SHAPE FEATURES FOR MASS DIAGNOSIS IN

MAMMOGRAPHIC IMAGES

Ali Cherif Chaabani, Atef Boujelben, Adel Mahfoudhi and Mohamed Abid

CES-Computer, Electronic and Smart Engineering Systems Design Laboratory, National School of Engineers, Sfax, Tunisia

Keywords: Breast Cancer, Mass, Diagnosis, Mammography, CAD, Shape Features, Region Features, Boundary

Features, XRDM, IA.

Abstract: Mammography is the most efficient method for early mass detection and diagnosis. This paper deals with

the problem of shape features extraction in digital mammogram for mass diagnosis. We propose to combine

a region and boundary features in order to ameliorate the diagnosis quality. For boundary analysis we

propose to ameliorate the RDM method by using an extended approach noted XRDM. We also define a new

feature (IA) based on angle calculation. Based on the literature, we exploit a set of region features that are

the most used and the simplest for mass description. For experiments, we use the DDSM database and some

classifiers as Multilayer Perception (MLP) and K-Nearest Neighbours (KNN). Using KNN classifiers, we

obtained 97.1% as sensitivity (percentage of pathological ROIs correctly classified). The results in term of

specificity (percentage of non-pathological ROIs correctly classified) grew around 95.63% using MLP

classifier.

1 INTRODUCTION

The breast cancer is considered one of the major

causes that increases mortality among women. More

specifically, breast cancer is the second most

common type of cancer and the fifth most common

cause of cancer related death (Nishikawa, 2007). To

reduce the high rate of mortality, the screening

mammography via CAD systems (computer-aided

diagnosis (CADi) and computer-aided detection

(CADe)) have been proposed at an early stage.

CADi system is used to identify a suspicious lesion

(masses, calcification…) via segmentation methods,

while CADe system aims at distinguishing

malignant lesions from benign ones via features

extraction.

Breast tumors and masses usually appear in

mammograms with different shape characteristics:

malignant tumors usually have rough,

microlobulated, or speculated contours; whereas

benign masses commonly have smooth, round,

macrolobulated, or oval contours. To separate the

benignant masses from malignant ones, two

techniques are most adopted: shape analysis (Cascio

et al., 2006; Boujelben et al., 2009) and texture

analysis (Oliver et al., 2006; Sheshadri et al., 2006).

Shape Analysis is based upon boundary and

region features. In the boundary analysis, the

majority of researchers applied a method based on

Radial Distance Measure (RDM), angular measure

(Radial Angle (Sheng-Chih et al., 2005) and Tuning

angle (Denise et al., 2008; Rangayyan et al., 2006)),

fractal dimension and Fourier Descriptor. In this

context, Sheng-Chih et al. (2005) used the Radial

Angle defined by the smaller included angle

between the direction of the gradient and the radial

direction of the edge: when the mass tends to be

more round, its Radial Angles tend to be near 180°

and the average of the Radial Angles tends to be

larger. Conversely, a mass with spiculated edge will

have a smaller averaged Radial Angle.

The Turning Angle (or tangent function) is

defined as the tangent to the contour (Rangayyan et

al., 2006). For a contour with concave and convex

portions, the turning angle function begins to

decrease at the beginning of a concave portion, and

keeps on decreasing until the direction of the tangent

to the contour changes at the beginning of the next

convex portion. In their work Rangayyan et al.

(2006) exploit the Turning Angle to derive two

features: Index of Speculation (IS) to measure the

boundary roughness, and Index of Convexity (IC) to

describe boundary convexity. However, the problem

255

Chaabani A., Boujelben A., Mahfoudhi A. and Abid M. (2010).

SHAPE FEATURES FOR MASS DIAGNOSIS IN MAMMOGRAPHIC IMAGES.

In Proceedings of the International Conference on Computer Vision Theory and Applications, pages 255-262

 SciTePress

of this approach lies in the enormous time of

calculation. Moreover, angle measure depends on

affine transformation (rotation).

The fractal dimension may be used to quantify

the complexity of a mass boundary. In first use of

fractal analysis in their approach, Nguyen et al.

