm/s

0.29:23

RT PROX ICA
(b)

FIGURE 3.1 (Color figure follows p. 274.) (a) An ultrasound B-scan image of the carotid
artery bifurcation with the atherosclerotic plaque outlined; (b) the corresponding color image
of blood flow through the carotid artery, which physicians use to identify the exact plaque
region.
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thrombolytic therapy, plaque pathology, coagulation studies, and more recently,
molecular biology have implicated atherosclerotic plaque rupture as a key mechanism responsible for the development of cerebrovascular events [10–12]. Atherosclerotic plaque rapture is strongly related to the morphology of the plaque [13].
The development and continuing technical improvement of noninvasive, high-resolution vascular ultrasound enables the study of the presence of plaques, their rate of
progression or regression, and most importantly, their consistency. The ultrasonic
characteristics of unstable (vulnerable) plaques have been determined [14, 15], and
populations or individuals at increased risk for cardiovascular events can now be
identified [16]. In addition, high-resolution ultrasound facilitates the identification
of the different ultrasonic characteristics of unstable carotid plaques associated with
amaurosis fugax, TIAs, stroke, and different patterns of computed tomography (CT)
brain infarction [14, 15]. This information has provided new insight into the pathophysiology of the different clinical manifestations of extracranial atherosclerotic
cerebrovascular disease using noninvasive methods.
Different classifications have been proposed in the literature for the characterization of atherosclerotic plaque morphology, resulting in considerable confusion.
For example, plaques containing medium- to high-level uniform echoes were classified as homogeneous by Reilly [17] and correspond closely to Johnson’s [18] dense
and calcified plaques, to Gray-Weale’s [19] type 3 and 4, and to Widder’s [20] type
I and II plaques (i.e., echogenic or hyperechoic). A recent consensus on carotid
plaque characterization has suggested that echodensity should reflect the overall
brightness of the plaque, with the term “hypoechoic” referring to echolucent plaques
[21]. The reference structure to which plaque echodensity should be compared with
is blood for hypoechoic plaques, the sternomastoid muscle for the isoechoic, and
the bone of the adjacent cervical vertebrae for the hyperechoic ones.

3.1.2 PREVIOUS WORK

ON THE

CHARACTERIZATION

OF

CAROTID PLAQUE

There are a number of studies trying to associate the morphological characteristics
of the carotid plaques as shown in the ultrasound images with cerebrovascular
symptoms. A brief survey of these studies is given below.
Salonen and Salonen [3], in an observational study of atherosclerotic progression, investigated the predictive value of ultrasound imaging. They associated ultrasound observations with clinical endpoints, risk factors for common carotid and
femoral atherosclerosis, and predictors of progression of common carotid atherosclerosis. On the basis of their findings, the assessment of common carotid atherosclerosis using B-mode ultrasound imaging appears to be a feasible, reliable, valid,
and cost-effective method.
Geroulakos et al. [2] tested the hypothesis that the ultrasonic characteristics of
carotid artery plaques are closely related to symptoms and that the plaque structure
may be an important factor in producing stroke, perhaps more than the degree of
stenosis. In their work, they manually characterized carotid plaques into four ultrasonic types: echolucent, predominantly echolucent, predominantly echogenic, and
echogenic. An association was found of echolucent plaques with symptoms and
cerebral infarctions, which provided further evidence that echolucent plaques are
unstable and tend to form embolisms.
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El-Barghouty et al. [4], in a study with 94 plaques, reported an association
between carotid plaque echolucency and the incidence of cerebral computed tomography (CT) brain infarctions. The gray-scale median (GSM) of the ultrasound plaque
image was used for the characterization of plaques as echolucent (GSM ≤ 32) and
echogenic (GSM > 32).
Iannuzzi et al. [22] analyzed 242 stroke and 336 transient ischemic attack (TIA)
patients and identified significant relationships between carotid artery ultrasound plaque
characteristics and ischemic cerebrovascular events. The results suggested that the
features more strongly associated with stroke were either the occlusion of the ipsilateral
carotid artery or wider lesions and smaller minimum residual lumen diameter. The
features that were more consistently associated with TIAs included low echogenicity
of carotid plaques, thicker plaques, and the presence of longitudinal motion.
Wilhjelm et al. [23], in a study with 52 patients scheduled for endarterectomy,
presented a quantitative comparison between subjective classification of the ultrasound images, first- and second-order statistical features, and a histological analysis
of the surgically removed plaque. Some correlation was found between the three
types of information, where the best-performing feature was found to be the contrast.
Polak et al. [5] studied 4886 individuals who were followed up for an average
of 3.3 years. They found that hypoechoic carotid plaques, as seen on ultrasound
images of the carotid arteries, were associated with increased risk of stroke. The
plaques were manually categorized as hypoechoic, isoechoic, or hyperechoic by
independent readers. Polak et al. also suggested that the subjective grading of the
plaque characteristics might be improved by the use of quantitative methods.
Elatrozy et al. [24] examined 96 plaques (25 symptomatic and 71 asymptomatic)
with more than 50% internal carotid artery stenosis. They reported that plaques with
GSM < 40, or with a percentage of echolucent pixels greater than 50%, were good
predictors of ipsilateral hemispheric symptoms related to carotid plaques. Echolucent
pixels were defined as pixels with gray-level values below 40.
Furthermore, Tegos et al. [25], in a study with 80 plaques, reported a relationship
between microemboli detection and carotid plaques having dark morphological characteristics on ultrasound images (echolucent plaques). Plaques were characterized using
first-order statistics and the gray-scale median of the ultrasound plaque image.

AbuRahma et al. [6], in a study with 2460 carotid arteries, correlated ultrasonic
carotid plaque morphology with the degree of carotid stenosis. As reported, the
higher the degree of carotid stenosis, the more likely it is to be associated with
ultrasonic heterogeneous plaque and cerebrovascular symptoms. Heterogeneity of
the plaque was more positively correlated with symptoms than with any degree of
stenosis. These findings suggest that plaque heterogeneity should be considered in
selecting patients for carotid endarterectomy.
Asvestas et al. [26], in a pilot study with 19 carotid plaques, indicated a significant difference of the fractal dimension between the symptomatic and asymptomatic
groups. Moreover, the phase of the cardiac cycle (systole/diastole) during which the
fractal dimension was estimated had no systematic effect on the calculations. This
study suggests that the fractal dimension, estimated by the proposed method, could
be used as a single determinant for the discrimination of symptomatic and asymptomatic subjects.
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In most of these studies, the characteristics of the plaques were usually subjectively defined or defined using simple statistical measures, and the association with
symptoms was established through simple statistical analysis. In the work we are
about to describe in this chapter, a large number of texture and morphological
features were extracted from the plaque ultrasound image and were analyzed using
multifeature, multiclassifier methodology.

