automatic detection of microcalcifications in digitized ...

Proceedings of the IASTED International Conference Visualization, Imaging and Image Processing (VIIP 2012) July 3 - 5, 2012 Banff, Canada

AUTOMATIC DETECTION OF MICROCALCIFICATIONS IN DIGITIZED MAMMOGRAMS USING FUZZY 2-PARTITION ENTROPY AND MATHEMATICAL MORPHOLOGY Baljit Singh Khehra, Amar Partap Singh Pharwaha* Department of Computer Science & Engineering Baba Banda Singh Bahadur Engineering College Fatehgarh Sahib-140407, Punjab, India baljitkhehra@ rediffmail.com *Department of Electronics and communication Engineering Sant Longowal Institute of Engineering and Technology Longowal-148106, Sangrur, Punjab, India [email protected]

ABSTRACT Cancer is a leading cause of death among men and women nowadays all over the world. Breast cancer is a most common form of cancer originated from breast tissue among women. Most frequent type of breast cancer is ductal carcinoma in situ (DCIS) and most frequent symptoms of DCIS recognized by mammography are clusters of Microcalcifications (MCCs). Automatic detection of Microcalcifications is an important task to prevent and treat the disease. In this paper, an effective approach for automatic detection of Microcalcifications in digitized mammograms is proposed. The proposed approach is based on fuzzy 2-partition entropy and mathematical morphology. In the proposed approach, first phase uses fuzzy Gaussian membership function for mammogram fuzzification. In this phase, fuzzy 2-partition entropy approach is used to find bandwidth of the Gaussian function. After this, mathematical morphological enhancement approach is used to enhance the contrast of Microcalcifications in mammograms. Finally, Microcalcifications are located using Otsu threshold selection method. Experiments have been conducted on images of mini-MIAS database (Mammogram Image Analysis Society database (UK)). In order to validate the results, several different kinds of standard test images (fatty, fatty-glandular and denseglandular) of mini-MIAS database are considered. Experimental results demonstrate that the proposed approach has an ability to detect Microcalcifications even in dense mammograms. The results of proposed approach are quite promising. The proposed approach can be a part of developing a computer aided decision (CAD) system for early detection of breast cancer.

DOI: 10.2316/P.2012.782-018

KEY WORDS Breast Cancer, Entropy, Gaussian Membership Function, Mathematical Morphology, Microcalcifications.

1. Introduction Breast Cancer is a leading cause of mortality among women each year all over the world. According to the statistics data, 1 in 8 women in the US have a chance of developing breast cancer in their life time. In year 2008, 1, 82, 000 breast cancer cases and 40,000 deaths were reported in the US (about 1 death for 4.5 detected cases). In India, 1, 15, 000 breast cancer cases and 53,000 deaths were reported in 2008 (about 1 death for every 2 cases detected) [1]. A ratio 2:1 in India is very bad as compared to 4.5:1 in the US. The main cause of this bad death ratio in India is that breast cancers are not detected at early stage while early detection is the key to improving breast cancer prognosis. Mammography is one of the most effective tools in early detection of breast cancer [2]. It is reliable, low cost and highly sensitive method. Mammography offers highquality images at low radiation doses. Mammography uses low-energy x-rays that pass through a compressed breast and are absorbed by film during an examination. Mammography is the only widely accepted imaging method for routine breast cancer screening. It is recommended that women at the ages of 40 or above should have a mammogram every one to two years [3]. Although mammography is widely used around the world for breast cancer detection, it is difficult for expert radiologists to provide both accurate and uniform evaluation for the enormous number of mammogram generated in widespread screening. There are some limitations of human observers such as some anomalies may be missed due to human error as a result of fatigue. These limitations are the main cause of false positive and false negative readings of mammogram. False-positive detection causes unnecessary biopsy. It has been estimated that only 15-30% of breast biopsy cases are

