ORIGINAL PAPER

A supervised classification-based method for coronarycalcium detection in non-contrast CT

Uday Kurkure • Deepak R. Chittajallu •

Gerd Brunner • Yen H. Le • Ioannis A. Kakadiaris

Received: 6 February 2009 / Accepted: 23 February 2010

� Springer Science+Business Media, B.V. 2010

Abstract Accurate quantification of coronary artery

calcium provides an opportunity to assess the extent of

atherosclerosis disease. Coronary calcification burden

has been reported to be associated with cardiovascular

risk. Currently, an observer has to identify the coronary

calcifications among a set of candidate regions,

obtained by thresholding and connected component

labeling, by clicking on them. To relieve the observer

of such a labor-intensive task, an automated tool is

needed that can detect and quantify the coronary

calcifications. However, the diverse and heterogeneous

nature of the candidate regions poses a significant

challenge. In this paper, we investigate a supervised

classification-based approach to distinguish the coro-

nary calcifications from all the candidate regions and

propose a two-stage, hierarchical classifier for auto-

mated coronary calcium detection. At each stage, we

learn an ensemble of classifiers where each classifier is

a cost-sensitive learner trained on a distinct asymmet-

rically sampled data subset. We compute the relative

location of the calcifications with respect to a heart-

centered coordinate system, and also use the neigh-

boring regions of the calcifications to better character-

ize their properties for discrimination. Our method

detected coronary calcifications with an accuracy,

sensitivity and specificity of 98.27, 92.07 and 98.62%,

respectively, for a testing dataset of non-contrast

computed tomography scans from 105 subjects.

keywords Computed tomography �Coronary calcium � Supervised classification

Introduction

Cardiovascular disease (CVD) is one of the major

causes of deaths in the western world. It is respon-

sible for almost one million deaths per year in the

United States [1]. Thus, appropriate preventive

measures need to be taken to decrease the cardiovas-

cular events. However, preventive measures can be

U. Kurkure (&) � D. R. Chittajallu � G. Brunner �Y. H. Le

Computational Biomedicine Lab,

Department of Computer Science, University of Houston,

Houston, TX 77204, USA

e-mail: ukurkure@uh.edu

D. R. Chittajallu

e-mail: drchittajallu@uh.edu

G. Brunner

e-mail: gbrunner@bcm.edu

Y. H. Le

e-mail: yhle@uh.edu

I. A. Kakadiaris

Computational Biomedicine Lab,

Departments of Computer Science,

Electrical and Computer Engineering

and Biomedical Engineering,

University of Houston, Houston,

TX 77054, USA

e-mail: ioannisk@uh.edu

123

Int J Cardiovasc Imaging

DOI 10.1007/s10554-010-9607-2

applied only when an accurate risk assessment can be

made. Thus, there is an urgent need to develop tools

to improve the assessment of the cardiovascular risk.

Recent studies [2–5] have shown that coronary

artery calcification (CAC) burden as measured by

non-contrast computed tomography (CT) is a signif-

icant and independent predictor of atherosclerosis

disease and is associated with future coronary events.

Therefore, accurate identification and quantification

of calcifications in the coronary arteries may allow

improved diagnosis and monitoring of progression

of atherosclerosis. Moreover, the regional coronary

calcium burden is related to the regional dysfunction

of the left ventricle [6]. Thus, the quantification of the

coronary calcifications provides a measure to assess

the risk of coronary artery disease (CAD).

With the advancements in imaging technology, the

non-invasive assessment of the coronary arteries and

their calcification is feasible. Figure 1 depicts typical

candidate regions for the coronary and the aortic

calcifications as well as the image noise present in a

CT scan. The calcifications are highly dense regions

compared to other soft tissues; hence, they appear as

bright structures in the CT scans. The coronary

calcifications are located in the three main coronary

arteries and their sub-branches—the left main/left

anterior descending artery (LM/LAD), the left cir-

cumflex (LCX), and the right coronary artery

(RCA)—that cover different portions of the heart

surface area.

The current clinical standard to detect the coronary

calcifications is to apply a connected component

labeling method using a threshold of 130 Hounsfield

units (HU) and a minimum size constraint of three/

four pixels (at least 1 mm2) [7]. This thresholding

results in candidate regions not only from coronary

calcifications but also from non-coronary calcifica-

tions, noise artifacts, and metal implants. The coro-

nary calcifications are then identified manually.

However, manual annotation is a labor intensive

and time-consuming task, especially for longitudinal

studies and large-scale screening. Hence, automated

computational methods for detecting the coronary

calcifications are needed to ease the manual burden as

well as to provide means to investigate possible

improvements in cardiovascular risk assessment.