3.2 MATERIALS
A database of digital ultrasound images of carotid arteries was created such that for
each gray-tone image, there was also a color image indicating the blood flow. The color

images were necessary for the correct identification of the plaques as well as their
outlines. The carotid plaques were labeled as symptomatic after one of the following
three symptoms was identified: stroke, transient ischemic attack, or amaurosis fugax.
Two independent studies were conducted. In the first study with Data Set 1, a
total of 230 cases (115 symptomatic and 115 asymptomatic) were selected. Two sets
of data were formed at random: one for training the system and another for evaluating
its performance. For training the system, 80 symptomatic and 80 asymptomatic
plaques were used, whereas for evaluation of the system, the remaining 35 symptomatic and 35 asymptomatic plaques were used. A bootstrapping procedure was
used to verify the correctness of the classification results. The system was trained
and evaluated using five different bootstrap sets, with each training set consisting
of 160 randomly selected plaques and the remaining 70 plaques used for evaluation.
In the second study, where the morphology features were investigated, a new
Data Set 2 of 330 carotid plaque ultrasound images (194 asymptomatic and 136
symptomatic) were analyzed. For training the system, 90 asymptomatic and 90
symptomatic plaques were used; for evaluation of the system, the remaining 104
asymptomatic and 46 symptomatic plaques were used.

3.3 THE CAROTID PLAQUE MULTIFEATURE,
MULTICLASSIFIER SYSTEM
The carotid plaque classification system was developed following a multifeature,
multiclassifier pattern-recognition approach. The modules of the system are
described in the following subsections and are illustrated in Figure 3.2. In the first
module, the carotid plaque ultrasound image was acquired using duplex scanning,
and the gray level of the image was manually standardized using blood and adventitia
as reference. In the second module, the plaque region was identified and manually
outlined by the expert physician. In the feature-extraction module, ten different texture
and shape feature sets (a total of 61 features) were extracted from the segmented plaque
images of Data Set 1 using the following algorithms: statistical features (SF), spatial
gray-level-dependence matrices (SGLDM), gray-level difference statistics (GLDS),
neighborhood gray-tone-difference matrix (NGTDM), statistical-feature matrix

(SFM), Laws’s texture energy measures (TEM), fractal dimension texture analysis
(FDTA), Fourier power spectrum (FPS), and shape parameters.
Copyright 2005 by Taylor & Francis Group, LLC


Patient

Image
Acquisition and
Standardization

Carotid
plaque
ultrasound
image

Plaque
Identification &
Segmentation

Carotid
plaque
segmented
image

Feature
Extraction and
Selection

Feature

set 1

Classifier 1

Feature
set 2

Classifier 2

Feature
set n

• Identification and outline
of the plaque region
manually by the human
expert

Classifier n

• Modular multiclassifier system
using the neural SOM
classifier
• Modular multiclassifier system
using the statistical
KNN classifier

Weighting
Factors
• Combining using
majority voting

• Combining by
averaging the
confidence
measures

FIGURE 3.2 Flowchart of the carotid plaque multifeature, multiclassifier classification system. (From Christodoulou, C.I. et al., IEEE Trans.
Medical Imaging, 22, 902–912, 2003. With permission.)

Medical Image Analysis

Texture features using:
• Statistical Features
• Spatial Gray Level
Dependence Matrices
• Gray Level Diff. Statistics
• Neighborhood Gray Tone
Difference Matrix
• Statistical Feature Matrix
• Laws Text. Energy Meas.
• Fractal Dimension Texture
• Fourier Power Spectrum
• Shape Parameters

Diagnosis:
• Symptomatic
• Asymptomatic

•
•
•

•
•
•

• Carotid plaque
ultrasound image
acquisition using
duplex scanning
• Image standardization

Classifier
Combiner

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THE CAROTID PLAQUE MULTIFEATURE MULTICLASSIFIER SYSTEM


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Following the feature extraction, several feature-selection techniques were used

to select the features with the greatest discriminatory power. For the classification,
a modular neural network using the unsupervised self-organizing feature map (SOM)
classifier was implemented. The plaques were classified into two types: symptomatic
or asymptomatic. For each feature set, an SOM classifier was trained, and ten
different classification results were obtained. Finally, in the system combiner, the
ten classification results were combined using: (a) majority voting and (b) weighted
averaging of the ten classification results based on a confidence measure derived
from the SOM. For the sake of comparison, the above-described modular system
was also implemented using the KNN statistical classifier instead of the SOM.

3.3.1 IMAGE ACQUISITION

AND

STANDARDIZATION

The protocols suggested by the ACSRS (asymptomatic carotid stenosis at risk of
stroke) project [1] were followed for the acquisition and quantification of the imaging
data. The ultrasound images were collected at the Irvine Laboratory for Cardiovascular Investigation and Research, Saint Mary’s Hospital, U.K., by two ultrasonographers using an ATL (model HDI 3000, Advanced Technology Laboratories, Leichworth, U.K.) duplex scanner with a 4- to 7-MHz multifrequency probe. Longitudinal
scans were performed using duplex scanning and color flow imaging [27]. B-mode
scan settings were adjusted so that the maximum dynamic range was used with a
linear postprocessing curve. The position of the probe was adjusted so that the
ultrasonic beam was vertical to the artery wall. The time gain compensation (TGC)
curve was adjusted (gently sloping) to produce uniform intensity of echoes on the
screen, but it was vertical in the lumen of the artery, where attenuation in blood was
minimal, so that echogenicity of the far wall was the same as that of the near wall.
The overall gain was set so that the appearance of the plaque was assessed to be
optimal and noise appeared within the lumen. It was then decreased so that at least
some areas in the lumen appeared to be free of noise (black). The resolution of the
images was on the order of 700 × 500 pixels, and the average size and standard

deviation of the segmented images was on the order of 350 ± 100 × 100 ± 30 pixels.
The scale of the gray level of the images was in the range from 0 to 255. The
images were standardized manually by adjusting the image so that the median graylevel value of the blood was between 15 and 20 and the median gray-level value of
the adventitia (artery wall) was between 180 and 200 [27]. The image was linearly
adjusted between the two reference points, blood and adventitia. This standardization
using blood and adventitia as reference points was necessary to extract comparable
results when processing images obtained by different operators and equipment and
vascular imaging laboratories.