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mammograms and labeled into potential individual Microcalcifications objects by their spatial connectivity. After this, individual Microcalcifications are detected by a set of the same features extracted from the potential individual Microcalcifications objects. Tomasz Arodz et al. [14] presented a computer-aided detection system to detect MCCs in small field digital mammography. In this system, first, a filter that sensitive to Microcalcification is used. After this, Microcalcifications are enhanced by using wavelet-based sharpening algorithm. Sung-Nien Yu et al. [15] presented a method to detect Microcalcifications in digital mammograms using wavelet filter and Markov random field model. In this method, first, all suspicious Microcalcifications are preserved by thresholding a filtered mammogram via a wavelet filter. Subsequently, Markov random field parameters are used to enhance true Microcalcifications. H. D. Cheng et al. [16] proposed a novel approach to micro detection using fuzzy logic technique. In this approach, first mammogram is enhanced using fuzzy logic. After this, global threshold is used to detect micro calcifications. In 2002, H. D. Cheng et al. [17] gave a novel fuzzy logic approach to contrast enhancement for mammogram image. This approach is based on the fuzzy entropy principle and fuzzy set theory. Jianmin Jiang et al. [18] proposed a combined approach with fuzzy logic and structure tensor towards improved enhancement of possible micro calcifications in digital mammograms. H. D. Cheng and Jianmin Jiang approaches are based on maximum fuzzy Shannon entropy principle. In 2009, J. Mohanalin et al. [19, 20] used Tsallis entropy to segment Microcalcifications in mammograms. In 2010, J. Mohanalin et al. [21, 22] used normalized Tsallis entropy and Tsallis entropy & a type II fuzzy index respectively to detect Microcalcifications in mammograms. J. Mohanalin approaches are based on H. D. Cheng et al. [17] approach. H. D. Cheng et al. [17] approach used Shannon entropy while J. Mohanalin approaches used Tsallis entropy, normalized Tsallis entropy and Tsallis entropy & a type II fuzzy index.

proved to be cancerous [4]. On the other hand, in a falsenegative detection an actual tumor remains undetected. Retrospective studies [5] have shown that 10-30% of the visible cancers are undetected. So, false-positive and false-negative have caused a high proportion of women without cancers to undergo breast biopsies or miss the best treatment time. Thus, there is a significant necessity to improve the correct diagnosis rate of cancer. Several solutions were proposed in the past to increase accuracy and sensitivity of mammography and reduce unnecessary biopsies. Independent double reading of mammograms by two radiologists is one of the solutions and has proved to significantly increase the sensitivity of mammographic screening. The basic idea for independent double reading is to read the mammograms by two radiologists independently. However, this solution is both highly costly and time consuming. Instead of double reading, radiologists have an opportunity to improve their diagnosis with the aid of computer aided detection system. It might provide a useful second opinion to radiologists during mammographic interpretation. The most frequent type of breast cancer, detected before the invasion stage, is ductal carcinoma in situ (DCIS). The carcinoma of the breast is still the most common invasive cancer in women from the ages of 1554, and the second most common cause of death in the age group 55-74 [6]. The most frequent symptoms of ductal carcinoma recognized by mammography are clusters of Microcalcifications (MCCs) [7]. Microcalcifications (MCs) are tiny granular deposits of calcium that appear on the mammogram as small bright spots [8]. A MCC is typically defined as a group of at least three or five MCs within a 1 cm2 region of the mammogram [9, 10]. Although Computer aided detection system has been studied over two decades, automated detection of Microcalcifications is a challenging task and a difficult problem for researchers. It is mainly due to fuzzy nature of Microcalcifications, low contrast and low distinguishability of Microcalcifications from their surrounding tissues.

This paper proposes a two-phase computer aided Microcalcification detection method to overcome the two main problems in the detection of Microcalcifications in mammograms, namely the fuzzy nature of Microcalcifications and low distinguishability of Microcalcifications from their surrounding tissues. In the first phase, a fuzzy Gaussian membership function is used for mammogram fuzzification. In this phase, fuzzy 2partition entropy approach is used to find bandwidth of the Gaussian function. In the second phase, mathematical morphological enhancement approach is used for high distinguishability of Microcalcifications from their surrounding tissues. At the end, Microcalcifications are located using Otsu threshold selection method. Experiments have been conducted on images of miniMIAS database (Mammogram Image Analysis Society database (UK)) [23] to verify the effectiveness of the