To the best of our knowledge, Ukai et al. [8, 9]

first proposed a method for coronary calcification

detection using some diagnostic rules, and later

improved their method by utilizing a neural networks

based classification method to discriminate between

the coronary calcifications and the artifacts. The

method was evaluated on helical CT scans (acquired

in mass screening for lung cancer) of subjects with

very few coronary calcifications and, thus, is limited

in scope. The calcium candidates were obtained using

an intensity threshold of 80 HU and size limit of 6

pixels, unlike the current clinical standards [7]. The

neural network was trained using six features—size,

presence of fat in surrounding region, maximum HU,

minimum HU, difference between maximum HU

inside the candidate and mean HU outside the

candidate, and region number obtained by dividing

heart into eight regions. However, the true samples

used for training in their study included aortic

calcifications and artifacts, that satisfied some inten-

sity contraints, resulting in a contaminated model.

Recently, Isgum et al. [10] proposed a two-stage

classification method using the k-nearest neighbor

classifier for coronary calcification detection. The CT

scans used in this study were originally obtained at

high resolution and were later resampled to a lower

resolution. The candidate regions with high proba-

bility of belonging to the negative class in the first

stage of classification were discarded and only the

Fig. 1 CT image of a heart depicting typical candidate

regions: coronary calcifications in LAD (a), RCA (b), aorta

(c), and image noise (d,e)

Int J Cardiovasc Imaging

123

remaining ones were considered for the second stage

of classification. For classification, the features used

were computed based on the size, shape, location, and

appearance of the candidate regions. The appearance-

based features were computed at the peak intensity

point of each candidate region from image deriva-

tives. The use of region-based features was limited to

the mean and the maximum intensity values. Addi-

tionally, aorta segmentation was performed to

improve the performance of the classifier in separating

aortic calcifications from coronary calcifications.

However, the segmentation results were not satisfac-

tory since the problem of segmenation is inherently

difficult in the absence of any contrast. Furthermore,

the classifiers were trained on the unbalanced data

owing to the large number of negative candidates;

hence, they were biased towards the majority class.

In this paper, we investigate various factors that

can make it feasible to build an automated coronary

calcium detection system. Though the coronary

calcifications appear as high-density structures in the

non-contrast CT scans, it is inherently difficult to

identify them automatically. The difficulty arises

because of the presence of other similar high-density

structures, including the non-coronary calcifications,

and the absence of any contrast agent to identify the

blood vessels. It is apparent that the choice of features

plays an important role in solving this problem. We

compute several features based on appearance, shape

and size of the calcifications. In addition, we inves-

tigate various clues that a human observer uses to

manually annotate the coronary calcifications in the

CT scans (e.g., expected location of the coronary

arteries and surrounding regions of calcifications).

Thus, in order to better characterize their properties

for discrimination, we additionally compute relative

location of the calcifications with respect to a heart-

centered coordinate system and region-based features

for the candidates and their neighboring regions. To

the best of our knowledge, it is the first time that the

relevance of the region-based features and the neigh-

borhood region of the calcifications is investigated.

Finally, we have developed a novel two-stage

hierarchical classification-based method to detect

coronary calcifications in the non-contrast cardiac

CT scans1. In the current problem of classification,

the positive class is composed of the coronary

calcifications, while the negative class consists of

the aortic calcifications, image noise, and metal

implants, if any. In the first stage, we explicitly learn

to distinguish the arterial (the coronary and the aortic)

calcifications from other highly dense regions present

within the heart region. In the second stage, we learn

to separate the coronary calcifications from the aortic

calcifications. We investigate the possibility of such

separation without requiring the segmentation of the

aorta in this work. At each stage of the hierarchy, we

construct an ensemble of classifiers, trained on

different data subsets that are generated using an

asymmetric sampling method, to overcome the

problem of a highly unbalanced and large data set.

The decisions of each individual classifier in the

ensemble are combined together to obtain the final

decision for that stage. Furthermore, each classifier in

the ensemble is designed to accommodate asymmet-

ric penalty costs for different types of errors.

Materials and methods

Data

The heart scans were obtained by electron-beam CT

(EBCT) imaging with a slice thickness of 3 mm and

an x-y pixel spacing of 0.508–0.586 mm. Scans from

205 subjects with approximately 20–35 image slices

per scan were used in our experiments. There were 20

coronary calcifications and 335 negative candidate

regions in the heart region per scan on average. We

created two mutually exclusive data subsets, D1 with

100 subjects and D2 with 105 subjects, for the

training and testing phases, respectively.