3.3.2 PLAQUE IDENTIFICATION

AND

SEGMENTATION

The plaque identification and segmentation tasks are quite difficult and were carried
out manually by the expert physician. The main difficulties are due to the fact that
the plaque cannot be distinguished from the adventitia based on brightness level
difference, or using only texture features, or other measures. Also, calcification and
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Symptomatic Plaques

Median = 19.60, Entropy = 5.51, Coars = 8.56

Median = 1.43, Entropy = 3.65, Coarseness = 4.96

Median = 6.05, Entropy = 4.35, Coars = 5.55

Median = 5.32, Entropy = 4.10, Coarseness = 5.45

Asymptomatic Plaques

Median = 40.13, Entropy = 6.86, Coars = 27.16

Median = 36.45, Entropy = 7.17, Coarseness = 59.83

Median = 58.92, Entropy = 7.93, Coars = 20.76

Median = 50.79, Entropy = 7.65, Coarseness = 44.30

FIGURE 3.3 Examples of segmented symptomatic and asymptomatic plaques. Selected texture values are given for the following features: median (2), entropy (14), and coarseness
(36). (The numbers in parentheses denote the serial feature number as listed in Table 3.1.)

acoustic shadows make the problem more complex. The identification and outlining
of the plaque were facilitated using a color image indicating the blood flow (see
Figure 3.1). All plaque images used in this study were outlined using their corresponding color blood flow images. This guaranteed that the plaque was correctly
outlined, which was essential for extracting texture features characterizing the plaque
correctly.
The procedure for carrying out the segmentation process was established by a
team of experts and was documented in the ACSRS project protocol [1]. The
correctness of the work carried out by the single expert was monitored and verified
by at least one other expert. However, the extracted texture features depend on the

whole of the plaque area and are not significantly affected if a small portion of the
plaque area is not included in the region of interest.
Figure 3.1 illustrates an ultrasound image with the outline of the carotid plaque
and the corresponding color blood flow image. Figure 3.3 illustrates a number of
examples of symptomatic and asymptomatic plaques that were segmented by an
expert physician.
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3.3.3 FEATURE EXTRACTION
Texture features, shape parameters, and morphological features were extracted from
the manually segmented ultrasound plaque images to be used for the classification
of the carotid plaques. Texture contains important information that is used by humans
for the interpretation and the analysis of many types of images. It is especially useful
for the analysis of natural scenes, since they mostly consist of textured surfaces.
Texture refers to the spatial interrelationships and arrangement of the basic elements
of an image [28]. Visually, these spatial interrelationships and arrangements of the
image pixels are seen as variations in the intensity patterns or gray tones. Therefore,
texture features have to be derived from the gray tones of the image. Although it is
easy for humans to recognize texture, it is quite a difficult task to define texture so
that it can be interpreted by digital computers.
In this work, ten different texture-features sets were extracted from the plaque
segments using the algorithms described in Appendix 3.1. Some of the extracted
features capture complementary textural properties. However, features that were

highly dependent on or similar to features in other feature sets were identified through
statistical analysis and eliminated. The implementation details for the texture-feature-extraction algorithms can be found in Appendix 3.1 at the end of the chapter.
3.3.3.1 Statistical Features (SF)
The following statistical features were computed [29]: (1) mean value, (2) median
value, (3) standard deviation, (4) skewness, and (5) kurtosis.
3.3.3.2 Spatial Gray-Level-Dependence Matrices (SGLDM)
The spatial gray-level-dependence matrices as proposed by Haralick et al. [30] are based
on the estimation of the second-order joint conditional probability density functions
that two pixels (k,l) and (m,n) with distance d in direction specified by the angle θ have
intensities of gray-level i and gray-level j. Based on the probability density functions,
the following texture measures [30] were computed: (1) angular second moment, (2)
contrast, (3) correlation, (4) sum of squares: variance, (5) inverse difference moment,
(6) sum average, (7) sum variance, (8) sum entropy, (9) entropy, (10) difference variance,
(11) difference entropy, and (12, 13) information measures of correlation.
For a chosen distance d (in this work d = 1 was used, i.e., 3 × 3 matrices) and
for angles θ = 0°, 45°, 90°, and 135°, we computed four values for each of the 13
texture measures. In this work, the mean and the range of these four values were
computed for each feature, and they were used as two different feature sets.
3.3.3.3 Gray-Level Difference Statistics (GLDS)
The GLDS algorithm [31] uses first-order statistics of local property values based
on absolute differences between pairs of gray levels or of average gray levels to
extract the following texture measures: (1) contrast, (2) angular second moment, (3)
entropy, and (4) mean. These features were calculated for displacements δ = (0, 1),
(1, 1), (1, 0), (1, −1), where δ ≡ (∆x, ∆y), and their mean values were taken.
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3.3.3.4 Neighborhood Gray-Tone-Difference Matrix (NGTDM)
Amadasun and King [28] proposed the neighborhood gray-tone-difference matrix
to extract textural features that correspond to visual properties of texture. The
following features were extracted, for a neighborhood size of 3 × 3: (1) coarseness,
(2) contrast, (3) busyness, (4) complexity, and (5) strength.
3.3.3.5 Statistical-Feature Matrix (SFM)
The statistical-feature matrix [32] measures the statistical properties of pixel pairs
at several distances within an image, which are used for statistical analysis. Based
on the SFM, the following texture features were computed: (1) coarseness, (2)
contrast, (3) periodicity, and (4) roughness. The constants Lr, Lc, which determine
the maximum intersample spacing distance, were set in this work to Lr = Lc = 4.
3.3.3.6 Laws’s Texture Energy Measures (TEM)
For Laws’s TEM extraction [33, 34], vectors of length l = 7, L = (1, 6, 15, 20, 15,
6, 1), E = (−1, −4, −5, 0, 5, 4, 1), and S = (−1, −2, 1, 4, 1, −2, −1) were used, where
L performs local averaging, E acts as edge detector, and S acts as spot detector. If
we multiply the column vectors of length l by row vectors of the same length, we
obtain Laws’s l × l masks. In order to extract texture features from an image, these
masks are convoluted with the image, and the statistics (e.g., energy) of the resulting
image are used to describe texture. The following texture features were extracted:
(1) LL, texture energy from LL kernel, (2) EE, texture energy from EE kernel, (3)
SS, texture energy from SS kernel, (4) LE, average texture energy from LE and EL
kernels, (5) ES, average texture energy from ES and SE kernels, and (6) LS, average
texture energy from LS and SL kernels.
3.3.3.7 Fractal Dimension Texture Analysis (FDTA)
Mandelbrot [35] developed the fractional Brownian motion model to describe the
roughness of natural surfaces. The Hurst coefficient H(k) [34] was computed for
image resolutions k = 1, 2, 3, 4. A smooth surface is described by a large value of

