BREAST MASS DETECTION USING BILATERAL FILTER

AND MEAN SHIFT BASED CLUSTERING

Farhang Sahba and Anastasios Venetsanopoulos

Department of Electrical and Computer Engineering, Ryerson University, Toronto, Canada

Keywords:

Mammography images, Mass detection, Mass segmentation, Bilateral ﬁlter, Mean shift, Computer-aided de-

tection.

Abstract:

This paper presents a new method for mass detection and segmentation in mammography images. The ex-

traction of the breast border is the ﬁrst step. A bilateral ﬁlter is then applied to the breast area to smooth

the image while preserving the edges. Image pixels are subsequently clustered using an adaptive mean shift

scheme that employs intensity information to extract a set of high density points in the feature space. Due to its

non-parametric nature, adaptive mean shift algorithm can work effectively with non-convex regions resulting

in suitable candidates for a reliable segmentation. The clustering is then followed by further stages involving

mode fusion. An artiﬁcial neural network is also used to remove the false detected regions and recognize the

real masses. The proposed method has been validated on standard database. The results show that this method

detects and segments masses in mammography images effectively, making it useful for breast cancer detection

systems.

1 INTRODUCTION

Breast cancer is one of the leading causes of cancer-

related deaths in women (Horner et al., 2009). There

is considerable evidence that early detection and treat-

ment of suspicious lesions is crucial for the prognosis

of the patient as well as signiﬁcantly increasing the

chance of survival. Mammography is proven to be

one of the most reliable methods for early detection

of breast cancer. However, mammography images are

among the most difﬁcult medical images to interpret

because the features that indicate disease are typically

very small and there is a wide range of anatomical

patterns that can occur. Furthermore, each individual

scan is also prone to interpretation error (reported to

be as high as around 30%) and visual analysis of ra-

diographic images is subjective (Lee, 2007; Berman,

2007). While one expert may identify a particular

lesion as a candidate for more investigation, another

radiologist may rate the same lesion as insigniﬁcant.

Consequently, some lesions are missed or misinter-

preted. Therefore, there is a growing interest in in-

corporating automated techniques, such as computer-

aided detection systems, to act as a “second look”

and analyze these images (Morton et al., 2006). To

this aim, over the past few years, different approaches

have been proposed that help radiologists in the detec-

tion of breast lesions in mammography images

(Cheng et al., 2006). An important category of these

approaches is based on statistical parametric models.

These models implicitly assume cluster convexity in

the feature space. A powerful alternative to these

models is to apply an unsupervised non-parametric

approach. Mean shift algorithm proves to be one of

the best of such approaches. In recent years, mean-

shift algorithm has been introduced and successfully

used to develop some techniques in image processing

tasks (Comaniciu and Meer, 2002; Jimenez-Alaniz

et al., 2006; Mayer and Greenspan, 2009). It is a non-

parametric feature-space clustering technique which

does not require prior knowledge of the cluster num-

bers, while also not restricting the shape of the clus-

ters. In this paper, we present a new method employ-

ing this technique to detect and segment breast masses

in a reliable manner. We have used mean shift algo-

rithm due to its ability to work successfully with non-

convex regions as well as its noise smoothing behav-

ior, which results in appropriate candidates for seg-

mentation. The proposed method is relatively easy

to implement with adaptivity with respect to the im-

age characteristics. Experimental results prove our

method to be both effective and efﬁcient and hence

of potential for such an application. The paper is or-

ganized as follows. The mean shift algorithm is de-

Sahba F. and Venetsanopoulos A. (2010).

BREAST MASS DETECTION USING BILATERAL FILTER AND MEAN SHIFT BASED CLUSTERING.

In Proceedings of the International Conference on Signal Processing and Multimedia Applications, pages 88-93

DOI: 10.5220/0002997600880093

 SciTePress

scribed in Section 2. The proposed methodology is

presented in Section 3. Section 4 contains the experi-

mental results and Section 5 concludes the paper.

2 MEAN SHIFT CLUSTERING

Given n data points x

, i = 1, ...,n in a `-dimensional

feature vectors ℜ

, the density estimate at point x with

kernel K(x) and window radius h

is obtained as (Co-

maniciu and Meer, 2002):

(x) =

∑

i=1



x − x



(1)

For radially symmetric kernels with bounded sup-

port it sufﬁces the following equation:

K(x) = c

k,d

k(kxk

) (2)

where c

k,d

is a normalization factor assuring K(x) in-

tegrates to 1 and h

is the window size or kernel band-

width which determines the range that the kernel lo-

cated in x

uses (Georgescu et al., 2003)(Comaniciu

and Meer, 2002). The following kernel function is

used in our work:

K(x) =



−1

(d + 2)(1 −x

x) i f x

x < 1,

0 otherwise,

(3)