For training and testing purposes, the arterial

calcifications were manually annotated. The manual

annotation was performed using a software developed

at the Computational Biomedicine Lab, specifically

for the purpose of calcium scoring. The vertical range

of the heart region was defined from the transverse

slice at the top in which the pulmonary artery splits to

the transverse slice at the bottom till which the

coronary arteries are present. To annotate the coro-

nary calcifications, the observer clicks points along

the trajectory of a coronary artery in the transverse

slices. Then, the software interpolates these points to

build an arterial trajectory, and detects the nearby1 Preliminary work on this topic has appeared in [11].

Int J Cardiovasc Imaging

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coronary calcium. It computes the extent of the

detected calcifications using the minimum HU con-

straint of 130 HU and the minimum size constraint of

four pixels. The observer is allowed to include

coronary calcium not detected by the software and

exclude any non-coronary calcium detected by the

software. To annotate the aortic calcifications, the

observer clicks at any point within a calcified region

in the aorta and the software computes its extent

using the minimum HU and size constraints.

Feature extraction

In classification-based methods, the representation

of the candidate samples (i.e., the features) play the

most important role. To uniquely represent the

coronary calcifications, it is imperative to investigate

their various characteristic properties that can be used

to distinguish them apart from other candidate

regions. The various types of features that were

designed and evaluated are discussed next.

Spatial location

To identify a coronary calcification among the

candidate regions, a human observer mostly relies

on prior knowledge of the expected location of the

coronary arteries relative to the heart. To incorporate

such information about the location, two sets of

location features are computed:

F1: absolute location (x, y, z) in the image

coordinate system, and

F2: relative location (x, y, z) in a heart-centered

coordinate system.

The heart-centered coordinate system is defined by

a unit bounding box around the heart region. The

heart region is extracted using a hierarchical

approach in which the peripheral structures are

detected first and then the heart region is determined

using dynamic programming and prior knowledge of

anatomical location of the heart.

In particular, the body region is segmented first

using thresholding and morphological operators.

Next, the lung is detected within the body region by

applying a threshold (-250 HU) and extracting the

largest connected-component region from the com-

plement of the thresholded result. The boundary of

the extracted lung region may have indentations

because of the pulmonary vessels that transport blood

between the lung and the heart. Since a part of the

lung boundary defines the lateral boundary of the

heart, it is important to smooth the jagged boundary

resulting from the indentations of pulmonary vessels.

To fill the indentations on the lung boundary, a binary

morphological closing operation is performed on

the extracted lung region [12]. Then, the bones are

detected using a threshold and a region growing

algorithm because they constraint the heart boundary

on anterior and posterior sides. The bone fragments in

the first k slices are extracted by applying a threshold

(130 HU) outside the convex hull of the lung region.

The extracted bone fragments are then provided as

input to the 3D region growing algorithm to obtain

the complete bone structure.

Since the heart region lies in-between the lung

halves that define the heart’s lateral boundary, one

could simply compute the convex hull of the lung and

then subtract the lung from it to obtain the in-between

region. However, such a scheme may miss some

portions of the heart on the anterior side and include

unnecessary structures on the posterior side. To avoid

such situation, the anterior and posterior boundaries are

obtained by determining optimal shortest paths

between the left and right lung using dynamic pro-

gramming in each axial slice. Since the spine, sternum

and other bone structures constrain the anterior and

posterior boundary of the heart, these bone structures

guide the dynamic programming method to detect the

boundaries. The region between the detected anterior

and posterior boundaries, and the lungs is smoothed

using morphological operators and extracted as the

heart region. Finally, a minimum size cube that

contains the complete 3D heart region is computed to

define the unit bounding box for the heart-centered

coordinate system.

Pixel-based texture features

Texture features have been proven to improve the

accuracy of the classification-based methods in

different medical image analysis applications. We

compute texture features using the Laws texture

energy measures [13]. These texture energy measures

are computed using convolution kernels generated

from one-dimensional convolution kernels of five

pixel length characterizing level, edge, spot, wave

and ripple patterns. Since the texture features are

Int J Cardiovasc Imaging

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pixel-based, we selected the maximum HU-density

pixel as the representative of the candidate region

for pixel-based texture features (F3).

Region-based texture features

Additionally, an observer uses the candidate’s

regional properties instead of individual pixel prop-

erties to distinguish between the coronary calcifica-

tion from the rest. Based on this observation, we

propose to extract region-based features to better

represent a candidate region in addition to the

individual pixel features.

Since the coronary arteries mostly span through the

pericardial fat after originating from the ascending

aorta, except in the distal section when they enter the

ventricular wall, the neighboring regions of the coro-

nary calcifications provide significant clues to distin-

guish the coronary calcifications from the image noise,

which mostly has blood in its neighboring region.

