Classification of Mammograms Tumors Using Fourier Analysis

Abstract

Breast cancer is one of the most common cancers among women in the developing countries. It has become a major cause of death. In this work a new algorithm for classifying mammograms by using an evolutionary approach known as signatures-distances from the centroid to all points on the boundary of the region of interest (ROI) as a function of a polar angle θ. The signature of a closed boundary is a periodic function, repeating itself on an angular scale of 2π. Then encode and describe this closed boundary to arbitrary function through 1-D (radial) Fourier expansion coefficients. The method was tested over several images from the image databases taken from Breast Imaging Reporting and Data System BIRADS developed by the American College of Radiology, and from MIAS (Mammogram Image Analysis Society, UK), that provides a standardized classification for mammographic studies. The implementation of the algorithm was carried out using MATLAB codes programming and thus is capable of executing effectively on a simple personal computer with digital mammogram as accumulated data for assessment. In this paper, we describe the formatting guidelines for IJCA Journal Submission.

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IJCSNS International Journal of Computer Science and Network Security, VOL.14 No.2, February 2014
110
Manuscript received February 5, 2014
Manuscript revised February 20, 2014
Classification of Mammograms Tumors Using Fourier
Analysis
Osama R.Shahin and Gamal Attiya,
University of Helwan Egypt, University of Menoufia Egypt
Summary
Breast cancer is one of the most common cancers among
women in the developing countries. It has become a major
cause of death. In this work a new algorithm for classifying
mammograms by using an evolutionary approach known as
signatures- distances from the centroid to all points on the
boundary of the region of interest (ROI) as a function of a
polar angle θ. The signature of a closed boundary is a periodic
function, repeating itself on an angular scale of 2π. Then
encode and describe this closed boundary to arbitrary function
through 1-D (radial) Fourier expansion coefficients. The
method was tested over several images from the image
databases taken from Breast Imaging Reporting and Data
System BIRADS developed by the American College of
Radiology, and from MIAS (Mammogram Image Analysis
Society, UK), that provides a standardized classification for
mammographic studies. The implementation of the algorithm
was carried out using MATLAB codes programming and thus
is capable of executing effectively on a simple personal
computer with digital mammogram as accumulated data for
assessment. In this paper, we describe the formatting
guidelines for IJCA Journal Submission.
Key words:
Microcalcifications, Mass lesions, Signature, Fourier
expansion coefficients.
1. Introduction
Breast cancer is currently the top cancer in women
worldwide, both in the developed and the developing
world. The majority of breast cancer deaths occur in
low- and middle-income countries, where most of the
women are diagnosed in late stages due mainly to lack
of awareness and barriers to access to health services.
7.6 million people worldwide died from cancer in 2008,
Approximately 70% of cancer deaths occur in low- and
middle-income countries [1].Breast cancer has placed
itself on top of the list of health problems for women in
Egypt, representing 35.1% of all female cancer cases,
according to the National Cancer Institute in Cairo [2].
No effective way to prevent the occurrence of breast
cancer exists. Therefore, early detection is the first
crucial step towards treating breast cancer. It plays a key
role in breast cancer diagnosis and treatment. This
process requires the selection of the effective features for
the process of detection and classification. Over recent
years there has been much research into the application
of breast cancer detection and classification with
numerous different features. Many of these involved
geometrical and statistical features with many problems
that associated with these analyses [3, 4]. The
fundamental problems which faced the last approaches
were the dependency of these approaches on the image
translation, scaling and rotation. So the needed of a
robust shape descriptor become the important factor to
solve such problem. The work presented in this paper
was concerned specifically with encoded the boundary of
the tumor by Fourier expansions which are certainly
translation invariant. In our experimental study, we will
use the digital mammogram images that were provided
from online mammogram database (MIAS database) [5].
Firstly, for each image the location for each suspicious
area will be decided and secondly a number of
significant features will be computed. After running the
algorithm, the results that obtained by the proposed
features – coefficients of Fourier expansion-will be
compared with the standard results which depend on the
geometric and texture features that discussed in [3, 4].
The remainder of the paper is organized as follows: we
discuss the main mammographic abnormalities in
section II. The methodology was described in section III.
Experimental results are presented in section IV. Finally,
conclusions are drawn in section V.
2. Mammographic Abnormalities
There are about eight typical kinds of abnormalities
revealed with a conventional mammogram. An
experienced radiologist is highly tuned to the
appearance of abnormalities in breast X-rays, and most
of the time has a pretty good idea whether a suspicious
abnormality is likely to be malignant or not. Typical
mammographic findings from breast cancer screening
mammograms would include asymmetrical breast tissue,
asymmetric density, architectural distortion, mass,
microcalcifications, interval changes compared with
previous films, adenopathy, and other miscellaneous