(2005) based their work upon 1D signatures of the

2D contours of breast masses via application of the

ruler method. After, Nguyen et al. (2006) employ the

box-counting method in addition to the ruler method

to compute the fractal dimension of the 2D contours

of breast masses as well as their 1D signatures. The

inconvenience of the fractal analysis is that return

values are not normalized. Consequently we risk

having a bad separation between malignant and

benignant cases.

Fourier descriptor is used in many diagnosis

works to characterize the mass boundary.

Rangayyan et al. (1997) use a four-step approach to

derive the feature noted Fourier Fraction (FF):

firstly, they use a complex representation of the

boundary. Secondly, they calculate the boundary

components. After that, the authors proceed to a

normalization of the components. Finally, they

generate a Fourier Fraction (FF) feature. Although

acceptable results found in (Rangayyan et al., 1997;

Shen et al., 1994), the problem of Fourier analysis is

in a high temporal complexity caused by the

complex representation of contour and the

normalization step.

The RDM descriptor is frequently adopted for

mass boundary description (Boujelben et al., 2009;

Alvarenga et al., 2006; Delogu et al, 2008) because

it is the less complex in terms of calculation and

implementation compared to other techniques;

moreover this method is invariant to affine

transformation. From the RDM, the authors extract

many features like Roughness (R), standard

deviation (SDEV), etc. In most of their approach, the

authors combine the RDM descriptor with region

features to ameliorate mass description. In this

context, Alvarenga et al. (2006) had evaluated the

performance and relevance of a set shape features

extract from RDM method and Convex_Hull. In

recent work of Delogu et al. (2008), a set of shape

features extracted from boundary (RDM) and region

(Circularity, Convexity) of mass have been used. Via

these shape features, the authors attempted to

discriminate between malignant and benign masses

by using classification techniques.

Region Analysis is used to describe the

regularity of the mammogram mass. In this context,

simple morphologic features like Circularity (C),

Eccentricity (Exc) are used (Sheng-Chih et al., 2005;

Delogu et al., 2008). Also, most authors benefit of

Convex-Hull to measure the mass convexity. From

Convex-Hull, Alvarenga et al. (2006) used the

Normalized Residual Value (NRV), the Convexity

(CVX) and the morphological-closing ratio

(Mshape). In this work, Alvarenga et al found that

NRV feature gives the best performance in the

description of mass region.

In this paper, we include the approach of shape

analysis in our diagnosis process of mammograms.

The objective of this paper is to evaluate the

combination of feature based on boundary and

region criteria. We evaluate the combination of

features in diagnosis analysis. First, a set of features

based on region is adopted. Second a set of features

based on boundary is adopted. Thirdly, a

combination of region and boundary features is

evaluated.

The rest of this paper is organized as follows:

section 2 describes the proposed block diagram for

mass diagnosis. Section 3 illustrates the adopted

method of shape features. Section 4 presents the

results obtained by the shape descriptor of the

proposed method. Finally, we draw conclusions and

some future issues in section 5.

2 BLOCK DIAGRAM FOR MASS

DIAGNOSIS

The proposed block diagram consists of three stages:

segmentation (identification of Regions Of Interest),

features extraction, and classification (Figure 1).

Figure 1: Block diagram for mass diagnosis.

Region of Interest (ROI) is selected from the

VISAPP 2010 - International Conference on Computer Vision Theory and Applications

256

image by fixing a rectangular box around the

suspicious lesion area. A classical method of

segmentation based on Sobel filter and thresholding

approach is adopted. After the isolation of the ROI,

the extraction of features is adopted in ROI: this is

the stage of diagram in which we are interested in

this paper. After that, a classification part that makes

decision, based on features proposed, is started.

3 SHAPE FEATURES

EXTRACTION

Having completed the mass segmentation, and

before starting the classification process, a set of

features that extracted from the mass region and the

boundary is adopted.

3.1 Region Features

Region Features aims at describe the mammographic

masses by features extracted from the tumour

region. In our method, we exploit three features

indicated as follows: the Circularity (C), the Internal

External Circle (IEC) and the Normalised Residual

Value (NRV).

3.1.1 Circularity (C)

Circularity describes the area which can be circular.

