Wavelet-based Feature Analysis for Classification of
Breast Masses from Normal Dense Tissue
Filippos Sakellaropoulos, Spyros Skiadopoulos, Anna Karahaliou,
George Panayiotakis, and Lena Costaridou
Department of Medical Physics, School of Medicine,
University of Patras, 265 00 Patras, Greece
Abstract. Automated detection of masses on mammograms is challenged by
the presence of dense breast parenchyma. The aim of this study was to
investigate the feasibility of using wavelet-based feature analysis for
differentiating masses, of varying sizes, from normal dense tissue on
mammograms. The dataset analyzed consists of 166 regions of interest (ROIs)
containing spiculated masses (60), circumscribed masses (40) and normal dense
tissue (66). A set of ten multiscale features, based on intensity, texture and edge
variations, were extracted from the ROIs subimages provided by the
overcomplete wavelet transform. Logistic regression analysis was employed to
determine the optimal multiscale features for differentiating masses from
normal dense tissue. The classification accuracy in differentiating
circumscribed masses from normal dense tissue is comparable with the
corresponding accuracy in differentiating spiculated masses from normal dense
tissue, achieving areas under the ROC curve 0.895 and 0.875, respectively.
Breast cancer is the most prevalent cancer among women . While screen/film
mammography is currently the primary imaging technique for early detection and
diagnosis of breast cancer, its high diagnostic performance is challenged by occult
disease signs (masses and/or microcalcifications) due to the masking effect of dense
breast parenchyma, often both characterized by quite similar radiographic densities
[2,3]. While microcalcification clusters are indicative of early malignant processes,
masses are the most important signs for detection of invasive breast cancer, with their
extent being a very important prognostic factor. Masses can be described as more or
less compact areas that appear brighter (radiopaque) than the parenchymal tissue. The
major morphological categories of masses are spiculated and circumscribed .
Various features in combination with classification methods have been proposed
for automated mass detection. Kegelmeyer et al.  have introduced edge orientation
features based on local edge orientation histogram analysis as well as Laws’ texture
energy measures to identify spiculated mass containing areas. Chan et al. [6,7]
proposed multiresolution texture analysis extracted from spatial Gray Level
Dependence Matrices (GLDM) for differentiation of masses from normal tissue. Later
on, Liu et al.  extended mass edge orientation analysis with a multiresolution
scheme for the detection of spiculated masses. Linear phase non-separable 2D
wavelet transform (WT) was used to extract features at each resolution on a pixel
basis. Petrick et al  and Kobatake et al.  have utilized a combination of
boundary (morphological) and multiresolution texture features (GLDM analysis) to
identify and segment the extent of masses, respectively. Another approach in
differentiating mass containing areas from normal tissue refers to area patterns
constructed using principal component, independent component and factor analyses
The performance of the proposed mass detection methods is characterized by high
sensitivity (84-96%) and is challenged by the high number of false positive detections
per image (1.0-4.4), especially in case of dense tissue [13,14].
The aim of this study is to investigate discriminant features for mass detection in a
demanding mass dataset. To capture significant information from intensity, texture
and edges of masses of various sizes and to differentiate them from normal dense
tissue, histogram, texture and orientation-based features were extracted from the
coefficients of an overcomplete wavelet transform. Stepwise forward logistic
regression analysis was employed to determine the most discriminating subset of
features in differentiating: (a) spiculated masses from normal dense tissue, (b)
circumscribed masses from normal dense tissue and (c) both types of masses from
normal dense tissue. The performance of the logistic regression models is evaluated
by means of Receiver Operating Characteristic (ROC) analysis.