According to this function, called Epanechnikov ker-

nel, the mean integrated square error between the

principal probability density function and the kernel

density estimation is minimized. The zeroes of the

gradient of the estimated density function

indi-

cate the modes of this function (Comaniciu and Meer,

2002):

∇

(x) =

k,d

∑

i=1

d+2

−x)g



x − x



(4)

where according to equation 3, k

(x), derivative of

function, k(x) exist and g(x) = −k

(x). The equa-

tion 4 can simply be rewritten in the following form

(Georgescu et al., 2003):

∇

(x) =

k,d

∑

i=1

d+2



x −x



× m

(x) (5)

where

(x) =

∑

i=1

d+2





X−X





∑

i=1

d+2





X−X





− x (6)

The ﬁrst term in equation 5, is proportional to the

density estimate at x computed using kernel function

G(x) = c

g,d

g(kxk

). The second term, m

(x), in this

equation however is the “mean shift”. It shows that

the mean shift vector always moves toward the direc-

tion of the higher density regions.

Clustering with mean-shift is obtained using an

iterative procedure starting from each feature vector

(data point) of the dataset and doing the following

(Comaniciu and Meer, 2002):

1 - Starting from point x

and calculation of the mean

shift vector m

(x),

2 - Shifting the window center from x

to x

t+1

+ m

It continues until converged to a point where the

gradient of density function is zero and then asso-

ciates the feature vector with the corresponding con-

vergence mode. In fact, this algorithm is an iteratively

climbing technique to the nearest stationary point of

the data with the highest local density where the den-

sity gradient is also zero. It is important to note that

in the mean shift algorithm there is no need to initial

the cluster positions. In addition, the cluster number

is the result of the algorithm and not to be speciﬁed in

advance. Figure 1 shows two clusters and two sample

points each going to the center of the relevant cluster

using the mean shift algorithm.

Figure 1: Mean shift algorithm for two clusters and two

sample points. The mean shift vector always moves toward

the direction of the higher density regions where points A

and B are ﬁnally assigned to the clusters C

and C

, respec-

tively. The circles show kernel bandwidths which determine

the range of the data used in a speciﬁc point.

3 METHODOLOGY

The purpose of this work is to introduce an approach

that detects and segments masses in mammography

images. The proposed model is shown in Figure 2

and the following subsections detail these algorithms.

BREAST MASS DETECTION USING BILATERAL FILTER AND MEAN SHIFT BASED CLUSTERING

Figure 2: Block diagram of the proposed method for detec-

tion of masses in mammography images.

3.1 Extraction of the Breast Region

The goal of this step is to ﬁnd the breast region. Breast

region estimation is an important requirement as it

can improve the accuracy of further analysis as well

as decreasing the processing time. First, the breast

area is initially extracted using a global thresholding

method. For this purpose, the technique presented in

(Ojalaa et al., 2001) is found to be more effective due

to its adaptive nature. In this technique, the automatic

threshold selection is based on the fact that there is

a local discontinuity among the histogram bins be-

tween the breast region and the background area. The

global threshold t

is determined by ﬁnding the his-

togram bin that has the maximum increase of the lo-

cal histogram discontinuity. The intensity of this bin

speciﬁes the intensity level of the breast boundary.

This method can yield acceptable results even in low-

quality mammograms in which the breast boundary

is difﬁcult to recognize (Ojalaa et al., 2001). For lo-

cating the ﬁnal breast boundary, a fast ﬁltering algo-

rithm based on robust regression is used (Sahba and

Venetsanopoulos, 2009). In this method, the center of

gravity of the initial thresholded region is used as the

central point of a polar coordinate system. Then the

area between the most elevated point and the lowest

point of this region is divided into equally spaced rays

originating from the central point. The rippled breast

boundary points located on the intersection of the bor-

der of the initial thresholded region and these rays are

indicated and used as the observed data for the local-

ly weighted ﬁlter (Cleveland and Devlin, 1988). This

ﬁlter smooths the rippled boundary points and re-

stores the shape of the breast boundary. Fig.3 (a), (b)

and (c) show a mammography sample image, the ini-

tial thresholded region, and the result of the robust

regression ﬁlter to ﬁnd the ﬁnal breast boundary, re-

spectively.

Figure 3: (a) Original breast image, (b) initial thresholded

region containing rippled boundary, (c) ﬁnding the breast

border using robust regression ﬁlter.

3.2 Bilateral Filtering

Bilateral ﬁltering is a simple and non-iterative edge-

preserving smoothing method. In contrast to many

other smoothing ﬁlters which simply replace the gray

level value of a pixel with its weighted average of its

neighbors, the bilateral ﬁlter uses both spatial and in-

tensity values for this purpose (Tomasi and Manduchi,

1998). In fact, the weighted sum of the pixels in a

neighborhood depends on both the spatial and inten-

sity distances. By using this strategy edges are pre-

served while noise is ﬁltered out.