IJCSNS International Journal of Computer Science and Network Security, VOL.14 No.2, February 2014
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findings. Usually, a mammographic abnormality is
followed by additional imaging studies, such as
ultrasound, and if the lesion still appears suspicious it
may be sent for biopsy [6].
1.1.Characteristics of Mass Lesion
In terms of shape, if it is round, oval, or slightly lobular,
the mass is probably benign. If the mass has a multi-
lobular contour, or an irregular shape, then it is
suggestive of malignancy. 'Margin' refers to the
characteristics of the border of the mass image. When
the margin is circumscribed and well-defined the mass
is probably benign. If the margin is obscured more than
75% by adjacent tissue, it is moderately suspicious of
malignancy. Likewise, there is moderate suspicion if the
margin having many small lobes. If the margin is
indistinct or speculated (consisting of many small
'needle-like' sections) then there is also high suspicion of
malignancy. 'Density' is usually classified as either fatty,
low, or high. The mass is probably benign for fatty and
low densities, moderately suspicious of malignancy for
high densities [7].
1.2 Microcalcifications
Microcalcifications are one of the main ways breast
cancer mammographically detected when it is in the
very early stages. Microcalcifications are actually tiny
specks of mineral deposits (such as calcium) they can be
distributed in various ways. Sometimes
microcalcifications are found scattered throughout the
breast tissue, and they often occur in clusters. Frequently,
microcalcification deposits are due to benign causes.
However, certain features and presentations of
microcalcifications are more likely to be associated with
malignant breast cancer Figure1. Three categories of
calcifications have been identified by the “The American
College of Radiology (ACR) BIRADS” [8]
(a) Typically benign
(b) Intermediate concern
(c) High probability of malignancy
The summary of BIRADS Classification of
Calcifications summarized in Table 1
Fig. 1: Microcalcifications
1.3Mass Lesions
Breast cancer is characterized with the presence of a
mass accompanied or not accompanied by calcifications
[9]. There is a possibility of a cyst, which is non-
cancerous collection of fluid to resemble a mass in the
film. The identical intensities of the masses and the
normal tissue and similar morphology of the masses and
regular breast textures makes it a tedious task to detect
masses in comparison with that of calcifications [10].
The location, size, shape, density, and margins of the
mass are highly beneficial for the radiologist to evaluate
the probability of cancer. A majority of the benign
masses are well circumscribed, compact, and roughly
circular or elliptical whereas the malignant lesions are
characterized by blurred boundaries, irregular
appearances and are occasionally enclosed within a
radiating pattern of linear speckles [11]. Nevertheless
some benign lesions may also possess speculated
appearances or blurred peripheries.
1.4 Roundness
The shape of particles is an important property in
determining their history and behavior [12]. For this
reason it is important to have an objective quantitative
measure of particle shape so that the changes in shape as
well as the differences between the shapes of different
populations can readily be identified. One of the
important methods that used in describing the shape is
roundness. Roundness is a measure of the extent to
which the edges and comers of a particle has been
rounded. A number of authors have proposed methods
using the Fourier transform to determine roundness [13,
14]. The basic method is to obtain coordinates on the
edge of the profile of the fragment being measured also
the centre point is determined, and all the edge
coordinates converted to polar coordinates using the
centre point as origin. The Fourier expansion
coefficients of the vector of radii (r (θ)) are then
calculated and the roundness determined from these
coefficients.