the parameter H, whereas the reverse applies for a rough surface.
3.3.3.8 Fourier Power Spectrum (FPS)
The radial sum and the angular sum of the discrete Fourier transform [31] were
computed to describe texture.
3.3.3.9 Shape Parameters
The following shape parameters were calculated from the segmented plaque image:
(1) X-coordinate maximum length, (2) Y-coordinate maximum length, (3) area, (4)
perimeter, and (5) perimeter2/area.
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3.3.3.10 Morphological Features
Morphological image processing allows the detection of the presence of specific
patterns, called structural elements, at different scales. The simplest structural element for near-isotropic detection is the cross ‘+’ consisting of five image pixels.
Using the cross ‘+’ as a structural element, pattern spectra were computed for each
plaque image as defined in the literature [36–38]. After computation, each pattern
spectrum was normalized.
All features of the ten feature sets were normalized before use by subtracting their
mean values and dividing by their standard deviations.

3.3.4 FEATURE SELECTION
The selection of features with the highest discriminatory power can reduce the
dimensionality of the input data and improve the classification performance. A
simple way to identify potentially good features is to compute the distance between

the two classes for each feature as
dis =

m1 − m2
σ12 + σ 22

(3.1)

where m1 and m2 are the mean values, and σ1 and σ2 are the standard deviations of
the two classes [39]. The best features are considered to be the ones with the greatest
distance. The mean and standard deviation for all the plaques, as well as for the
symptomatic and asymptomatic groups, were computed, and the distance between
the two classes for each feature was calculated as described in Equation 3.1. The
features were ordered according to their interclass distance, and the features with
the greatest distance were selected to be used for the classification.
Another way to select features and reduce dimensionality is through principal
component analysis (PCA) [40]. In PCA, the data set is represented by a reduced
number of uncorrelated features while retaining most of its information content.
This is carried out by eliminating correlated components that contribute only a small
amount to the total variance in the data set. In this study, the 61-feature vector was
reduced to nine transformed parameters by retaining only those components that
contributed more than 2% to the variance in the data set. A new feature set comprising
the nine PCA parameters was used as input to the SOM and the KNN classifiers.

3.3.5 PLAQUE CLASSIFICATION
Following the computer-aided feature extraction and selection, feature classification
was implemented based on multifeature, multiclassifier analysis. The SOM classifier
and the KNN classifier were used to classify the carotid plaques into one of the
following two types:
Copyright 2005 by Taylor & Francis Group, LLC

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1. Symptomatic because of ipsilateral hemispheric symptoms
2. Asymptomatic because they were not connected with ipsilateral hemispheric events
The different features sets described in Subsection 3.3.3 were used as input to
the classifier.
3.3.5.1 Classification with the SOM Classifier
The SOM was chosen because it is an unsupervised learning algorithm where the
input patterns are freely distributed over the output-node matrix [41]. The weights
are adapted without supervision in such a way that the density distribution of the
input data is preserved and represented on the output nodes. This mapping of similar
input patterns to output nodes that are close to each other represents a discretization
of the input space, allowing a visualization of the distribution of the input data. The
output nodes are usually ordered in a two-dimensional grid, and at the end of the
training phase, the output nodes are labeled with the class of the majority of the
input patterns of the training set assigned to each node. In the evaluation phase, an
input pattern is assigned to the output node with the weight vector closest to the
input vector, and it is said to belong to the class label of the winning output node
where it has been assigned.
Beyond the classification result, a confidence measure was derived from the
SOM classifier characterizing how reliable the classification result was. The confidence measure was calculated based on the classes of the nearest neighbors on the
self-organizing map. For this purpose, the output nodes in a neighborhood window
centered at the winning node were considered. The confidence measure was computed for five different window sizes: 1 × 1, 3 × 3, 5 × 5, 7 × 7, and 9 × 9. For each
one of the ten feature sets, a different SOM classifier was trained. The implementation steps for calculating the confidence measure were as follows:

Step 1: Train the classifier. An SOM classifier is trained with the training set,
using as input one of the ten feature sets.
Step 2: Label the nodes on the SOM. Feed the training set to the SOM
classifier again and label each output node on the SOM with the number
of the symptomatic or asymptomatic training input patterns assigned to it.
Step 3: Apply the evaluation set. In the evaluation phase, a new input pattern is
assigned to a winning output node. The number of symptomatic and asymptomatic training input patterns assigned to each node in the given neighborhood
window (e.g., 1 × 1, …, 9 × 9) around the winning node are counted.
Step 4: Compute the confidence measure and classify plaque. Calculate the
confidence measure as the percentage of the majority of the training input
patterns to the total number of the training input patterns in the given neighborhood window. To set its range from 0 to 1 (0 = low confidence, 1 = high
confidence), the confidence measure is calculated more specifically as
conf = 2 (max{SN1, SN2}/(SN1 + SN2)) − 1
Copyright 2005 by Taylor & Francis Group, LLC

(3.2)


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101

where SNm is the number of the input patterns in the neighborhood window
for the two classes m = {1, 2}:
L

SN m =

∑N

Wi

mi

(3.3)

i =1

where L is the number of the output nodes in the R × R neighborhood window with L = R2 (e.g., L = 9 using a 3 × 3 window), and Nmi is the number
of the training patterns of the class m assigned to the output node i. Wi =
1/(2 di), is a weighting factor based on the distance di of the output node i
to the winning output node. Wi gives the output nodes close to the winning
output node a greater weight than the ones farther away (e.g., in a 3 × 3
window, for the winning node Wi = 1, for the four nodes perpendicular to
the winning node Wi = 0.5 and for the four nodes diagonally located around
Wi = 0.3536, etc). The evaluation input pattern was classified to the class
m of the SNm with the greatest value as symptomatic or asymptomatic.
3.3.5.2 Classification with the KNN Classifier
For comparison reasons, the KNN classifier was also used for the carotid plaque
classification. To classify a new pattern in the KNN algorithm, its k nearest neighbors
from the training set are identified. The new pattern is classified to the most frequent
class among its neighbors based on a similarity measure that is usually the Euclidean
distance. In this work, the KNN carotid plaque classification system was implemented for values of k = 1, 3, 5, 7, and 9, and it was tested using for input the ten
different feature sets. In the case of the KNN, the confidence measure was simply
computed as given in Equation 3.2 and Equation 3.3, with SNm being the number
of the nearest neighbors per class m.

