Feature extraction of the lesion in mammogram images … · segmentation by minimizing the energy and orthogonal transformation adaptive ... ENSA,University of ibn Zohr ... We analyse

Feature extraction of the lesion in mammogram images usingsegmentation by minimizing the energy and orthogonal

transformation adaptive

Khalid El Fahssi1, Abdelali Elmoufidi1, Abdenbi Abenaou2,Said Jai-Andaloussi1 ,Abderrahim Sekkaki11 Computer Sciences Department, Faculty of Sciences, University of Hassan II

Casablanca, Morocco2 Computer Sciences Department, ENSA,University of ibn Zohr

Agadir, [email protected], [email protected], [email protected]

[email protected], [email protected]

Abstract: Segmentation and classification of breast masses in mammography play a crucial role in Computer AidedDiagnosis system (CAD) . In this paper we propose an approach consisting of two methods. The first is the mainstage in image processing which is the mammograms segmentation. This method is based on the theory of alllevels and minimization of the energy of the active contour which enables the selection of regions of interest of themammograms images. While the second method is based on the theory of adaptive orthogonal transformation thatwill calculate the informative characteristics of regions of interest of mammography images. The characteristicsobtained by this computing method allow the increase of the diagnostic certainty. To illustrate the effectiveness ofthe method we present the results of experiments carried out on the basis of images MIAS mammograms.

Key–Words:segmentation; mammography; active contours; levels set;classification

1 Introduction

Breast cancer is the second cause of death amongwomen in the world [1], [2], [3]. Prevention of thedisease is very difficult because the risk factors are ei-ther poorly understood or not influenced. Scientificstudies have provided insight into the development ofcancer, but it is not yet clear why such a person de-velops breast cancer. It should be noted that only 5-10% of breast cancers are hereditary origin relatedto the transmission of deleterious genes most com-monly implicated are BRCA1 and BRCA2 (acronymsfor breast cancer) associated with a predisposition tothe disease[4]. Due to its delayed diagnosis, that oftenresults into a heavy treatment, mutilating and costlywhich is accompanied by a high mortality rate. Vari-ous studies have confirmed that this is the early stagedetection which can improve the prognosis and mam-mography in this case it is the best diagnostic tech-nique [5]. However, it remains difficult for expertradiologists to provide a good interpretation of shotsmammography due to low differences in densities ofvarious tissues of the breast in the image. The in-terpretation of mammograms by radiologists is per-

formed in the aim of finding the anomalies that in-dicate the changes associated with cancer. The in-dicators of probable presence of cancer are the mi-crocalcifications and the opacities [6]. We analysethe mammography for the purpose of finding theseindicators to characterize and classify Benign typeand malignant, thus the importance of tools of aid todiagnostic (CAD) developed during these last years[7],[8]. Generally, CAD systems of aid to diagnosticbased on a range of approaches including the steps ofpre-processing, segmentation, extraction of classifica-tion parameters (size, shape, density and grouping inhearth) and finally the classification of anomalies sus-pect [7], [8], [9],[10],[11] and [12]. As general thesegmentation of image mammography is a very im-portant step in solving the problem of detecting breastcancer. Currently there are many different methodsof segmentation, which are: the segmentation basedon regions [13], [14], [15], the segmentation based oncontours [16], [13], [18] and the segmentation withthresholding [19], [20], [21]. The analysis of these di-versity methods allows concluding that the applicationof such a method or another can influence on rates ofcertainty of diagnostic. Given the low contrast and the

WSEAS TRANSACTIONS on BIOLOGY and BIOMEDICINEKhalid El Fahssi, Abdelali Elmoufidi, Abdenbi Abenaou, Said Jai-Andaloussi, Abderrahim Sekkaki

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highly textured nature of the images mammography,all segmentation methods proposed depend on the val-ues of selected parameters (thresholds, mean values,variances, etc..) And the models exploited by thesemethods (probability of density, function of belong-ing ...). Therefore, a low error of estimation of theseparameters or these models can lead to segmentationresults of poor qualities in terms of error rate at thepixel level. This bad estimation may also jeopardizethe detection of small parts contained in the mammog-raphy images. So, this opens in a path to propose an-other method that can lead to a correct interpretation.In this article we propose a method for segmentationthe image mammography based on theory of Level Setand the principle of the minimization of the energy ofactive contours.