If I(p) deﬁnes the image value at a pixel location p

with q pixels in its W (p) neighborhood, the output of

the bilateral ﬁlter,

I(p), is calculated as follows:

I(p) =

∑

q∈W (p)

−kq−pk

2σ

−kI(q)−I(p)k

2σ

I(q) (7)

where σ

and σ

are the parameters adjusting the

weights in spatial and intensity domains, respectively,

and C is a normalization factor. As can be seen, bi-

lateral ﬁlter combines gray levels based on both their

spatial proximity and gray level similarity such that

more weights are given to near values in both do-

mains. In our application, the bilateral ﬁlter is ap-

plied to the pixels located in the breast area of the

mammography images to smooth gray levels while

preserving the edges around the masses which is fun-

damental for the further stages.

3.3 Adaptive Mean Shift based

Clustering

Intensity values are the input for the non-parametric

adaptive mean shift clustering stage. As described in

SIGMAP 2010 - International Conference on Signal Processing and Multimedia Applications

Section 2, the adaptive mean shift algorithm is started

from each feature point in the image, being pixel in-

tensity values, and move it to a convergence peak rep-

resenting a mode. The starting pixels, having consis-

tent features, fall to the same convergence mode and

make a uniform cluster. Therefore, the output of this

algorithm is a set of clusters (modes presenting a com-

pact form of the data).

The size of the window, h

, is the only parame-

ter of the mean shift algorithm that should be speci-

ﬁed. When an unchanging h

is used for all feature

points and iterations, the algorithm is called the ﬁxed

bandwidth mean shift. In contrast, when a different

window size h

is used for each feature point x

the

algorithm is called adaptive mean shift (Georgescu

et al., 2003). It has been shown that the adaptive

mean shift works better than the ﬁxed bandwidth

(Mayer and Greenspan, 2009). In the technique in-

troduced in (Georgescu et al., 2003), an approximate

method for neighborhood ﬁnding is used to achieve a

fast adaptive mean shift implementation (Mayer and

Greenspan, 2009). We adopt this strategy for our al-

gorithm. In this technique, the bandwidth value is

computed based on the norm distance between x

and

its m-nearest neighbors feature vectors as follows:

= kx − x

i,m

k (8)

This is applied to each feature vector. They have

suggested that the number of associated neighbors m

should be chosen such that there is adequate increase

in the density of inside feature points for supporting

the kernel functions having bandwidths h

. The way

that the possible values of m can be derived is ex-

plained in (Georgescu et al., 2003).

After this stage, each pixel is labelled by its con-

vergence mode where each mode states the local char-

acteristics of the intensity values. Figure 4 shows a

sample mammography image containing a mass and

the result after applying the bilateral ﬁlter and adap-

tive mean shift clustering. An important advantage of

the above procedure is that the core of a mass (cen-

tral high intensity area of the mass) makes an isolated

cluster. This is because of the high density and uni-

form behavior of the intensities present in this area.

This is specially true after smoothing using the bilat-

eral ﬁlter. We use this fact for the further stages.

3.4 Detection of the Initial Positions

After data ﬁltering and clustering, the detection of the

initial position of the masses is essential. Therefore,

the position of the isolated clusters corresponding

to the core of the masses must be identiﬁed. This

is performed using a three-layer artiﬁcial neural

network (ANN) classiﬁer. For this purpose, the core

Figure 4: (a) Original image containing a mass, (b) The

result after applying the bilateral ﬁlter and adaptive mean

shift algorithm. The mass and its corresponding clusters are

marked in these images.

regions corresponding to the masses and non-masses

were selected to train the classiﬁer. The features used

to represent core regions are:

Intensity features:

- Average intensity

- Variance of their intensities

- Contrast measure

- Entropy and,

Shape features:

- Area

- Perimeter

- Compactness

- Convexity

- Boundary roughness

- Mean and standard deviation of the normalized

radial length.

The above features are used as the inputs of the

neural network where its output is a binary value indi-

cating whether the core of a mass exists or not. Exper-

imental evaluation shows that these features can suit-

ably distinguish the cores corresponding to the real

masses. Of course, some false cores may also pass the

test and generate non-relevant initial positions which

can be removed in the further stages.