3.3.6 CLASSIFIER COMBINER

In the case of difficult pattern-recognition problems, the combination of the outputs
of multiple classifiers, using for input multiple feature sets extracted from the raw
data, can improve the overall classification performance [42]. In the case of noisy
data or of a limited amount of data, different classifiers often provide different
generalizations by realizing different decision boundaries. Also, different feature
sets provide different representations of the input patterns containing different classification information. Selecting the best classifier or the best feature set is not
necessarily the ideal choice, because potentially valuable information contained in
the less successful feature sets or classifiers may not be taken into account. The
combination of the results of the different features and the different classifiers
increases the probability that the errors of the individual features or classifiers will
be compensated by the correct results of the rest. Furthermore, according to Perrone
[43], the performance of the combiner is never worse than the average of the
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individual classifiers, but it is not necessarily better than the best classifier. Also,
the error variance of the final result is reduced, making the whole system more
robust and reliable. The use of a confidence measure to establish the reliability of
the classification result can further improve the overall performance by weighting
the individual classification results before combining.
In this work, the usefulness of combining neural-network classifiers was investigated in the development of a decision-support system for the classification of
carotid plaques. Two multifeature modular networks, one using the SOM classifier
and one using the KNN classifier, were implemented. The first ten feature sets,
described in Subsection 3.3.3, were extracted from the plaque ultrasound images of

Data Set 1 and were inputted into ten SOM or KNN classifiers. The ten classification
results were combined using: (a) majority voting and (b) weighted averaging based
on a confidence measure.
3.3.6.1 Majority Voting
In majority voting, the input plaque under evaluation was classified as symptomatic
or asymptomatic by the ten classifiers using as input the ten different feature sets.
The plaque was assigned to the majority of the symptomatic or asymptomatic votes
of the ten classification results obtained at the end of step 4 of the algorithm described
in Subsection 3.3.5. The diagnostic yield was computed for the five window sizes:
1 × 1, 3 × 3, 5 × 5, 7 × 7, and 9 × 9.
3.3.6.2 Weighted Averaging Based on a Confidence Measure
In combining with the use of a confidence measure, the confidence measure was
computed from the ten SOM classifiers, as given in Equation 3.2. When combining,
the confidence measure decided the contribution of each feature set to the final result.
The idea is that some feature sets may be more successful for specific regions of
the input population. The implementation steps for combining using weighted averaging were as follows:
Step 1: Assign negative confidence measure values to the symptomatic
plaques. If an input plaque pattern was classified as symptomatic, as given
in step 4 of the algorithm described in Subsection 3.3.5, then its confidence
measure is multiplied by −1, whereas the asymptomatic plaques retain their
positive values.
Step 2: Calculate the average confidence. Calculate the average of the n
confidence measures that is the final output of the system combiner as
1
conf =
n

n

∑ conf

j

(3.4)

j =1

Step 3: Classify plaque. If conf < 0, then the plaque is classified as symptomatic, else if conf > 0, then the plaque is classified as asymptomatic.
Copyright 2005 by Taylor & Francis Group, LLC


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Texture and Morphological Analysis of Ultrasound Images

103

The final output of the system combiner is the average confidence, conf , and its
values are ranging from −1 to 1. Values of conf close to zero mean low confidence
of the correctness of the final classification result, whereas values close to −1 or 1
indicate a high confidence.
In the case of the KNN classifier the n classification results were combined in
a similar way to that of the SOM classifier, i.e., (a) with majority voting and (b) by
averaging of the n confidence measures. The algorithmic steps described in the
previous subsections for the SOM classifier apply for the KNN classifier as well.
When averaging, the final diagnostic yield was the average of the n confidence
measures obtained when using the n different feature sets.

3.4 RESULTS
3.4.1 FEATURE EXTRACTION

AND

SELECTION

In Data Set 1, a total of 230 (115 symptomatic and 115 asymptomatic) ultrasound
images of carotid atherosclerotic plaques were examined. Ten different texturefeature sets and shape parameters (a total of 61 features) were extracted from the
manually segmented carotid plaque images as described in Subsection 3.3.3 [39, 44].
The results obtained through the feature-selection techniques described in Subsection 3.3.4 and the selected features with the highest discriminatory power are
given in Table 3.1 [39]. The mean and standard deviation for all the plaques, and
for the symptomatic and asymptomatic groups, were computed for each individual
feature. Furthermore, the distance between the two classes was computed as
described in Subsection 3.3.4 in Equation 3.1, and the features were ordered according to their interclass distance. The best features were the ones with the greatest
distance. As shown in Table 3.1, for all features the distance was negative, which
means that the feature values of the two groups overlapped. The high degree of
overlap in all features makes the classification task of the two groups difficult.
The best texture features, as tabulated in Table 3.1, were found to be: the
coarseness of NGTDM, with average and standard deviation values for the symptomatic plaques 9.3 ± 8.2 and for the asymptomatic plaques 21.4 ± 14.9; the range
of values of angular second moment of SGLDM with 0.0095 ± 0.0055 and 0.0050
± 0.0050 for the symptomatic and the asymptomatic plaques, respectively; and the
range of values of entropy also of SGLDM with 0.28 ± 0.11 and 0.36 ± 0.11 for
the symptomatic and the asymptomatic plaques, respectively. Features, from other
feature sets that also performed well were: the median gray-level value (SF), with
average values for the symptomatic plaques 15.7 ± 16.6 and for the asymptomatic
plaques 29.4 ± 22.9; the fractal value H1, with 0.37 ± 0.08 and 0.42 ± 0.07 for the
symptomatic and the asymptomatic plaques, respectively; the roughness of SFM,
with 2.39 ± 0.13 and 2.30 ± 0.10 for the symptomatic and the asymptomatic plaques,
respectively; and the periodicity also of SFM, with 0.58 ± 0.08 and 0.62 ± 0.06 for
the symptomatic and the asymptomatic plaques, respectively.
In general, texture in symptomatic plaques tends to be darker, with higher

contrast, greater roughness, and with less local uniformity in image density and
being less periodical. In asymptomatic plaques, texture tends to be brighter, with
Copyright 2005 by Taylor & Francis Group, LLC


Symptomatic
No.