To deal with these problems, several researchers in recent years have been developed methods to detect Microcalcifications in digitized mammograms. Some selected examples are briefly discussed in the following. Jong Kook Kim et al. [11] used statistical texture features to detect Microcalcifications in digitized mammograms. Extracted statistical texture features are used to classify ROI’s into positive ROI’s containing MCCs and negative ROI’s containing normal tissues. Thor Ole Gulsrud et al. [12] developed an optimal filter to extract texture features in mammograms. Extracted features are used to segment the digital mammograms into classes: MCCs and normal tissues. Songyang Yu et al. [13] presented a Computeraided diagnosis system for the automatic detection of MCCs in digitized mammograms. In this system, first, wavelet features and gray level statistical features are used to segment potential Microcalcification pixels in the

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proposed method.

k =

The rest of this paper is organized as follows: Section 2 describes the proposed approach to detect Microcalcifications in digitized mammograms; Experimental results are given and discussed in Section 3; the paper is concluded in Section 4.

Mammogram is converted into fuzzy domain. Fuzzy set theory [24] is used to handle uncertainty. Microcalcifications in mammogram images have fuzzy nature like variation in size and shape, variation in contrast from their surrounding tissues and different densities of breasts. So, fuzzy logic is a good choice to handle fuzzy nature of mammogram images. Gaussian function [21, 25] is the most common used membership function to convert mammogram into fuzzy plane. The standard Gaussian function is defined as

max

[ f ( x , y )− L max ]2 2b2

(1)

( x , y ) is input mammogram image, g ( x , y ) is fuzzy image, Lmax is maximum gray level of

where f

opt

)(

)}

(2)

Gaussian

membership

− k , L max − t opt

Graphical representation of function is shown in Figure 1.

(M

×N

)

(4)

where h j is the gray level histogram of mammogram i.e.

h j is the number of pixels in mammogram with gray

input mammogram image and parameter b is bandwidth of the Gaussian function that calculated from the following equation:

{(t

(3)

x,y R

distribution of gray level values of mammogram, where p j is the normalized histogram of mammogram i.e.

pj = hj

b = max

N

2) Selection of Parameter topt for Bandwidth of Gaussian Function Parameter topt plays an important role for optimal selection of bandwidth of Gaussian function. Gaussian membership function transformed gray level values of mammogram to an interval [0, 1]. Optimal selection of bandwidth of Gaussian function will high light Microcalcifications intensities and suppresses heavily remaining. Parameter topt is an optimal threshold that separate suspicious region from breast and tissue background. The procedure for optimal threshold selection from mammogram is as follows: Let f ( x , y ) be the gray level value of input mammogram image at the pixel (x, y) and p 0 , p 1 , p 2 ,......., p j ,......., p L be the probability

2.1 Image Fuzzification

g (x , y ) = e

M

∑ ∑ε f (x , y )

where M and N are dimensions of the mammogram, R is the region having gray level values greater than 100, n is the number of pixels in this region.

2. Proposed Approach

−

1 n

level j, j=0, 1, 2,……………,Lmax

1) Selection of Parameter k for Bandwidth of Gaussian Function Mammogram is a combination of 3 individual objects namely breast background, tissue background and suspicious region. Breast background does not provide any information in diagnosis. So, breast background can be ignored in mammogram analysis study. Approximately, more than one-third of a mammogram is breast background. It could affect the average gray level value of the breast tissues. Hence, the average gray level value of the breast tissues is defined as follows by excluding breast background pixels [17, 21]

Figure1. Graphical representation of Gaussian membership function To separate suspicious region from breast and tissue background, mammogram can be modeled by two fuzzy membership functions (S-function and Z-function) [26, 27]. Z-fuzzy membership function is a membership

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L max  L max  H B (a , b , c ) = − ∑ µ B ( j ) p j log  ∑ µ B ( j ) p j  (8) j=0  j=0 

function of the breast and tissue background class and Sfuzzy membership function is a membership function of the suspicious region class. Thus, S and Z membership functions divide mammogram into two parts. Such partitioning is called fuzzy 2-partition of mammogram. Sfuzzy membership function defined as 0  2  ( j − a)  (c − a )(b − a ) µ S ( j ) = S ( j; a, b, c) =  2 1 − ( j − c)  (c − a)(c − b)  1

The sum of the two entropies can be written as

H (a , b , c ) = H S ( a , b , c ) + H B ( a , b , c )

j≤a a< j≤b

(9)

The optimal values of a, b and c that maximize H (a, b, c) are used to find parameter topt (optimal threshold) that separates the suspicious region from the breast and tissue background i.e.