Hence, the observer also uses appearance clues from

the candidate region and its surrounding neighboring

region to distinguish the coronary calcification from

the rest of the candidate regions. Based on these

observations, we extract three set of the region-based

features:

F4: the set of features computed for the candidate

calcium region,

F5: the set of features computed for its neighbor-

hood region, and

F6: the set of features computed for the combined

region of the candidate and its neighborhood.

The neighborhood region is defined as a ribbon-like

region of a certain width around the candidate region.

Specifically, we compute the mean, standard devia-

tion, skewness, kurtosis, and entropy of the pixel-

based Laws texture energy measures [13] for the

region of interest. Additionally, we compute the

difference of means normalized by the sum of standard

deviations of the Laws measures inside and outside the

candidate region as a feature for the combined region.

We also compute the grey-level co-occurrence matri-

ces (GLCM) proposed by Haralick et al. [14]. The

GLCM provides the probability of occurrence of a

particular pair of the HU-density at a particular spatial

arrangement. Based on the cost statistics, we compute

the contrast, correlation, energy, and homogeneity

features for four different spatial arrangements.

Additional features

We include object-related features (F7) based on the

size, shape, and appearance of the region of inter-

est—area, shape moments, eccentricity, compactness,

anisotropy, inertia, and HU density-based first-order

statistics (e.g., mean, maximum, minimum, standard

deviation, skewness, kurtosis, and entropy), length of

major axis, length of minor axis, equivalent radius,

mean radial length and so on. To list all features

and explain their details is beyond the scope of this

paper.

Feature selection

The classification accuracy of a classifier depends

largely on the selection of useful features. One of the

criterions, often termed as maximum relevance, to

find useful features is to select features that are

individually highly correlated with the target class

distribution. However, the features thus selected may

be highly intercorrelated too. When two features are

intercorrelated, one of them can be removed without

affecting the classification performance to reduce the

computational load. Also, individually powerful

features may not be so powerful together. Thus, we

need to select features which have maximum rele-

vance and minimal redundancy.

The relevance of a feature with respect to a

particular outcome or the redundancy between any

two features can be characterized in terms of

correlation or mutual information. We used a mutual

information (MI)-based minimum-redundancy-max-

imum-relevance (mRMR) feature selection heuristic

proposed by Peng et al. [15]. The feature selection is

performed in two steps. First, a subset G of N features

is selected from the large feature set F such that an

mth feature is added incrementally to the currently

selected set Gm-1 with m - 1 features, if it

maximizes the following condition:

maxfi2fF�Gm�1g

MIðfi; LÞ �1

m� 1

X

fj2Gm�1

MIðfi; fjÞ

2

4

3

5; ð1Þ

where the first term corresponds to the relevance,

the second term corresponds to the redundancy, L is

the target class, and fi is the ith feature. In the second

step, we form P sequential feature subsets in multi-

ples of k features such that G1*k , G2*k , ... ,Gp*k

Int J Cardiovasc Imaging

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and select the feature subset that corresponds to the

minimum cross-validation error obtained from a

classifier.

Coronary calcium detection method

For classification-based coronary calcium detection,

the negative class (aortic calcifications, image noise,

and metal implants, if any) is broader and richer than

the positive class (coronary calcifications), introduc-

ing complex class compositions. Such complex class

composition may increase the complexity of the

learner and introduce a significant number of false

positives. Moreover, the majority of the candidate

regions belong to the image noise and hence, the

negative class. Thus, there is large number of

candidates and the classes are highly unbalanced in

terms of the number of candidates. Training on such

unbalanced classes will bias the classifier towards the

majority class, and will degrade its performance.

To account for the complex class composition, we

divide the problem of detecting coronary calcifica-

tions in to two sub-problems: (1) detection of arterial

(aorta and coronary arteries) calcifications among all

the candidates, and (2) detection of the coronary

calcifications among the arterial calcifications. We

construct a two-stage hierarchical classifier to solve

these two sub-problems (Fig. 2). At the first stage of

the hierarchy, a classifier is constructed using the

features selected specifically to discriminate the

arterial (coronary and aortic) calcifications from the

rest of the candidate regions. At the second stage of

the hierarchy, another classifier is constructed using

the features selected specifically to separate the

coronary calcifications from the aortic calcifications.

The final decision of the two-stage classifier is a

combination of decisions of the individual classifiers

of each stage and is given by:

DðxÞ ¼þ1; if D2ðxÞ ¼ þ1

�1; if D2ðxÞ ¼ �1

�1; if D1ðxÞ ¼ �1

;

8<

: ð2Þ

where D1 and D2 are the hard-output decisions of the

classifiers from the two stages of the hierarchy,

respectively.