2 Materials and Methods
2.1 Case Sample
Mammographic images corresponding to extremely dense or heterogeneously dense
(density 3 and 4, according to BIRADS lexicon) originating from the Digital Database
for Screening Mammography (DDSM) of the University of South Florida  were
selected. Images were digitized with Lumisys or Howtek scanner, at 12 bits pixel
depth with spatial resolution of 50 µm and 43.5 µm, respectively. Regions of interest
(ROIs) were selected with an image visualization tool developed in our department
. The sample consists of 166 ROIs, 60 ROIs containing spiculated masses, 40
ROIs containing circumscribed masses and 66 ROIs of normal dense tissue. The mean
size (longest dimension) was 19 mm (range: 7-49 mm) and 12 mm (range: 6-31 mm)
for spiculated and circumscribed masses, respectively. Histogram of mass subtlety
(from 1=subtle to 5=obvious), according to DDSM database, is provided in Figure 1.
Frequency of occurrence
Fig. 1. Histogram of subtlety for spiculated and circumscribed masses of the sample.
2.2 Wavelet Transform
A fast, biorthogonal, Redundant Discrete Wavelet Transform (RDWT), originally
used to derive multiscale edges from signals, is utilized in this work. It is based on a
family of wavelet functions ψ(x) with compact support, which are derivatives of
corresponding Gaussian-like spline functions θ(x). The algorithm is implemented
using a filter bank algorithm, called “algorithm a trous” [17,18], which does not
involve subsampling. The discrete wavelet transform is a uniform sampling of the
wavelet transform series, discretized over the scale parameter s at dyadic scales
(wavelet transform series). [17,18]. The RDWT is calculated up to a coarse dyadic
scale J. Therefore, the original image is decomposed into a multiresolution hierarchy
of subband images, consisting of a coarse approximation image
of wavelet images(
but have disappeared in
number of pixels as the original, thus the representation is highly redundant. The
RDWT computes the multiscale gradient vector. Coefficient subband images are
proportional to the sampled horizontal and vertical components of the multiscale
gradient vector, and thus they are related to local contrast . The magnitude-
orientation representation of the gradient vector, in the discrete case, is given by:
and a set
))n ,m ( fW ),n ,m ( fW
, which provide the details that are
. All subband images have the same
arctan),( , ),(),(),(
2.3 Feature Extraction
The aim was to capture significant information from intensity, texture and edges of
masses for their differentiation from normal dense tissue. Information from intensity,
texture and edges from each ROI, containing spiculated or circumscribed mass, was
extracted by means of histogram, texture and orientation features, respectively.
2.3.1 Histogram-based Features
Significant information from intensity variations was extracted by computing features
based on histogram of low-frequency band (approximation image) for each ROI at
three resolution scales (three to five). These features depend only on individual pixel
values and not on the interaction or co-occurrence of neighboring pixel values. In this
study, four features corresponding to the four moments of each ROI subimage
histogram were calculated: Mean value, Standard Deviation, Skewness and Kurtosis.
2.3.2 Texture-based Features
Laws’ texture energy features have been computed by first applying small
convolution kernels to ROI subimages, and then performing a nonlinear windowing
operation. In this study, the most discriminant set of convolution kernels  were
used: L5*E5, E5*S5, L5*S5 and R5*R5, for texture discrimination between masses
and normal dense tissue.
2.3.3 Orientation-based Features
To capture significant information from mass edges, two multiscale gradient-
orientation features were extracted from each ROI:
Standard Deviation of Gradient-Orientation [5,8]:
where histij is the histogram of gradient orientations θ, calculated from high-frequency
wavelet coefficients (detailed orientation image) for three scales (three to five), within
N(i,j) using 256 orientations (bins). Therefore, histij(n) is the number of pixels in
N(i,j) that have gradient orientations
Standard Deviation of Folded Gradient-Orientation :
) 256/1n2/, 256/n2/(
is the average bin height of histij.