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3. Methodology
The automatic massive lesions classification algorithm
can be summarized in the following points:
a- Detect the region of interests (ROIs): These
regions can be easily detected in an image if the
area has sufficient contrast from the
background. In this phase, the algorithm in
[15] was applied. Once the Region of Interest
(ROI) is automatically extracted, A Sobel filter
was applied on the image to detect the edges of
the region of interest (ROI). The ROI is the
tumor of the digital mammogram and the goal
is to isolate this area from the image. A dilation
operation was performed after filtering to
connect edges. Dilation was followed by filling
the remaining holes of the ROI.
Table 1. .Summary of BIRADS Classification of
Calcifications [8]
Type of
calcification
Characteristics
Typically
benign
Skin
Typical polygonal
shape.
Vascular
Parallel tracks or
linear tubular.
Coarse or pop-
corn like
Involving fibro
adenomas.
Rod-shaped
Large rod usually
> 1mm.
Round
Smooth, round
clusters.
Punctuate
Round or oval
calcifications.
Spherical or
lucent centered
Found in debris
collected in ducts,
or necrosis areas.
Rim or egg-shell
Found in wall of
cysts.
Milk or calcium
Calcium
precipitates.
Dystrophic
usually large >
0.5mm in size
Intermediat
e concern Indistinct or
amorphous
Appear round and
hazy uncertain
morphology
High risk
Pleomorphic or
heterogenous
irregular in shape,
size and < 0.5mm
raises suspicion
Fine, linear or
branching
Thin, irregular
that appear linear
from a Distance
b- Determine the centroid for any (ROI).
c- Boundary Signature: Calculate the distances
from the centroid to the all points on the
boundary of the region of interest (ROI) as a
function of a polar angle θ. A signature is the
representation of a 2-D boundary as a 1-D
function. The signature of a closed boundary is
a periodic function, repeating itself on an
angular scale of 2π. Such distance called Radial
Distance (RD), see Figure 2.
d- Evaluation of Fourier Expansion: Encode this
closed boundary by an arbitrary function
through 1-D (radial) Fourier expansion
coefficients. One simple and neat way to
encode and describe a closed boundary to
arbitrary and accuracy is through a 1-D (radial)
Fourier expansion.
Fig. 2: Radial Distance Measure (RDM)
The signature can be expressed in real or complex form
as follows:
(1)
∑∑
∞
=
∞
=
θ
+θ+
=θ
11
0
2
nn
nn
)nsin(b)ncos(a
a
)(r
(2)
)in(
nneC)(r θ
∞
−∞=
∑
=θ
The shape can be parametrically encoded by the real
Fourier expansion coefficients
{ }
nn
b,a
or by the
complex coefficients
{ }
n
C
.These coefficients can easily
be calculated through use of the orthogonality relations
for Fourier series [14] . The real coefficients for a radial
signature are given by:
(3)
θθθ
π
=
∫
π
π−
d)ncos()(ran1