The problem of unbalanced classes persists even in

the two-stage hierarchical classification-based

approach. At the first stage, the number of arterial

calcifications is significantlty lower than the the

number of candidates belonging to the image noise.

At the second stage, the number of aortic calcifica-

tions is very small as compared to the number of

coronary calcifications. We address the problem of

the unevenness of the positive and negative classes by

employing an asymmetric random sampling strategy.

In asymmetric random sampling, the candidates are

randomly selected from the majority class until the

number of the selected candidates is equal to the

number of the candidates from the minority class.

However, a single learning agent or classifier

trained on an under-sampled data subset assumes that

the distribution of candidates in the sampled subset is

the same as in the original dataset, which may not be

true in practical situations. Thus, some potentially

relevant candidates may get eliminated during the

sampling process, hampering the performance of the

classifier. An ensemble of multiple classifiers that are

trained on different independently sampled subsets

would improve the accuracy of prediction over a

single classifier. Moreover, distortion of data distri-

bution that can be introduced via data sampling will

be minimized. Thus, for each stage of the hierarchy,

we train individual classifiers whose decisions are

combined to obtain the final decision at that stage

(Fig. 3). We investigated two combination rules—

simple majority voting rule (MVR) and weighted

majority rule (WMR)—to combine the decisions of

the individual classifiers. In the WMR, the weights

are directly related to the competency or accuracy of

the classifiers, and are computed as the logarithm of

odds of competency, wi ¼ logð Ai

1�AiÞ; where Ai is the

prior probability for correct classification of ith

classifier, computed from the validation set.

Fig. 2 A schematic of the classification framework for

coronary calcium detection

Int J Cardiovasc Imaging

123

To further reduce the error of classification,

asymmetric penalty cost may be applied to the

different types of errors. Support vector machines

(SVMs) [16] are capable of incorporating different

costs for the positive and the negative classes by

modifying their objective function as follows:

1

2wTwþ Cp

X

ijyi¼þ1

ni þ Cn

X

ijyi¼�1

ni; ð3Þ

where w is a normal vector perpendicular to the

separating hyperplane; yi is a label for each ith data

sample with ?1 for positive outcome and -1 for

negative outcome; ni is a slack variable allowing soft

margins (i.e., training errors for data that may not be

completely separable); and Cp and Cn are the cost

parameters for the positive and the negative classes,

respectively [17]. However, the specific costs for this

problem are not easy to determine. We employ a grid

search algorithm in which a classifier determines the

optimal costs based on the cross-validation accuracy

obtained using three-fold cross-validation. In n-fold

cross-validation, the training data is first partitioned

into n subsets and then, classifier uses one of the n

subsets for validation and the rest n - 1 subsets for

training. The cross-validation accuracy is computed by

averaging the accuracy of classifier from the n-folds.

In grid search method, a discrete grid is constructed

in the parameter space and the parameter values at

each grid node are evaluated using the n-fold cross-

validation method. The parameter values at the node

having the highest cross-validation accuracy are

finally selected to train the classifier [18].

Training

The candidate regions are extracted from the training

CT scans using the minimum size and HU-density

constraints. From the training set, we generate four

asymmetrically-sampled training subsets for each

stage of the hierarchy with equal number of candi-

dates in the positive and negative classes. Next, we

compute the features for all the candidate regions.

Then, we apply the feature selection method to select

the most relevant and non-redundant feature subset

for each stage of the hierarchy. The feature subset

with highest cross-validation accuracy is selected.

Finally, we construct a two-stage classifier using

multiple classifiers trained on the selected subsets of

features for each stage. We use LIBSVM [19] to train

the individual SVMs using a nonlinear Gaussian

radial basis kernel function. The width parameter c,

the penalty cost parameter C, and the ratio of

asymmetric misclassification costs Cp/Cn are opti-

mized using a grid search technique and the three-

fold cross-validation method.

Deployment

In the deployment or testing phase, the candidate

regions are extracted using the size and HU-density

constraints from the CT scan. The features from the

selected feature subsets are computed for the candi-

date regions and provided as input to the two-stage

hierarchical classifier. The classifier then predicts for

each candidate region whether it is a coronary

calcium region or not.