It can be useful in this direction and can give an

indication on the regularity of a given mammogram

mass. This feature is given by the following

equation:

4 PAC





(1)

where: P is the perimeter and A the area of the

segmented mass. The perimeter was measured by

summing the number of pixels on the border of the

mass, and the area was the number of pixels inside

the border.

3.1.2 Internal External Circle (IEC)

This feature can be used to measure the elongation

of shape (Chettaoui et al, 2005). In our work, we

exploited this feature in the description of the mass

region. It is given by the following equation:

where: Inf_Radius represents the largest internal

circle and Sup_Radius represents the smallest

external circle (Figure 2).

For a round mass, the value of IEC is close to 1

since the value of Inf_Radius is very close to the

value of Sup_Radius, whereas for a lengthened mass

the value of IEC becomes close to 0 since the value

of Inf_Radius is far from the value of Sup_Radius.

The advantage of this feature is that it is

invariant to affine transformation and it is adequate

with our work. However, its calculation is slower,

because of the determination of internal and external

circles.

Figure 2: Calculation of IEC feature.

3.1.3 Normalized Residual Value (NRV)

This feature is extracted from the convex-hull by

using the residual region (red region in figure 3

represents the difference between mass region in

black and convex-hull).

Figure 3: Residual region.

Alvarenga et al. (2006) showed that NRV gave

the best performances compared to the

characteristics that can be extracted from the

convex-hull, and which can be useful in the

distinction between the regular and irregular area. It

is given by the following equation:

where: P_CH is the perimeter of the convex-hull

and A_RES is the area of the residual region.

3.2 Boundary Features

In this section, we show how to optimize RDM is

called eXtended RDM (XRDM). We propose a new

RadiusSupRadiusInfIEC __

(2)

)_()_( CHPRESANRV 

(3)

SHAPE FEATURES FOR MASS DIAGNOSIS IN MAMMOGRAPHIC IMAGES

257

feature noted Index of Angle (IA), inspired of the

XRDM method and of the angular calculation. Also,

we benefit of the efficiency of the characteristic of

convexity (CVX) to describe the mass boundary.

3.2.1 Extended Radial Distance Measure

(XRDM)

The RDM descriptor is one of the methods most

used in the analysis of the shape in order to

characterize the mass boundary. It is based on the

euclidian distances d(i) that calculated between the

centroid of the region and all the points in boundary

region (Figure 4(a)):

where: (Xc, Yc) and (Xi,Yi)) are respectively the

coordinates of the centroid C and the boundary pixel

at the i-th location, N is the number of contour

pixels.

All radial distances d(i) are normalized by using

the maximum value (normalised factor) of the radial

distances:

Several features can be extracted from the RDM

method. In our work, the features extracted from the

RDM are cited below:

 The Standard Deviation (SDEV) is defined as the

variance of the distances

 

around the radius

(the average radial distance measure) of a circle.

SDEV permits to give better quality of

information on the irregularity of contour.

Indeed, the value of SDEV feature tends to 0.5

when it is about a malignant tumour. On the

other hand, the value of SDEV tends towards 0 in

the case of benign tumour.

 The Roughness (R) treats the micro-lobulated

contours. It is defined as the average distance

between neighbouring pixels over tumor contour:

 The Area Ration (AR) computes the percentage

of tumor outside the circular region defined by

 

(the average value of

 

). More contour

is irregular, more the value of AR is high. This cha-

racteristic permits to discriminate between the

speculated and smoothed contours:

where: AR=0, if

   

idid



(a)

(b)

Figure 4: Illustration of (a) RDM and (b) XRDM.

However, computation of these features

increases their temporal complexity. To overcome

this problem, we propose to extend RDM method

(Boujelben et al., 2009) by replacing the calculation

of the features: we are interested only in a limited

number of points noted as concave and convex

points (Figure 4(b)). The concave and convex points

are defined as follows:

 The concave point (Pconcave (i)): is a point

which has a radial distance d(i) lower than the

radial distance d(i-1) and lower than the radial

distance d(i+1).

 The convex point (Pconvex (i)): is a point which

has a radial distance d(i) higher than the radial

distance d(i-1) and higher than the radial distance

d(i+1).