This paper is organized as follows: Section 2.1describes the database used for evaluation, section 2.2we give a reminder on the theory of level sets, section2.3 and section 2.4 present the formulation of problemand method proposed for minimizing the energy forthe segmentation of mammography image.Section 2.5present the segmentation algorithm and we proposedin section 3 method for classification and detection ofthe lesion. The result is presented in section 4 and weend with a conclusion and perspective in section 5.

2 Materials and Method2.1 DatabaseThe mini-MIAS [22] database contains a total of data322 MLO view mammography images. This databaseis divided into categories such margin: speculated, cir-cumscribed or poorly defined. The images have a res-olution of 1024 1024 pixels. From this data set, a totalof 111 lesions was selected. These include 60 benignand 51 malignant masses. An example of a series ofthe image is given by Figure 1.

Figure 1: Example of mammography study.

2.2 Level Set TheoryA level set is a vital category of deformable models.Level set theory, a formulation to implement active

contours was proposed by Osher and Sethian [23].They represent a contour implicitly via two dimen-sional Lipchitz continuous function ϕ(x, y) : Ω→ R,defined in the image plane. The function ϕ(x, y) iscalled level set function, and a particular level, usu-ally the zero level of ϕ(x, y) is defined as the contour,such as

C = (x, y) : ϕ(x, y) = 0,∀(x, y) ∈ Ω (1)

Figure 2: Level set evolution and the correspondingcontour propagation: (a) Topological view of levelsets ϕ(x, y) evolution (b) the changes on the zero levelsets

Fig.2 (a) shows the evolution of level set func-tion ϕ(x, y) and Fig.2 (b) shows the propagation ofthe corresponding contour C . As the level set func-tion ϕ(x, y) increases from its initial stage, the cor-responding set of contours C, propagate towards out-side. With this definition, the evolution of the con-tour is equivalent to the evolution of the level set func-tion,i.e. ∂C

∂t = ∂ϕ(x,y)∂t the advantage of using the zero

level set is that a contour can be defined as the borderbetween positive and negative areas, so the contourscan be identified by just checking the sign of ϕ(x, y)the initial level set function ϕ0(x, y) : Ω→ R may beprovided by the signed distance from the initial con-tour such as

ϕ(x, y) = ϕ(x, y) : t = 0 = ±D((x, y), Nxy(C0))(2)

Where ±D(a, b) denotes a signed distance between aand b, and Nxy(C0) denotes the nearest neighboringpixel on initial contours C0 = C (t = 0) from (x, y)as a pixel (x, y) is located further inwards from theinitial contours C0. The initial level set function iszero at the initial contour points given by ϕ0(x, y) =0,∀(x, y) ∈ 0.

The deformation of the contour is generally rep-resented in a numerical form as a partial differential


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equation. A formulation of contour evolution usingthe magnitude of the gradient of ϕ(x, y) was initiallyproposed by Osher and Sethian [24] and is given by:

∂ϕ(x, y)

∂t= |∇ϕ(x, y)| = (ϑ+ εk(ϕ(x, y))) (3)

Where ϑ denotes a constant speed term to push orpull the contour,k denotes the mean curvature of thelevel set function ϕ(x, y) and ε controls the balancebetween the regularity and robustness of the contourevolution.

2.3 Image Model and Problem FormulationTo cope with intensity inhomogeneity in image seg-mentation, we formulate our method based on an im-age model which describes the composition of im-ages of the real-world, in which inhomogeneity of in-tensity is assigned to a component of an image. Inthis paper, we consider the following inhomogene-ity intensity multiplicative model. From the physicsof imaging in a variety of modalities (Mammographyimages), an observed image can be modeled as

I = bJ + n (4)

Where J is the true image, b is the component thataccounts for the intensity inhomogeneity, and n is ad-ditive noise. The component b is designated as a biasfield (or shading image). The real image J measuresan intrinsic physical property of the objects to be im-aged, which is therefore assumed to be piecewise (ap-proximately) constant. The bias field b is assumed tobe slowly varying. The additive noise n can be con-sidered to be zero-mean Gaussian noise.