Family of classifiers

To demonstrate the importance of using an ensemble

of multiple classifiers over a single classifier, and a

two-stage hierarchical classifier over a single stage

classifier, we constructed the following classifiers:

L1: single stage, single classifier

L2: single stage, ensemble classifier with MVR rule

L3: single stage, ensemble classifier with WMR

rule

L4: two-stage classifier using a single classifier at

each stage

L5: two-stage classifier using an ensemble classifier

with MVR rule at each stage

Fig. 3 Depiction of the construction of an ensemble classifier

using multiple classifiers

Int J Cardiovasc Imaging

123

L6: two-stage classifier using an ensemble classifier

with WMR rule at each stage

L7: two-stage classifier using an ensemble classifier

with MVR rule and asymmetric penalty costs at

each stage

L8: two-stage classifier using an ensemble classifier

with WMR rule and asymmetric penalty costs at

each stage.

Results

The performance of the classifiers was evaluated in

terms of sensitivity, specificity and accuracy based on

metrics derived from confusion matrix. These statis-

tical performance measures can be computed in terms

of true-positives (TP), true-negatives (TN), false-

positives (FP) and false-negatives (FN) as following:

Sensitivity ¼ TP

TPþ FN;

Specificity ¼ TN

TN+FP;

Accuracy ¼ TPþ TN

TP+TN+FP+FN:

First, we present the results of the feature analysis

experiments that were conducted using single stage

classifiers to emphasize the choice of the features

used. Then, we evaluate the performance of the

proposed two-stage hierarchical classifiers and ana-

lyze the errors in detail.

Feature analysis

To systematically assess the effectiveness of different

types of feature groups to detect the coronary

calcium, we constructed various feature sets by

combining different types of feature groups incre-

mentally. The various feature sets that were con-

structed are listed in the Table 1. Each of the feature

set was further reduced to a subset of the most

relevant and non-redundant features, independently,

through the feature selection process. The effective-

ness of each feature set was assessed using the single

stage classification approach. Thus, three single stage

classifiers (i.e., L1, L2, and L3) were applied to detect

the coronary calcifications.

Table 2 presents the performance metrics for

these. Using the heart-centered coordinate system-

based features (F2) instead of the absolute image

coordinate system-based features (F1) improved the

sensitivity by approximately 7.0 and 1.5% when used

independently and in combination with the other

Table 1 The feature sets formed by combining various feature

groups

Feature set Feature groups

S1 F1

S2 F2

S3 F2 ? F7

S4 F2 ? F7 ? F3

S5 F2 ? F7 ? F3 ? F4 ? F5 ? F6

S6 F2 ? F7 ? F3 ? F4

S7 F2 ? F7 ? F3 ? F6

S8 F1 ? F7 ? F3 ? F6

Table 2 Performance evaluation of single stage classifiers

Classifier Feature

set

Sensitivity

(%)

Specificity

(%)

Accuracy

(%)

L1 S1 70.62 92.97 91.79

S2 77.64 95.61 94.65

S3 85.41 97.36 96.73

S4 89.50 97.43 97.01

S5 91.32 97.38 97.06

S6 88.39 96.18 95.77

S7 93.29 98.34 98.07

S8 91.67 97.97 97.64

L2 S1 69.46 93.30 92.04

S2 76.98 96.07 95.06

S3 85.01 97.78 97.10

S4 88.49 97.92 97.42

S5 91.62 98.41 98.05

S6 88.24 98.07 97.55

S7 92.63 98.48 98.17

S8 91.52 98.12 97.77

L3 S1 69.71 93.12 91.88

S2 77.34 95.88 94.90

S3 85.82 97.54 96.92

S4 88.89 97.72 97.26

S5 92.33 98.14 97.83

S6 88.69 97.83 97.34

S7 92.98 98.38 98.09

S8 91.82 97.99 97.66

Bold values indicate the best performing feature test

Int J Cardiovasc Imaging

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features, respectively. Adding object features (F7) to

the spatial location features improved the sensitivity

and specificity by almost 10.0 and 1.5%, respectively,

in feature set S3. The pixel-based texture features

computed at the peak HU pixel (F3) further improved

the sensitivity by 3.5% in feature set S4. Addition of

the region-based features computed for the candidate

region (F4) in feature set S6 didn’t have significant

effect on the prediction of the classifiers. However,

addition of the region-based features computed for

the combined candidate and neighborhood region

(F6) in feature set S7 improved the sensitivity by

almost 5%. Inclusion of all the region-based features

in feature set S5 reduced the sensitivity over the

feature set S7 by almost 2.0, 1.0, and 0.7% for L1, L2,

and L3, respectively. Thus, the best performance was

obtained for the feature set S7 comprising of the

features F2, F7, F3, and F6 for all the three classifiers.