IJCSNS International Journal of Computer Science and Network Security, VOL.14 No.2, February 2014
113
(4)
θθθ
π
=
∫
π
π−
d)nsin()(rb
n
1
Whereas the complex coefficient
{ }
n
C
is given by:
(5)
θ
θ
π
=
θ−
π
π−
∫de)(rC
)in(
n
2
1
Typically, a good approximation to the shape can be
encoded using a relatively small number of parameters,
and more terms can be included if higher accuracy is
required. The use of radial Fourier expansions can,
however, become problematic on complicated boundary
shapes, particularly those in which the boundary
‘meanders back’ on itself .The signature function r(θ)
may not be single valued, there being two or more
possible radial values for a given value of θ. In such
cases, the choice of which value of r(θ) to select is
somewhat arbitrary and the importance of these
unavoidable ambiguities will depend on the specific
application. In general, however, strongly meandering
boundaries. The Fourier descriptors calculated according
to Equations [3-5] are certainly translation invariant.
This follows because the radial distance in the signature
is calculated with respect to an origin defined by the
centroid coordinates of the boundary. Multiplication of
the signature by an arbitrary scale factor is reflected in
the same scale factor multiplying each of the individual
Fourier coefficients. A form of scale invariance can thus
be achieved most simply by dividing the signature by its
maximum value (thus fixing its maximum value as one).
The extraction features that can be calculated from the
last two steps are:
Number of zero crossing: the mean value of the radial
distances r(θ) can be taken as a reference axis , so it is
easy to find the number of points which the r(θ) passing
through this axis.
The Fourier expansion coefficient
{ }
nn
b,a
also used as
important feature because these values increased with
the complexity of the boundary (signature) and
conversely.
Find the mean value and the variance for the first 200
Fourier expansions, Where:
(6)
∑
=
=
=
m
1n nnn
a
m
1
)a()a(mean
µ
(7)
∑
=
==
m
1n nnn
b
m
1
)b()b(mean
µ
(8)
2
n
m
1n nn ))a(a(
1m1
)a(iancevar
µ
−
−
=
∑
=
(9)
2
n
m
1n nn
))b(b
(
1m1
)b(iancevar
µ
−
−
=
∑
=
Classify the massive lesion according to the values of
last extraction features that obtained in the previous step.
A flowchart of the whole algorithm for the breast masses
classification is shown in Figure3
4. Results
The method suggested for the detection of micro-
calcifications and mass lesions from mammogram
images was described above. The mammograms of our
study were analyzed to detect possible clusters of micro-
calcifications and mass lesions taken from MIAS
(Mammogram Image Analysis Society, UK), and
BIRADS databases. Figure4 shows an example of an
original image containing a mass lesion, and the results
of the classification procedure. Figures [5] show these
resulted signatures. Table 2 shows the feature values
that described above. The value of each feature at its
corresponding image is also illustrated. The results
show high classification rate. The summarizes of the
features range was depicted in Table 3, thus the feature-
set formed is well suited for any CAD system. Also these
features have an additional advantage of involving less
computational complexity, translation invariant. This
follows because the radial distance in the signature was

IJCSNS International Journal of Computer Science and Network Security, VOL.14 No.2, February 2014
114
calculated with respect to an origin defined by the
centroid coordinates of the boundary. This can prove
helpful in increasing efficiency of any CAD system. To
check the validity of these features we compare it by the
geometrical and statistical features for the same images
were calculated in Tables [4, 5] for predefined size. The
value of each features in geometric and statistical not
enough to discriminate between the different types of
masses conversely for the proposed features.

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(a)
(b)
(c)
Fig.4: (a) Mammographic ROI , (b) Boundary of ROI,
(c) Signature pattern.
5. Conclusion
As a preliminary investigation toward the
implementation of a complete CAD system for the early
detection of breast cancer, in this paper we present an
algorithm for the classification and features extraction of
microcalcifications. The fundamental problems which
faced the geometric and statistical features were the
dependency on the image translation, scaling and
rotation. So the needed of a robust shape descriptor
become the important factor to solve such problem, that
solved by using Fourier expansion coefficients which are
certainly translation invariant.
6. References
[1] World health organization, http://www.who.int/cancer/en.
[2] National Cancer Institute in Cairo,
http://www.nci.edu.eg/
[3] Hala Al-Shamlan and Ali El-Zaart, “Feature Extraction
Values for Breast Cancer Mammography Images”,
International Conference on Bioinformatics and
Biomedical Technology 2010.
[4] D. C. Hope E. Munday S. L. Smith., “ Evolutionary
Algorithms in the Classification of Mammograms”,
Proceedings of the 2007 IEEE Symposium on
Computational Intelligence in Image and Signal
Processing (CIISP 2007)
[5] MAIS database, http:// peipa.essex.ac.uk/info/mias.html
[Accessed: September 3, 2011].
[6] Bijay Ketan Panigrahi Assistant, Manas Ranjan “Feature
Extraction for Classification of Micro-calcifications and
Mass Lesions in Mammograms”, IJCSNS International
Journal of Computer Science and Network Security,
VOL.9 No.5, May 2009 255 Manuscript
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