In this paper, we consider the image I : Ω →R as defined on a continuous domain function. Theassumptions about the true image and the bias fieldcan be stated more precisely as follows:

• b Bias field varies slowly, which means that b canbe well approximated by a constant in a neigh-borhood of each point in the image domain. (a1)

• The real image J approximately takes about Ndistinct values constant C1, C2, ..., CN in disjointregions Ω1....ΩN respectively, where ΩiNi=1forms a partition of the image domain, i.e Ω =⋃Ni=1 Ωi and Ωi

⋂Ωj = ∅ for i 6= j.(a2)

Based on the model in (4) and the assumptionsa1 and a2, we suggest a method for estimating re-gions ΩiNi=1, the constants CiNi=1, and the bias

field b. The resulting estimates of them are appointedby ΩiNi=1, the constants CiNi=1, and the bias fieldb, respectively. The obtained bias field b should beslowly varying and the regions Ω1...ΩN should sat-isfy certain regularity property to avoid spurious seg-mentation results caused by image noise. We will de-fine a criterion for the search of this estimates basedon the model and assumptions of the above image a1and a2. This criterion will be defined in terms of theregion, constants, and function, as energy in a varia-tional framework, which is minimized to find the op-timal regions ΩiNi=1 , constants CiNi=1, and biasfield b. Consequently, the image segmentation andbias field estimation are simultaneously achieved.

2.4 Energy FormulationLet Ω be the image domain, and I : Ω → R be agray level image. In [25], a segmentation of the im-age I is carried out by finding a contour C, which di-vides the area of the image domain into disjoint re-gions Ωi...ΩN , and a piecewise smooth function u thatapproximates the image I and is smooth within eachregion Ωi. This can be formulated as a problem ofminimizing the following Mumford-Shah functional

FMS(u, C) =

∫Ω

(I − u)2dx+ u

∫Ω/C∇u2dx+ ϑ|C|

(5)Where |C| is the length of the contour C.In the rightpart of (5), the first term is the term data, which re-quires u to be close to the image I , and the secondterm is the term of smoothness, which causes it to besmooth in each of the regions separated by the con-tour C. The third term is introduced to regularize thecontour C.

To be written in a continuously the local inten-sity property combination indicates that the intensitiesin the neighborhood oy can be classified into N clus-ters, with centers mi

∼= b(y)Ci, i = 1...N , this allowsto apply the K-means clustering standard to classifythese local intensities.More specifically, the intensi-ties I(x) in the neighborhood oy, the K-means algo-rithm is an iterative process to minimize the clusteringcriterion [26], which can form as

Fy =

N∑i=1

∫oy

|I(x)−mi|2ui(x)dx (6)

We can rewrite as

Fy =

N∑i=1

∫Ωi

⋂Ωy

|I(x)−mi|2dx (7)


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Therefore, we define the energy

ε ,∫εydy (8)

i.e

ε =

∫(

N∑i=0

∫Ωi

k(y − x)|I(x)− b(y)Ci|2dx)dy (9)

In this paper, omit the domain Ω in the index in-tegral symbol (as in the first integral above) if the in-tegration is over the entire domain Ω the mammogra-phy Image segmentation by minimizing energy withrespect to the region Ωi...ΩN , constants Ci...CN andbias field b. The kernel functionK is chosen as a trun-cated Gaussian function defined by

K(u) = 1ae−|u|22σ

0,otherwise (10)

Where a is a normalization constant such that∫K(u) = 1, σ is the standard deviation (or the scale

parameter) of the Gaussian function.Our suggested energy in (9) is expressed in terms

of the regions Ω1...ΩN . It is difficult to draw a so-lution to the energy minimization problem from thisexpression. In this section, the energy ε is convertedto a level set formulation by representing the disjointregions Ω1...ΩN with a number of level set functions,with a regularization term on these level set functions.In the level set formulation, the energy minimizationcan be solved by using well-established variationalmethods [27].

Note that for a given C, there is more than onepossible level set representation: if ϕ is a level setfunction for Ω. ϕ Can only represent two regions, in-side and outside the contour C, as Ω1 = inside(C) =ϕ > 0 and Ω2 = outside(C) = ϕ < 0, re-spectively. In this case, a level set function is usedto represent the two regions Ω1 and Ω2. The regionsΩ1 and Ω2 can be represented with their membershipfunctions defined by

TwoPhaseM1(ϕ)=H(ϕ)M2(ϕ)=1−H(ϕ) (11)

Where H(•) is the Heaviside functional, ϕ representsthe set of the level set functions such that ϕ = ϕ forthe Two-Phase model and ϕ = ϕ1, ϕ2 for the Four-Phase model.