   

( ) , 1d i Xi Xc Yi Yc i N     

(4)

     

 

ididid

max

(5)

   

 

NididSDEV





(6)

   





ididNR 1*1

(7)

 

   

 





idid

idN

AR *

(8)

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258

3.2.2 Index Angle (IA)

Basing on XRDM method, we introduce a new

feature in our boundary descriptor noted Index

Angle (IA). This feature is based on concave and

convex points defined in XRDM method and is

defined by the ratio of all the external angles (



)

by internal ones (



): the external is the angle

between a central convex point (Convex point pi)

and their neighbours convexes points (Convex point

pi-1, p+1), however, the internal is the angle

between a central convex point and their neighbours

concaves points (Figure 5).

The IA is applied to make a distinction between

the micro-lobulated boundaries and the round ones:

when the mass tends to be more rounded, its IA

tends to be near the 1. Conversely, a mass with

micro-lobulated edge will have a value of IA smaller

than 0.5.

Figure 5: Calculation of IA feature.

IA feature is used only for the concave and

convex points and not for all points, in order to

minimize the temporal complexity, differently with

features extracted from angle calculation used in

(Rangayyan et al., 2006). On the other hand, the

advantage of this characteristic is that it is

normalized and invariant to any affine

transformation.

3.2.3 Convexity (CVX)

This feature is based on boundary of mass and his

convex-hull (Figure 6). It is defined by the ratio of

perimeter of mass region (P_MR) and perimeter for

his convex-hull (P_CH):

CVX can be used to separate between the

speculated boundaries and the rounded ones: when

the mass tends to be more rounded, its CVX tends to

be near the 1. In the case of speculated mass, the

CVX is smaller than 0.5.

Figure 6: Mass and Convex_Hull boundary.

4 CLASSIFICATION AND TEST

The evaluation criteria used to determine the

performance of a CADi System are defined as

follows:

 Sensitivity: percentage of pathological ROIs

correctly classified.

 Specificity: percentage of non-pathological ROIs

correctly classified.

The parameters used by the evaluation criteria

are summarized in the following table:

Table 1: Parameters used for evaluation.

Case

Classifier

In reality

FP (False Positive)

Malign

Benign

FN (False Negative)

Malign

TP (True Positive)

Benign

Malign

TN (True Negative)

Benign

4.1 Image Data Set

The DDSM (Digital Dataset for Screening

Mammography) is the largest publicly available

database of mammographic data. It contains

approximately 2620 screening mammography cases.

The Digital for Screening Mammography

(DDSM) is the largest publicly available database of

mammographic data (Heath et al., 2001). It contains

approximately 2620 screening mammography cases.

From the total number of images included in the

DDSM database a total of 500 ROIs were used in

this work (table 2). For training step, we used 240







(9)

CHPMRPCVX __

(10)

FNTPTPySensitivit 

(11)

FPTNTNySpecificit 

(12)

SHAPE FEATURES FOR MASS DIAGNOSIS IN MAMMOGRAPHIC IMAGES

259

ROIs (120 benign and 120 malign). For the

evaluation, we used 260 ROIs that contain 130

malign and 130 benign.

Table 2: Distribution of ROIs.

Training

Test

Malign

Benign

Malign

Benign

120

130

4.2 Experimental Results

To measure the performance given by our shape

features, two methods of classification are used: the

first is KNN (K-Nearest Neighbours) and the second

is MLP (Multilayer Perception).

4.2.1 Region Features

Table 3 illustrates the importance of region

information for mass description. As shown in this

table the best result is given by MLP classifier: the

result in terms of sensitivity tends towards 96%

while the result in terms of specificity exceeds 94%.

Table 3: Results from Region Features.

Classifier

KNN

MLP

Sensitivity (%)

95.45

96.70

Specificity (%)

92.96

94.50

Although MLP gives the best result, the

difference with the result given by KNN is not great.

We note that the region features give good results

despite the use of different classifiers. So, we

observe that the characteristics of cregion can be

exploited to differentiate the benign from the malign

mass.

4.2.2 Boundary Features

Table 4 shows the results given by boundary

features for mass description. As in the case of

region features, MLP gives the best result in terms

of sensitivity (97.90%) and specificity (94.20%).