Comparison of the classifiers

The two-stage hierarchical classifiers (i.e., L4, L5, L6,

L7 and L8) were constructed for the two feature sets

(S5 and S7) that provided highest sensitivity and

accuracy for the single stage classifiers. The perfor-

mance metrics of the single stage classifiers and the

two-stage hierarchical classifiers are presented in the

Tables 2 and 3, respectively. The ensemble-based

classifiers exhibited the highest accuracy for both

single stage and two-stage classifiers. The MVR rule

proved to be the best decision fusion rule for the

ensemble-based classifiers in terms of accuracy.

Among the ensemble-based classifiers using the

MVR rule, the single stage classifiers provided higher

sensitivity; however, the two-stage hierarchical clas-

sifiers provided higher accuracy.

The feature set S7 proved to be better than the

feature set S5 for the ensemble-based classifiers in

terms of the sensitivity with specificity remaining

almost same. Using the asymmetric penalty costs

improved the sensitivity by 0.10–0.50% for the two-

stage ensemble-based classifiers. Overall, the highest

accuracy of 98.27% (sensitivity: 92.07%, specificity:

98.62%) was achieved for the two-stage hierarchical

L7 classifier for the feature set S7.

Misclassification error analysis

Table 4 presents the misclassification error analysis

for the L1, L2, and L7 classifiers. The misclassification

error percentage, E1, was computed as the ratio of the

number of misclassifications of a particular candidate

to the overall number of misclassfications. The

category-wise misclassification error percentage,

Table 3 Performance evaluation of two-stage hierarchical

classifiers

Classifier Feature

set

Sensitivity

(%)

Specificity

(%)

Accuracy

(%)

L4 S5 91.12 98.25 97.87

S7 91.67 97.66 97.34

L5 S5 90.51 98.59 98.16

S7 91.62 98.63 98.26

L6 S5 91.12 98.30 97.92

S7 92.28 98.30 97.98

L7 S5 90.66 98.63 98.21

S7 92.07 98.62 98.27

L8 S5 91.22 98.36 97.98

S7 92.48 98.35 98.04

Bold values indicate the best performing feature test

Table 4 Misclassification error analysis of L1, L2, and L7 classifiers

Classifier Error Noise AA DA LM LAD LCX RCA

L1 E1 73.02 8.58 0.00 3.60 1.52 3.46 9.82

E2 1.52 21.60 0.00 27.95 1.54 7.26 8.52

L2 E1 69.64 9.05 0.00 3.94 1.75 5.26 10.36

E2 1.37 21.60 0.00 29.03 1.68 10.46 8.52

L7 E1 70.90 4.49 0.31 6.04 1.70 3.56 13.00

E2 1.31 10.10 0.50 41.93 1.54 6.68 10.08

E1 depicts the % of misclassifications in a particular category of all the misclassifications. E2 depicts the % of the candidate regions

misclassified in a particular category of all the candidate regions in that category

Int J Cardiovasc Imaging

123

E2, was computed as the ratio of the number of

misclassified candidate regions in a particular category

to the total number of candidate regions in that

category. In the negative class, the noise artifacts had

the highest misclassification error percentage (E1),

while the ascending aorta calcifications had the highest

category-wise misclassification error percentage (E2).

Likewise in the positive class, the right coronary artery

calcifications had the highest misclassification error

percentage (E1), while the left main artery calcifica-

tions had the highest category-wise misclassification

error percentage (E2). The two-stage classifier L7

misclassified 50% less aortic calcifications, 4% less

image noise, and 7.5% more coronary calcifications

than the single stage classifier L2.

Discussion

Our results demonstrate the feasibility of an auto-

mated coronary calcium detection system using a

classification-based method. However, the choice of

features and the classification approach have played

an important role toward calcification detection. Our

analysis provides the starting point to automate the

coronary calcium detection process by careful choice

of the features and the classification approach.

Our results suggest that a heart-centered coordi-

nate system provides a compact representation for the

spatial location of the coronary arteries as opposed to

the absolute image coordinate system. However, in

this paper we have used a simple bounding box-based

coordinate system to represent the location of the

calcifications. The currently used coordinate system

is not compact, nor rotation-invariant, nor patient-

invariant. A more compact frame of reference using a

local heart-centered coordinate system, as recently

proposed by our group [20, 21], which is invariant to

translation, scale, and rotation, could further improve

the accuracy of the calcification detection system.

However, development of a patient-invariant coordi-

nate system may require actual segmentation of the

coronary arteries which is a difficult problem owing

to the low resolution, anisotropy, and lack of contrast.