FourPhase

M1(ϕ) = H(ϕ1)H(ϕ2)M2(ϕ) = H(ϕ1)(1−H(ϕ2))M3(ϕ) = (1−H(ϕ1))H(ϕ2)M4(ϕ) = (1−H(ϕ1))(1−H(ϕ2))

(12)Where

H(ϕ) = [1

2[1 +

2

πarctan(

ϕ

ε)]] (13)

Thus, for the case of N ≥ 2, the energy in (9) canbe re-written as:

ε ,∫

(

N∑i=0

k(y−x)|I(x)− b(y)Ci|2Mi(ϕ(x))dx)dy

(14)

2.5 Algorithm of segmentation

Enter :I Initial Imageµ Regularization parameter4t the Pas in timeγ Proportionality constantIterNum Number of iterationsυ speed constantInitialisation :

ϕ0 =

+1 where (x, y) is inside C,−1 where (x, y) is outside C.

estimate :For n ranging from 1 to IterNum do. - Calculate the contour carte by Algorithm ofCanny. - Calculate the gradient carte ϕ(x, y)

. ϕ(x, y) =√∑

s∈ηs |Ip − Is|2

. - Calculate the gradient g

. For i ranging from 1 to nl do

. For j ranging from 1 to nc do

. g(ϕ(x, y)) = 11+ϕ(x,y)

. - Calculate the mean curvature term K

. For i ranging from 1 to nl do

. For j ranging from 1 to nc do

. K(i, j) = div( ∇ϕ(i,j)|∇ϕ(i,j)|)

. - Calculate ϕn+1(i, j)

ϕn+1i,j = ϕni,j

+ 4 t[−γδε(ϕ)(c1 − c2)

(I(ϕ)− c1+c2

2

)


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+ µ(4ϕ− div

(∇ϕ|∇ϕ|

))+ υδε(ϕ)div

(g. ∇ϕ|∇ϕ|

)]. -end.

wherec1 = Kσ∗[Hε(ϕ)I]

Kε∗Hε(ϕ)

andc2 = Kσ∗I−Kσ∗[Hε(ϕ)I]

Kσ∗1−Kσ∗Hε(ϕ)

(1 is a function with a constant value of 1).

Hε(ϕ) is the Heaviside function.σε is the Dirac function smoothed given by

σε(ϕ) = H ′(ϕ) =

[1

2[1 +

2

πarctan(

ϕ

ε)]

]′=

1

π.

ε

ε2 + ϕ2

3 The Proposed Method for Classifi-cation

The first part of the approach proposed in this arti-cle has allowed the segmentation and selection of re-gions of interest of mammography images of varioustypes of disease. The classification of mammogramsdepending on the type of disease images requires theextraction of the most relevant features in these re-gions of interest [28],[11].

the calculation of characteristics vectors informa-tive regions is ensured by the use of an adaptableorthogonal transformation [29]for each class regions(type of disease). The spectrum of informative char-acteristics of a given area (class) obtained decreasesrapidly. In other words, the analysis of the spectraobtained allows a considerable difference between theclasses of regions. This property will subsequentlydevelop a simple decision rule which ensured a highcertainty of classification.

The principle of the proposed method is to syn-thesize an adaptable operator orthogonal transforma-tion to generate functions of bases parameterizable.Using these transformations [29],[30] is favored bythe ability to adapt to the shape of their basic functionsdepending on the nature of the standard vector formedby mammograms each class images. In other words,for each type of disease a system of basis functions areassociated parameterizable for showing his images. Inaddition, these functions of base parameterizable meetthe criteria for completeness of the system ensuringthe transformation of vectors without loss of informa-tion content. The system of basis functions formed is

expressed as a factorisable orthonormal matrix oper-ator, which therefore allows a transformation with afast calculation algorithm:

Y =1

NHX (15)

where:- X = [x1, x2, ..., xN ]T is the vector representing theregion of interest in the segmented image mammogra-phy given initial vector transform (of size N = 2n).- Y = [y1, y2, ..., yN ]T is the vector of informationalcharacteristics calculated by the spectral operator or-thogonal H of dimension N x N.Factorization of Good [31] showed a possibility ofrepresenting the matrix operatorH as productGi (16)Sparse matrix with a higher proportion of zero whichhas allowed the construction the quick transformationalgorithms of Fourier , Haar and Walsh. The matricesGi(i = 1, ..., n) are constructed by blocks of matri-ces Vi,j of minimum dimension that is called spectralnuclei [29]:

With

Hence equation (15) can be written as follows:

Y =1

NHX =

1

NG1G2....GNX =

1

NΠNi=1Gi (17)

By defining the parametersϕi,j and θi,j can train oper-ators orthogonal of transformations with basic func-tions complex , and θi,j = 0 operators with real func-tions. Adapting Operator H in (15) is provided by thecondition:

1

NHaZsd = Yc = [Yc,1, 0, 0, ..., 0], Yc,1 6= 0 (18)


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where:- Yc is the target that builds the basis for adjusting thevector operator Ha.- Zsd represents the calculated by means of the esti-mates of the statistical characteristics of images of agiven class standard vector.- Ha is adaptable to synthesize operator.Synthesis adaptable operator Ha based standard Zsd(for a given class) is to calculate the angular parame-ters ϕi,j matrices Gi according to condition (18). Theprocedure for calculation of the parameters is basedon an iterative algorithm to calculate the target vectorYc by step according to the equation:

Yi = GiY(i−1) (19)

The final calculation of the vector Yc allows obtainingadaptable operator Ha.

4 Results and DiscussionThis section presents the results of experimentsperformed on 111 selected mammography databasemini-MIAS images. To evaluate the effectivenessof the proposed method, we used the informationprovided by the Mammographic Image AnalysisSociety database (MIAS) including the class ofanomalous images and coordinates of their centers ofregions of interest. To test our method, the algorithmof segmentation is applied to each image containinga mass lesion, then verified if the algorithm detectsa region of interest containing the abnormally andsegment the mass, finally calculates the percentage ofabnormally detection on all cases. The example forresult of segmantation is presented a figure 3.

Figure 3: (a) The original image with Calcificationbenign. (b) Detection the region of interest (containsthe abnormally) (c) The original image with Calcifi-cation malignant. (d) Detection the region of interest(contains the abnormally)

The result of experiment carried on the 111mammogram image to detect the region of interestthat contains the disease and segment the mass givesthe percentage of precision equal to 92.27%.

To illustrate the effectiveness of the proposedmethod of calculate the informative characteristics ofregions of interest of mammography images, Figure4 shows the result of an experiment at diagnosis oftwo types of mammograms Image ’malignant’ and’benign’.

Figure 4: (a) Spectre of projection the regions of inter-est with Calcification benign in new base. (b) Spectreof projection the regions of interest with Calcificationmalignant in new base.

Figure 4 reflects a considerable distinction of vec-tors informative characteristics of regions in different


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classes mammography images (benign, malignant) .The projection vectors of the regions of interest intheir system basic function provides adaptable vec-tors informative features that converge quickly to thestandard vector class. While the projection regions ofother classes results in obtaining wider spectra char-acteristics sufficiently distinguished and compared toother classes (other types of diseases ). The results ob-tained by the developed method, illustrated in Figure4 indicate its effectiveness and show that it ensures ahigh distinction that will help to make the classifica-tion of mammograms image using a decision makingor calculates similarity.

5 Conclusion and Perspective

In this work we presented an approach consisting oftwo methods.The first is segmentation of masses indigital mammograms, this approach consists of threemain stages which are the (ROI) detection, edge ex-traction and mass segmentation. The experimenta-tion gives a percentage of 92.27% for all cases stud-ied. The second method consisting to calculate theinformative characteristics of regions of interest ofmammography images. The results of the algorithmcan contribute to solving the main problem in mam-mography image processing such as diagnostic andclassification. The efficiency of the proposed methodconfirms the possibility of its use in improving thecomputer-aided diagnosis.

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Feature extraction of the lesion in mammogram images … · segmentation by minimizing the energy and orthogonal transformation adaptive ... ENSA,University of ibn Zohr ... We analyse

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