1
2
3
4
5

Mean
Median
Standard deviation
Skewness
Kurtosis

Angular second moment
Contrast
Correlation
Sum of squares: variance
Inverse difference moment
Sum average
Sum variance
Sum entropy
Entropy
Difference variance

Difference entropy
Information measures
of correlation

Mean,
m1

Std. Dev.,
σ1

Statistical Features (SF)
28.61
16.78
15.71
16.62
36.39
11.80
2.790
1.548
15.57
13.44

Mean,
m2

41.16
29.40
40.04
2.083
10.87

Std. Dev.,
σ2

22.38
22.87
11.30
1.429
12.94

Spatial Gray-Level-Dependence Matrices (SGLDM): Mean Values
0.1658
0.1866
0.0646
0.1201
324.8
143.9
267.3
82.2
0.812
0.138
0.876
0.104
1315.2
1081.3
1621.8
957.5
0.4856
0.1827
0.3545

0.1613
57.091
33.671
82.675
44.953
4,936.2
4,288.7
6,219.8
3,803.3
3.759
1.163
4.619
1.000
4.730
1.619
5.972
1.456
280.5
119.8
219.7
65.8
2.210
0.613
2.504
0.495
−0.417
0.051
−0.404
0.048
0.937

0.062
0.965
0.034

Distance

dis =

m1 – m2
2

2

X1 + X2

Rank
Order

0.449
0.484
0.224
0.335
0.251

17
10
45
34
42

0.456
0.347
0.372
0.212
0.538
0.456
0.224
0.561
0.570
0.445
0.373
0.192
0.399

11
30
26
48
6
13
44
5
4
12
27
50
20

Medical Image Analysis

6
7
8
9
10
11
12
13
14
15
16
17
18

Texture Feature

Asymptomatic

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104

Copyright 2005 by Taylor & Francis Group, LLC

TABLE 3.1
Statistical Analysis of 61 Texture and Shape Features Computed from 230 (115 Symptomatic and 115
Asymptomatic) Ultrasound Images of Carotid Atherosclerotic Plaques of Data Set 1


Gray-Level-Difference Statistics (GLDS)

324.26
143.26
267.01
0.259
0.181
0.161
2.228
0.619
2.526
6.107
2.427
6.451

82.03
0.125
0.501
2.168

0.347
0.446
0.374
0.106

31
16
25
54

14.909
1.512

0.00034
14,346
783,246

0.710
0.113
0.235
0.217
0.328

1
53
40
47
36

4.476
3.459
0.064
0.100

0.241
0.353
0.452
0.527

43
32
15
8

32
33
34
35

Contrast
Angular second moment (Energy)
Entropy
Mean

36
37
38
39
40

Coarseness
Contrast
Busyness
Complexity
Strength

41
42
43
44

Coarseness
Contrast

Periodicity
Roughness

Neighborhood Gray-Tone-Difference Matrix (NGTDM)
9.265
8.236
21.354
0.902
1.564
0.656
0.00060
0.00207
0.00011
22,446
16,005
27,120
772,828
703,980
1,118,719
Statistical-Feature Matrix (SFM)
10.424
5.406
8.730
24.999
4.971
22.863
0.578
0.081
0.625
2.386

0.127
2.301

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2
35
33
28
49
19
24
29
3
22
39
58
14

105

0.611
0.313
0.331
0.354
0.196
0.402
0.357
0.365
0.571

0.380
0.310
0.048
0.448

Angular second moment
Contrast
Correlation
Sum of squares: variance
Inverse difference moment
Sum average
Sum variance
Sum entropy
Entropy
Difference variance
Difference entropy
Information measures
of correlation

Texture and Morphological Analysis of Ultrasound Images

Copyright 2005 by Taylor & Francis Group, LLC

Spatial Gray-Level-Dependence Matrices (SGLDM): Range of Values
0.0095
0.0055
0.0050
0.0050
174.3
121.8

131.7
60.8
0.108
0.105
0.066
0.070
42.06
30.97
29.77
15.68
0.090
0.029
0.098
0.025
0.955
0.683
0.657
0.287
324.5
231.4
233.4
108.4
0.0656
0.0283
0.0505
0.0302
0.277
0.109
0.365
0.106

148.64
108.30
103.52
48.93
0.394
0.113
0.440
0.097
0.103
0.019
0.102
0.018
0.0314
0.0189
0.0214
0.0120

19
20
21
22
23
24
25
26
27
28
29
30
31

Symptomatic

Distance

m1 – m2

Rank
Order

Mean,
m2

Std. Dev.,
σ2

45
46
47
48
49
50

Laws’s Texture Energy Measures (TEM)
LL: texture energy from LL kernel
113,786
57,837
139,232
EE: texture energy from EE kernel

1,045.3
534.0
1,090.4
SS: texture energy from SS kernel
131.82
64.53
110.14
LE: average texture energy from LE and EL kernels
8,369.1
3754.8
9,514.1
ES: average texture energy from ES and SE kernels
335.64
174.69
312.85
LS: average texture energy from LS and SL kernels
1,963.5
1,008.5
2,054.6

53,432
489.9
53.64
3,639.9
149.85
907.2

0.323
0.062
0.258

0.219
0.099
0.067

37
57
41
46
55
56

51
52
53
54

H1
H2
H3
H4

0.068
0.059
0.045
0.034

0.531
0.521
0.400
0.148

7
9
23
51

55
56

Radial sum
Angular sum

2,047.5
1,500.8

0.447
0.414

18
21

57
58
59
60
61

X-coord. max. length
Y-coord. max. length
Area

Perimeter
Perimeter2/area

95.92
27.19
10,761
261.28
11.834

0.034
0.034
0.144
0.031
0.315

60
59
52
61
38

No.