Regarding the results given by boundary features,

we notice a slight optimization over the results given

by region features (table 3).

Table 4: Results from Boundary Features.

Classifier

KNN

MLP

Sensitivity (%)

95.10

97.90

Specificity (%)

93.67

94.20

In fact, the increase in the performance of

boundary features is justified by optimization of

features given by classic RDM as shown at Table 5:

according to the results that found in (Boujelben A.

et al., 2009), we find that XRDM gives the best

sensitivity and specificity for the two classifiers.

Table 5: RDM features vs XRDM features (Boujelben A.

et al., 2009).

RDM Features

Classifier

KNN

MLP

Sensitivity (%)

89.74

86.88

Specificity (%)

85.22

85.43

XRDM Features

Classifier

KNN

MLP

Sensitivity (%)

90.28

88.88

Specificity (%)

89.64

92.82

Subsequently, the inclusion of XRDM in a

feature vector described the contour can improve the

performance of classification of mammographic

masses.

4.2.3 Combinated Features

Table 6 presents the results given by the

combination of features of region and of boundary

ones. The best result in term of sensitivity tends

towards 97.10% in KNN classifier while the best

result in term of specificity tends towards 95.63% in

MLP classifier.

Table 6: Results from features combination (Boundary and

Region).

Classifier

KNN

MLP

Sensitivity (%)

97.10

96.74

Specificity (%)

94.53

95.63

The real contribution of this work lies in the

combination of features that based on region and

those based on the boundary. From Table 6, we

notice that the two classifiers used gave the best

performance: in fact, the combined characteristics

(region and the border) have improved the

specificity of two classifiers compared to results

found previously by only the use of the region or

contour (table 3 and 4). Regarding sensitivity, the

result is increased with the KNN classifier but it is

decreased with the MLP classifier.

Subsequently, the fusion of features improves the

accuracy of distinguishing between malign and

benign ones tumors.

In order to study the effectiveness of the

proposed features, we present in table 7 a

comparison of our found results with those found by

other works. As this table shows, the best results are

VISAPP 2010 - International Conference on Computer Vision Theory and Applications

260

given by our combination of features. But, despite

acceptable results found by our proposed features,

we can not conclude that we have the best results

because we did not use the same database used by

other works. In fact, the digitization can reflect the

final result. Also, the other works use an automatic

system for detection of masses whereas in our work

the task of mass detection is realized of a semi-

automatic manner.

Table 7: Results of comparison.

Approach

Sens

(%)

Spec

(%)

Classifier

Data Set

Alvarenga

et al.

(2006)

90.4

LDA

Local

(125

cases)

Rangayyan

et al.

(1997)

LDA

Local

(32

cases)

Retico et

al. (2007)

78.1

79.1

MLP

Local

(226

cases)

Chang et

al. (2005)

88.89

92.5

SVM

Local

(210

cases)

Our

proposition

97.1

94.53

KNN

DDSM

(500

cases)

96.74

95.63

MLP

However, we can say that the use of our

proposed features in the other works can be

important in the increase of the rate of success of the

distinguishing between the benign and malignant

mass.

5 CONCLUSIONS

Characterization of mammographic mass and its

classification as being benign or malignant is

difficult. In this paper, we have tried to improve the

performance of the mass classification. We have

proposed a shape features that based on the region

features and the boundary ones. The results have

been validated by two algorithms of classification:

KNN and MLP. The found results were acceptable

with a rate of sensitivity and of specificity that

passed 95%.

The shape features can characterize the types of

mammographic masses. Since the signs of

malignancy of breast tumour are related to shape and

texture, shape features are insufficient, by

themselves, for a description of the masses more

effective. For this reason, it is better to add texture

features to our descriptors in order to increase the

accuracy rate for discriminating between benign

masses and malignant ones. In future work, we will

illustrate the effectiveness of the combination of the

texture features and shape ones in the diagnostic

process.

Detection phase is the most difficult step in a

CAD system. For this reason, the future work will be

dedicated to the automation of detection by using of

our approach of mass detection, based on Level Set,

presented in (Boujelben. A. et al, 2009) and using of

our approach of mass description indicated in this

paper.

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