Our experiments show that the texture features are

able to characterize the coronary calcifications well

and the neighborhood region of the coronary calcium

plays an important role in distinguishing the coronary

calcium from the other candidate regions. Using the

combined region—the neighborhood region and the

candidate region—to compute the region-based

texture features significantly improved the sensitivity

of the system over using these regions individually.

Our analysis indicates that the proposed hierarchi-

cal classification approach proves to be effective in

reducing the false positives from the aorta calcifica-

tions and the image noise as compared to the single

stage classifiers. Our method achieved sensitivity of

92.07% at the expense of 4.65 false positives per

scan. Also, the ensemble of multiple classifiers

further reduces the false positives occuring due to

the image noise. Nevertheless, there is high percent-

age of the misclassification errors for the calcifica-

tions in the aorta, left main artery and the right

coronary artery. This is because of the significant

overlap in the relative positions of the ascending

aorta near the origin, the left main artery and the

proximal region of the right coronary artery in

different subjects due to anatomical variations. Fur-

ther investigation is required into the design of

informative features to discriminate between the

ascending aorta calcifications and the coronary cal-

cifications near the ostia.

None of the previous studies have attempted to

explicitly deal with the issues of unbalanced class

priors, and complex class compositions that are the

characteristics of the given problem. Such issues have

been extensively studied in other applications that

have similar requirements. Wu et al. [22] proposed a

hierarchical classification scheme to overcome the

above mentioned asymmetries in face detection

problem. Yan et al. [23] proposed an ensemble of

SVMs for predicting rare classes in scene classifica-

tion. Various techniques for ensemble construction

can be categorized mainly in four categories [24]: (1)

manipulating the feature space, (2) manipulating the

training sets, (3) manipulating the output labels, and

(iv) introducing randomness in the learning process.

We have utilized the advantages of such hierarchical

and ensemble-based techniques in our classification

approach to overcome the issues of asymmetry in the

given problem.

The current cardiovascular risk scoring methods

do not take into account the wealth of information

that is available in the non-contrast CT data. Studies

indicate that pericardial fat may be a significant

cardiovascular risk factor [25]. Other studies have

shown that calcification of the thoracic aorta, aortic

Int J Cardiovasc Imaging

123

arch and aortic valve are associated with increased

risk of cardiovascular disease [26, 27]. Moreover, a

recent study [28] indicated that the spatial distribu-

tions of coronary calcifications plays an important

role in prediction of cardiovascular heart disease and

can be used to improve the current coronary calcium

scoring technique. However, there is a dearth of

automatic techniques to mine the imaging data for

required information. Furthermore, validation in large

epidemiological studies is needed to determine which

type of information will offer additive predictive

value. Our long term goal is to contribute to the

development of quantitative methods to assess cumu-

lative risk of vulnerable patients by developing new

techniques to mine additional information from the

imaging data [29–31]. Toward this goal, we are

developing novel robust computational methods for

segmentation and classification of various anatomical

structures and tissues (e.g., thoracic cavity [32], heart

[33], aorta [34, 35], and fat [36]) from non-contrast

CT data.

Study limitations

Though our study have demonstrated that a classifi-

cation-based method can detect coronary calcifica-

tions with proper selection of the type of features and

classification approach, the findings of this study are

limited with respect to the imaging modality of

EBCT. With the increased use of multi-detector CT

(MDCT) in the routine practice for calcium scoring, it

would be interesting to assess the results of our method

on MDCT scans. Another major limitation of our study

is that the cohort constitutes a higher risk population

(i.e., the patients were physician-referred for CHD risk

stratification). Currently, our method requires the user

to input the start and end slice numbers to define the

extent of the heart in transverse slices. However, we

are developing methods to automate the detection of

the heart extent in the z-axis in order to deploy our

method on a larger cohort.

Conclusion

In this paper, we have presented a classification-

based method to detect the coronary calcifications

from the non-contrast CT scans. We have demon-

strated that a two-stage hierarchical classifier using

multiple classifiers is more robust, in reducing the

false positives keeping a high detection rate than

the single stage classifiers. At the first level of the

hierarchy, the method discriminates between the

arterial (the coronary and the aortic) calcifications

and other highly dense regions present within the

heart region. At the second level, the method

distinguishes the coronary calcifications from the

aortic calcifications without requiring explicit seg-

mentation of the aorta. Our results indicate that the

neighborhood region of the coronary calcium con-

tains significant clues to distinguish them apart from

the other high density structures. Thus, a classifica-

tion-based method has potential to be used in the

calcium scoring softwares to ease the burden of the

observers by reducing the manual interaction required

and eventually, eliminate them completely.

Acknowledgments This work was supported in part by NSF

Grants IIS-0431144 and CNS-0521527.

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