Texture Feature

Mean,
m1

Std. Dev.,
σ1

Asymptomatic

Fractal Dimension Texture Analysis (FDTA)
0.367
0.081
0.423
0.291
0.063
0.336
0.244
0.045
0.270
0.207
0.050
0.216

Shape Parameters
349.24
110.89
100.95
36.42
18,797
11,744
927.71
291.21
51.266
15.608

354.27

99.39
21,092
939.84
45.089

2

2

X1 + X2

Medical Image Analysis

Fourier Power Spectrum (FPS)
3,073.7
1,546.0
4,219.7
2,462.3
1,362.5
3,301.7

dis =

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TABLE 3.1

Statistical Analysis of 61 Texture and Shape Features Computed from 230 (115 Symptomatic and 115
Asymptomatic) Ultrasound Images of Carotid Atherosclerotic Plaques of Data Set 1 (continued)


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107

TABLE 3.2
Verbal Interpretation of Arithmetic Values of Some Features
from Table 3.1 for Symptomatic vs. Asymptomatic Plaques
Symptomatic Plaques

Asymptomatic Plaques

Texture Feature

Value

Interpretation

Value

Interpretation

Median gray scale
Contrast

Low
High

High
Low

Entropy

Low

Roughness
Periodicity
Coarseness

High
Low
Low

Fractals H1, H2

Low

Darker
More local variations
present in the image
Less local uniformity in
image density
More rough
Less periodical
Less local uniformity in

intensity
Rough texture surface

Brighter
Fewer local variations present
in the image
Image intensity in neighboring
pixels is more equal
More smooth
More periodical
Large areas with small graytone variations
Smooth texture surface

High
Low
High
High
High

less contrast, greater smoothness, and with large areas with small gray-tone variations and being more periodical. These results are in agreement with the original
assumption that smooth surface, echogenicity, and a homogeneous texture are characteristics of stable plaques, whereas irregular surface, echolucency, and a heterogeneous texture are characteristics of potentially unstable plaques. Table 3.2 gives
a verbal interpretation of the arithmetical values of some of the features from Table
3.1 for the symptomatic vs. the asymptomatic plaques [39]. Figure 3.4 illustrates
several box plots of some of the best features as selected with Equation 3.1.
Principal component analysis (PCA) was also used as a method for feature
selection and dimensionality reduction [40]. The 61-feature vector was reduced to
nine transformed parameters by retaining only those components that contributed
more than 2% to the variance in the data set. The nine PCA parameters were used
as a new feature set for classification.
In Data Set 2, where the usefulness of the morphological features was investigated, a total of 330 ultrasound images of carotid atherosclerotic plaques were

analyzed [45]. The morphological algorithm extracted 98 features from the plaque
images. Using the entire pattern spectra for classification yielded poor results. Using
Equation 3.1, the number of features used was reduced to only five, which proved
to yield satisfactory classification results. The selected features represent the most
significant normalized pattern spectra components. We determined that small features due to: P1,' +' , P2,' +' , P3,' +' , P−4,' +' , and P−5,' +' (see Equation 3.60 in Appendix 3.1)
yield the best results. Table 3.3 shows the good performance of P1,' +' , which may be
susceptible to noise. However, it is also the feature that is most sensitive to turbulent
flow effects around the carotid plaques. Table 3.3 tabulates the statistics for the five
selected morphological features for the two classes and their interclass distance as
computed with Equation 3.1. Additionally, for Data Set 2, the SF, the SGLDM, and
the GLDS texture-feature sets were computed and compared with the morphological
features [45].
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FIGURE 3.4 Box plots of the features gray-scale median (2), entropy (14), and coarseness
(36) for the symptomatic and asymptomatic plaques. (The numbers in parentheses denote the
serial feature number as listed in Table 3.1.) The notched box shows the median, lower and
upper quartiles, and confidence interval around the median for each feature. The dotted line
connects the nearest observations within 1.5 of the interquartile range (IQR) of the lower and
upper quartiles. Crosses (+) indicate possible outliers with values beyond the ends of the 1.5
× IQR.

3.4.2 CLASSIFICATION RESULTS

OF THE

SOM CLASSIFIERS

For the classification task, the unsupervised SOM classifier was implemented with
a 10 × 10 output node architecture, and it was trained for 5000 learning epochs. For
training the classifier, 80 symptomatic and 80 asymptomatic plaques were used,
whereas for evaluation of the system, the remaining 35 symptomatic and 35 asymptomatic plaques were used. To estimate more reliably the correctness of the classification results, a bootstrapping procedure was followed. The system was trained
and evaluated using five different bootstrap sets where, in each set, 160 different
plaques were selected at random for training, and the remaining 70 plaques were
used for evaluation. The SOM classifier yielded a confidence measure (see Subsection 3.3.5) on how reliable the classification result was, based on the number of the
nearest neighbors on the self-organizing map. Five different neighborhood windows
were tested: 1 × 1, 3 × 3, 5 × 5, 7 × 7, and 9 × 9. The confidence measure was
calculated using a weighting mask giving the output nodes nearest to the winning
output node a greater weight than the ones farther away.
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109

TABLE 3.3
Statistical Analysis of the Five Best Morphological Features Computed from
330 (194 Asymptomatic and 136 Symptomatic) Ultrasound Images of Carotid
Plaques of Data Set 2
Symptomatic Plaques

Feature
P1.'+'
P3.'+'
P2.'+'
P–4.'+'
P–5.'+'

Asymptomatic Plaques

Mean,
m1

Std. Dev.,
σ1

Mean,
m2

Std. Dev.,
σ2

0.0433
0.1922
0.1102
0.0080
0.0108

0.0407
0.1218
0.0888

0.0061
0.0079

0.0249
0.1355
0.0713
0.0119
0.0158

0.0229
0.0870
0.0520
0.0084
0.0109

Distance

dis =

m1 – m2
2

2

X1 + X2
0.393
0.379
0.378
0.370
0.367

Note: For each feature, the mean and standard deviation were computed for the asymptomatic group and
for the symptomatic group. The distance between the symptomatic and the asymptomatic groups was
computed as described in Equation 3.5.