(5)

b< j≤c L max

( a * , b * , c * ) = Arg max [H (a , b , c )]

j>c

(10)

a ,b , c = 0

Z-fuzzy membership function defined as 1  2 1 − ( j − a)  (c − a)(b − a) µB ( j) = Z ( j; a, b, c) =  2  ( j − c) (c − a)(c − b)  0

The optimal threshold topt that separates the suspicious region from the breast &tissue background can be calculated from the optimal values of a, b and c that maximize H (a, b, c) as follows:

j≤a a < j ≤b

(6)

a* + (c* − a* )(b* − a*) / 2 topt =  c* − (c* − a* )(c* −b* ) / 2

b< j ≤c j >c

determine the shape of S and Z fuzzy membership functions as shown in Figure 2. Now, from the above mentioned probability distribution of gray level values of mammogram, we can derive two probability distributions, one for the suspicious region and second for the breast and tissue background. The probability distributions of the suspicious region and the breast & tissue background are shown as follows: Probability distribution of suspicious region: Probability background:

distribution

of

breast

and

max

tissue

µ B ( 0 ) p 0 , µ B (1) p 1 ,......... .......... .., µ B ( L max ) p L

max

In terms of the definition of Shannon entropy [29], the entropy of suspicious region pixels and breast & tissue background pixels can be defined as follows: Shannon Fuzzy Entropy for suspicious region pixels:

Figure2. Graphical representation of Z and S fuzzy membership functions

  H S (a , b , c ) = − ∑ µ S ( j ) p j log  ∑ µ S ( j ) p j  (7) j=0  j=0  L max

(11)

a* ≤ b* ≤ (a* + c*) / 2

However, finding the optimal combination of (a, b, c) to maximize H (a, b, c) is a NP-Complete problem while a, b and c may take any values from {0, 1, 2,…………., Lmax}. The optimal combination of (a, b, c) is found using recursive procedure [30].

where 0 ≤ a ≤ b ≤ c ≤ L max , parameters a, b and c

µ S ( 0 ) p 0 , µ S (1) p 1 ,......... .......... .., µ S ( L max ) p L

(a* + c*) / 2 ≤ b* ≤ c*

L max

2.2 Enhancement of Fuzzy Mammogram using Mathematical Morphology

Shannon Fuzzy Entropy for breast & tissue background pixels:

Mathematical morphology provides tools for highlighting objects in image based on size and shape. Thus, mathematical morphology tools can be used to highlight suspected micro calcifications and suppress tissues. Tophat transform is one of the mathematical morphology

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(Mammogram Image Analysis Society database (UK)) database. Mini-MIAS database is a standard benchmark database for mammographic image analysis research community. In order to validate the results, several different kinds of standard mammogram images (fatty, fatty-glandular and dense-glandular) of mini-MIAS database are considered. In order to reduce computational burdens, we select ROI (Region of Interest) of each mammogram image of size 256×256. Due to page constraint, we pick randomly one mammogram of each kind to show the results. In order to demonstrate the efficiency of the proposed algorithm, the results of the proposed algorithm are displayed in Figures 3-9.

tools that can be used to extract micro calcifications even if the micro calcifications are located on a non-uniform background [30]. Mathematical morphology top-hat transformation of fuzzy mammogram image is defined as

g ' = g − [g o SE ]

(12)

g o SE is the opening of the image g(x, y) by structure element SE that is defined as where

g o SE =

[( g Θ SE ) ⊕

SE

]

(13)

The optimal values of parameter topt to optimize bandwidth of Gaussian function for separating the suspicious regions from the breast and tissue background in different kind of mammograms are shown in Tables 1. Otsu's threshold values, which are used to detect Microcalcifications from enhanced mammograms, are shown in Table 2.