( , )
( , )
N i j
( , )
( , )
( , )
where the folded gradient orientation β (i, j) is defined as:
( , )
if ( , )
( , )
( , )
( , )
if ( , )
( , )
( , ) otherwise
i j KP KN
( , ) 0,( , )m n
( , )N i j
( , )
( , )
( , ) 0,( , ) m n
( , ) N i j
( , )
( , )
are the mean values of positive and negative gradient orientations within N(i,j),
respectively. KP and KN are the number of positive and negative gradient orientations
within N(i,j), respectively.
Fig. 2. Regions of a spiculated mass (B-3390_LCC) (a) and a normal dense tissue (C-
0166_LCC) (b) as well as their gradient orientation histograms respectively (c and d).
Figure 2 provides two regions of mammograms, one with a spiculated mass (fig.
2a) and one with normal tissue (fig. 2b), along with their corresponding normalized
gradient-orientation histograms (fig. 2c, 2d). The directions of spicules of the mass
differ from the directions of normal tissue. Specifically, pixels at normal areas have
gradient orientations pointing to a certain direction range, while pixels at spiculated
masses tend to have gradient orientations distributed in more directions. Therefore,
the standard deviation of gradient orientations in the neighborhood of a mass pixel
will be larger than that in the neighborhood of a normal pixel. As a result, the gradient
orientation histogram is flat near a mass area (fig. 2c), but has a peak in areas
containing normal dense tissue (fig. 2d).
2.4 Mass vs. Normal Tissue Classification
Logistic regression analysis was employed to determine the optimal subset of features
that can differentiate masses from normal dense tissue. Specifically, feature-based
logistic regression model was constructed by means of the forward feature selection
method based on the area under ROC curve (Az) as a feature performance metric. The
feature with the best Az value is first entered in the logistic regression model. The
second feature selected is the one that in conjunction with the first feature yields the
highest Az value among the remaining features. This process continues until no
significant increase in terms of Az value is offered by adding features. After logistic
regression model construction the half-half training and testing methodology was
applied. The performance of the logistic regression model was evaluated in terms of
Az area and standard error.
To study the effect of mass type (spiculated and circumscribed) in classification
accuracy, logistic regression models were constructed for three differentiation tasks:
(a) spiculated masses from normal dense tissue (S-N), (b) circumscribed masses from
normal dense tissue (C-N) and (c) both spiculated and circumscribed masses from
normal dense tissue (B-N).
The ROC curves produced from the feature-based logistic regression models for the
three differentiation tasks are presented in Figure 3. The Az values are 0.895±0.036,
0.875 ±0.033 and 0.813±0.032 for the C-N, S-N and the B-N datasets, respectively.
The differences in Az values between C-N and B-N, as well as between S-N and B-
N are statistically significant (two-tailed student’s t-test, p<0.05), indicating the
reduction in classification accuracy when all masses (spiculated and circumscribed)
are considered in the differentiation task.
Fig. 3. The ROC curves for mass classification in the three differentiation tasks.
4 Discussion and Conclusion
Our preliminary results suggest that histogram, texture and orientation-based features
extracted from the coefficients of an overcomplete wavelet transform in combination
with logistic regression analysis can provide a successful classification scheme for the
detection of spiculated and circumscribed masses in dense parenchyma, as proved by
ROC analysis. The most discriminating features seem to be the Skewness, Standard
Deviation of Gradient-Orientation and Standard Deviation of Folded Gradient-
Orientation. On the other hand, Laws’ texture measures do not possess any significant
information, although they have been used in similar classification tasks .
The performances (Az values) achieved in the mass classification accuracy are
higher than those reported in other studies for dense breast category [13,14]. These
encouraging results are in support of further development of the proposed method into
a fully automated mass detection method. Future efforts will focus on: (a) extraction
of additional features (e.g. coherence, entropy), (b) use of other classification
techniques and (c) validation using a larger dataset.
We would like to thank the European Social Fund (ESF), Operational Program for
Educational and Vocational Training II (EPEAEK II), and particularly the Program
PYTHAGORAS I (B.365.011), for funding the above work.
True Positive Fraction
False Positive Fraction
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