Table 3.4 tabulates the diagnostic yield of the SOM classifiers for the evaluation
set of Data Set 1 [39]. The best feature sets in average for all windows were: the SGLDM
(range of values) with 65.3%, the TEM with 63.0%, followed by the NGTDM with
62.2%, the SGLDM (mean values) with 61.7%, and the GLDS with 61.5%. The worst
feature set was the shape parameters, with an average diagnostic yield of only 49.2%.
The best SOM window sizes in average were the large ones 5 × 5, 7 × 7, and 9 × 9,
with an average DY of about 65%. The worst window size was the 1 × 1, with an
average DY of only 43.3%. As given in Table 3.4, the best individual DY was 70%,
and it was obtained by the SGLDM (range of values) using a 5 × 5 neighborhood
window and by the NGTDM with a 9 × 9 window size. Figure 3.5 illustrates the
distribution of 160 carotid plaques of the training set (80 symptomatic and 80 asymptomatic) on a 10 × 10 SOM using as input all the 61 features (* = symptomatic, o =
asymptomatic). Similar plaques are assigned to neighboring SOM matrix nodes. The
figure demonstrates the overlap between the two classes and the difficulty of the
problem. For comparison reasons, the diagnostic yield was computed using as a separate
feature set the first 15 best features that were selected through univariate selection, as
described in Subsection 3.3.4 using Equation 3.1. Using the first 15 best features yielded
an average DY for the five windows of 63.0%, with the highest DY of 68.5% obtained
with the 7 × 7 window size. This was better than the average success rate of the
individual feature sets but lower than the diagnostic yield of the best feature set, and it
was much worse than the overall success rate of the combiner.
Furthermore, the 15 best features selected through multivariate selection were
also used for classification. The average diagnostic yield was poor (about 50%), and
it was much lower than the diagnostic yield obtained by the univariate selection.
These results show the high degree of overlap between the two classes, demonstrating
the difficulty of using the search algorithms to identify feature combinations with

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110

Medical Image Analysis

TABLE 3.4
Average Diagnostic Yield (DY) of the Self-Organizing Map (SOM) Classifier
System for the Evaluation Set of Data Set 1 (35 Symptomatic and 35
Asymptomatic Plaques) of the Modular Neural Network Diagnostic System
after Bootstrapping Available Data for Five Different Sets of Plaques
Diagnostic Yield (%)
Window Size
Feature Set

1 × 1 3 × 3 5 × 5 7 × 7 9 × 9 Average

1 SF
2 SGLDM (mean)
3 SGLDM (range)
4 GLDS
5 NGTDM
6 SFM
7 TEM
8 FDTA
9 FPS
10 Shape parameters

Average

46.0
45.7
49.4
40.3
39.1
39.4
46.9
40.9
44.6
40.3
43.3

59.7
65.7
69.4
66.0
64.0
59.7
65.4
62.0
61.4
52.9
62.6

65.7
66.3
70.0
66.9

68.3
65.1
67.4
63.7
62.6
52.9
64.9

66.6
65.7
68.3
66.6
69.4
65.1
67.4
64.9
64.3
50.6
64.9

66.6
65.1
69.4
67.7
70.0
65.1
67.7
65.1
63.4
49.4

65.0

60.9
61.7
65.3
61.5
62.2
58.9
63.0
59.3
59.3
49.2
60.1

Combine the ten feature sets with majority voting
Combine by averaging the ten confidence measures

64.0
68.9

67.7
71.1

66.0
73.1

66.6
72.6

66.9

72.0

66.2
71.5

15 best features

45.6

65.0

68.0

68.5

68.0

63.0

Note: DY is given for the ten feature sets, their average, and when combined using (a) majority voting and
(b) by averaging the ten confidence measures. DY is also given for the first 15 best features as selected using
Equation 3.5. DY was computed for five different SOM neighborhood windows: 1 × 1, 3 × 3, 5 × 5, 7 × 7,
and 9 × 9.

good class separability. The nine parameters obtained through principal component
analysis (PCA) were also used as input to the SOM classifier. The average diagnostic
yield was about 64%, which was slightly better than the average DY of the best 15
features obtained by the univariate feature selection but still much lower than the
diagnostic yield obtained by combining the ten feature sets.
In the second data set, where the usefulness of the morphological features was

investigated, 90 asymptomatic and 90 symptomatic plaques were used for training
the classifier, whereas for evaluation of the system the remaining 104 asymptomatic
and 46 symptomatic plaques were used [45]. Table 3.5 tabulates the diagnostic yield
for the SOM classifier for the different feature sets and for different neighborhood
window sizes on the self-organizing map. The highest diagnostic yield was 69.6%,
and it was obtained with a 9 × 9 window size, using as input the GLDS feature set.
On average, the results with the highest diagnostic yield were obtained by the GLDS
feature set, which was 64.6%, followed by the morphological feature set with a
diagnostic yield of 62.9%, the SGLDM with 62.2%, and the SF with 59.9%.
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Texture and Morphological Analysis of Ultrasound Images

111

11
10
9
8
7
6
5
4
3
2
1
0

0

1

2

3

4

5

6

7

8

9

10

11

FIGURE 3.5 Distribution of 160 carotid plaques of the training set (80 symptomatic and 80
asymptomatic) on a 10 × 10 SOM using as input all 61 features from Table 3.1 (* =
symptomatic, o = asymptomatic). Similar plaques are assigned to neighboring-output matrix
nodes. A new plaque is assigned to one winning output node and is classified based on the
labels of the neighboring nodes in an R × R neighborhood window. The output nodes near

the winning node are given a greater weight than the ones farther away.

3.4.3 CLASSIFICATION RESULTS

OF THE

KNN CLASSIFIERS

The KNN classifier was also used for the carotid plaque classification. The KNN
algorithm was implemented for values of k = 1, 3, 5, 7, and 9, and the results are
tabulated for Data Set 1 in Table 3.6. Highest diagnostic yields were achieved with
k = 7 and k = 9, which shows the need to consider a large number of neighbors
because of the overlap of the two classes. The best feature set was, in average for
all k, the SGLDM (range of values) with a DY of 66.9%, which was also the best
feature set for the SOM classifier. The best individual classification results were
with the SGLDM (range of values) with DY 70.9%, and with the SGLDM (mean
values) with 66.9%. In both cases k = 9 was used.
Table 3.7 tabulates the results of the KNN classifier for the second data set. The
highest diagnostic yield was 68.7%, and it was obtained with k = 3, using as input
Copyright 2005 by Taylor & Francis Group, LLC