where Θ is called morphological Erosion operation that is defined as

g Θ SE ( x , y ) = min [g ( x + i , y + j ) − SE (i , j ) ] (14) and ⊕ is called morphological Dilation operation that is defined as

g ⊕ SE ( x , y ) = max [g ( x − i , y − j ) + SE (i , j ) ] (15) Structure element SE is usually much smaller that the input image. By selecting the shape and size of the structure elements, different results can be obtained in the output image. In this experiment, a non-flat, ball-shaped structuring element [31] (actually an ellipsoid) is used whose radius in the X-Y plane is 7 and whose height is 10.

(a)

(b)

2.3 Detection of Microcalcifications in Enhanced Mammograms The areas containing Microcalcifications are usually heterogeneous and the variances of these areas would be larger than those of tissue background regions. Therefore, a threshold can be played an important role to separate Microcalcifications from breast tissues according to nonuniformity [16]. So, we use Otsu's method [32], which chooses the threshold to minimize the intra class variance of Microcalcifications and breast tissues in enhanced mammograms.

(c) (d) Figure3. (a) Original Fatty-glandular benign mammogram (mdb219), (b) Fuzzified mammogram, (c) Enhanced mammogram and (d) Microcalcifications extracted

3. Experimental Results and Discussions In this section, the performance of the proposed approach is evaluated through the simulation results using MATLAB 7.7.0 (R2008b) for a set of mammogram images containing Microcalcifications. A set of benign and malignant mammogram images containing Microcalcifications is taken from mini-MIAS

(a)

224

(b)

(c)

(a)

(d) Figure4. (a) Original Dense benign mammogram (mdb227), (b) Fuzzified mammogram, (c) Enhanced mammogram and (d) Microcalcifications extracted

(b)

(c)

(a)

(d) Figure7. (a) Original Dense-glandular malignant mammogram (mdb216), (b) Fuzzified mammogram,(c) Enhanced mammogram and (d)Microcalcifications extracted

(b)

(c)

(d) Figure5. (a) Original Fatty benign mammogram (mdb252), (b) Fuzzified mammogram, (c) Enhanced mammogram and (d) Microcalcifications extracted

(a)

(b)

(c) (a)

(d) Figure8. (a) Original Dense-glandular malignant mammogram (mdb241), (b) Fuzzified mammogram, (c) Enhanced mammogram and (d) Microcalcifications extracted

(b)

(c)

(d) Figure6. (a) Original Fatty-glandular malignant mammogram (mdb213), (b) Fuzzified mammogram,(c) Enhanced mammogram and (d)Microcalcifications extracted

(a)

225

(b)

Microcalcifications in mammogram. The proposed approach can be a part of developing a computer aided decision (CAD) system for early detection of breast cancer. Thus, this study will be useful to control breast cancer. In future work, detected Microcalcifications will be characterized as benign or malignant.

References (c)

(d) Figure9. (a) Original Fatty malignant mammogram (mdb245), (b) Fuzzified mammogram, (c) Enhanced mammogram and (d) Microcalcifications extracted

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Table 1 Optimal value of parameter topt for bandwidth of Gaussian function Mammogram Value of Parameter topt Mdb213 Mdb216 Mdb219 Mdb227 Mdb241 Mdb245 Mdb252

128 214 141 174 130 122 153

Table 2 Threshold for microcalcifications detection using Otsu’s method Mammogram Thresholds obtained Mdb213 Mdb216 Mdb219 Mdb227 Mdb241 Mdb245 Mdb252

114 105 84 103 101 99 98

4. Conclusion and Future Work In this paper, an attempt is made to propose an effective approach for automatic detection of Microcalcifications in digitized mammograms using fuzzy 2-partition entropy and mathematical morphology. To evaluate the effectiveness of proposed approach, a number of different kinds of mammogram images (fatty, fatty-glandular and dense-glandular) containing Microcalcifications of miniMIAS database have been taken. The experimental results indicate that the proposed approach has an ability to detect Microcalcifications even in dense mammograms. The Results of this study are quite promising. This study can be very useful for radiologists to detect

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