3.5 Mass Segmentation using Mode

Fusion

Due to the ability of adaptive mean shift clustering

in terms of work with non-convex regions, the shapes

of the clusters around the core, have a close similar-

ity with the local structure of the mass. Therefore, a

fusion procedure is performed to combine these clus-

ters and make the ﬁnal segmentation. It is important

to note that in this stage, a mean shift algorithm is ap-

plied to the original (non-ﬁltered) pixel values within

the areas of the initial detected positions, generated in

BREAST MASS DETECTION USING BILATERAL FILTER AND MEAN SHIFT BASED CLUSTERING

the previous stage (section 3.4). This is essential for

achieving the accurate clusters for the ﬁnal segmen-

tation. After the clustering of the original pixels in

the areas of the initial detected positions, a window

around the centroid point of the cluster corresponding

to the core of the mass is considered and gradually

grows to capture more areas. In fact, spatial properties

are also incorporated to perform a proximity analysis.

The initial window is corresponding to the largest cir-

cle surrounded by the core area. After each growth,

the modes located in the area of the window are an-

alyzed. If the difference between their mode values

and the mode of the core area is less than a preset

value, it merges to the core to make a larger region.

The windowing routine is again performed with the

newly obtained area. This procedure proceeds until

no more modes satisfy the above intensity closeness

condition or the captured area is more than a speciﬁc

value. As an important property of the mean shift

algorithm, clusters can form arbitrary shapes and it

can consequently produce an appropriate segmenta-

tion after the fusion procedure. Figure 5 shows sam-

ple windowing and fusion procedure for two masses.

Figure 5: Fusion procedure using the growing windows

method for two masses.

3.6 Final Mass Detection

Some false cores may pass the test carried out in sec-

tion 3.4 and generate non-relevant detected areas after

the mode fusion. To eliminate these areas, a similar

artiﬁcial neural network classiﬁer is again applied, but

this time with the same features corresponding to the

new areas created after the mode fusion. The new

classiﬁer uses the features obtained from the mass an

non-mass regions (not their core regions) for training

and testing. Due to the good segmentation result after

the mode fusion, sufﬁcient discrimination in the fea-

tures of these regions is expected and many of those

false detected masses are removed. Subsequently, the

positions of the real masses are recognized. Figure 6

shows one of these false regions that passes the initial

position detection test but is removed after the ﬁnal

mass detection.

Figure 6: (a) An area containing no mass ,(b) The false de-

tected core indicated by dashed circle which will be further

removed.

4 EXPERIMENTAL RESULTS

In this study, the mammography images were se-

lected from MIAS databases so that all the masses are

marked by experts. The images had resolution of 8-

bit gray scale. In our experiment, we used 65 images

containing 80 relevant regions (benign and malignant)

and 100 negative samples extracted from non-mass ar-

eas to train the classiﬁers. Then the system was tested

on 35 images containing 42 masses. According to the

detection result, the true positive (TP) detection rate

was 88% with a false-positive fraction of 2.1 marks

per image. The estimated value for A

of ROC curve

was 0.86. We observed that due to some similarity

between the features of masses and regions contain-

ing no mass, there are some false positives after the

initial position detection. The ﬁnal mass detection

stage, however, improved the performance and re-

moved many of these false areas. Compared to the re-

sults from some other statistical approaches reported

in (Cheng et al., 2006)(Petrick, Sahiner , and Comer)

in terms of detection rate, and false positive rate, our

proposed system obtain superior performance indi-

cating better discrimination capacity and robustness.

Figure 7 shows two sample images containing the de-

tected mass as well as the results of segmentation af-

ter the mode fusion. This shows that the proposed

method can detect and segment masses, making it

practical to be used in a computer-aided detection sys-

tem for breast cancer analysis.

5 CONCLUSIONS

In this paper, we presented a new, and effective mass

detection and segmentation approach for mammogra-

phy images. The proposed method is based on bilat-

eral ﬁltering and non-parametric adaptive mean shift

clustering. The proposed method also generates re-

SIGMAP 2010 - International Conference on Signal Processing and Multimedia Applications

sults using an adaptive bandwidth adjustment scheme

as well as follow-up stages for further improvement

of the initial clustering results. Due to the ability of

the adaptive mean shift in terms of working with non-

convex clusters as well as its noise smoothing behav-

ior, we are able to obtain good results after the ﬁnal

segmentation. Moreover, the method was validated

on real mammography database and comparing to the

similar statistical approaches, it shows improvement

in sensitivity of mass detection and better false posi-

tives rate. One of the main objectives of this work is

to provide radiologists with a computer-aided detec-

tion system aimed at studying the risk of developing

breast cancer.

For further improvement of the proposed ap-

proach, we can consider the following works:

- Applying the method to a different data set.

- Applying parameter optimization methods.

- Using other classiﬁers such as SVM.

- Reﬁnement of the segmentation method based on

shape attributes to capture all lesion extension.

Figure 7: Final results. The ﬁnal segmentation after the

mode fusion is indicated by solid black contour where the

clusters are shown by different colors. (a) and (c) are

the results of the ﬁnal segmentation; (b) and (d) are their

corresponding detected areas in the original breast images

(zoomed in for better visualization).

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