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Neutrosophic and Fuzzy C-Means Clustering for Breast Ultrasound Image Segmentation

Neutrosophic and Fuzzy C-Means Clustering for Breast Ultrasound Image Segmentation

Abstract— Breast ultrasound image segmentation is one of the most difficult tasks due to its speckle noise, poor quality and location of the breast nodule. In this research, we proposed normalization algorithm to enhance image contrast in order to be segmented using neutrosophic and fuzzy c-means clustering. At first, the input image is filtered using speckle reduction anisotropic diffusion to reduce speckle noise and normalized to increase the contrast. Secondly, the normalized image is transferred to neutrosophic domain with three membership subset T, I and F to define the nodule area. Finally, the fuzzy c-mean method is used to segment the nodule area from the background. To evaluate and compare the performance of the proposed method, this research uses several measurements, namely Area Metric and Boundary Metric. The result shows that implementation of normalization improves the performance of segmentation results.

Keywords—Breast ultrasound; neutrosophic; fuzzy c-mean; segmentation;

I.     Introduction

According to the statistics, the most frequent diagnose cancer and the highest cause of cancer death among women worldwide is breast cancer. It is estimated that there are 1.7 million cases and 521,900 deaths in 2012. A quarter of all cancer cases and 15% of all cancer deaths among female are  accounted for breast cancer. However, mortality can be reduced by early detection and treatment appropriately [1].

One of the imaging modalities commonly used to detect and to classify the mass abnormalities is ultrasound image. Compared to other modalities, ultrasound has several benefits such as no radiation, safer, cheaper, faster and possible to increase the number of detected nodules. However, it is highly dependent on the operator capability and the experience of the radiologist [2][3]. Computer aided diagnosis (CAD) has a potential to detect abnormal masses and it can be used as a tool to obtain second opinion for the radiologist to make an accurate diagnosis [4][5].

Segmentation remains an active field in machine vision and image processing research. Moreover, it is one of the hardest tasks in computer vision systems design. Segmentation often becomes the vital first step which must be taken successfully before subsequent tasks, e.g. feature extraction, classification, and description [6].

In the last decades, the segmentation methods in breast ultrasound images have been proposes whether automatically, semi-automatically or manually. Huang et al [7] categorizes segmentation methods into seven groups: thresholding-based, clustering-based, watershed-based, graph-based methods, active contour model, Markov random field and neural network. Then, Cheng et al  [8] classified segmentation methods into four class, such as histogram thresholding method, active contour model, Markov random field, and neural network.

Neutrosophy is a statistic method to handle indeterminate condition, such condition that cannot be handled by fuzzy logic. The image is transformed into neutrosophic set based on neutrosophic domain. Several research using neutrosophic methods have been proposed. Akhtar et al [9] used neutrosophic and K-means algorithm, Cheng et al [10] used neutrosophic and fuzzy c-means (FCM) clustering algorithm and Zhang et al used neutrosophic and watershed method  [11]. All of them used non-medical images. Meanwhile Anter et al [12] used neutrosophic and FCM clustering , Shan et al used neutrosophic and l-means clustering [13] and Guo [14] et al used neutrosophic and level set. All of them used medical images.

Based on the reviewed literature, the segmentation in breast ultrasound is still big challanges for futher research. In this paper, we proposed a normalization method to enhance breast ultrasound image contrast in order to be segmented using neutrosophic and FCM algorithm.

The paper is organized as follows: Section II describes the methods. Section III discusses the evaluation, results and comparison. The conclusion of this study is presented in Section IV.

II.    Methods

A.    Pre-processing

The stages in pre-processing are cropping the image to the area of ​​interest (RoI), converting the image into a gray scale image, use normalization to contrast the image and then filter the image using the SRAD filter.

1)   Normalization image is scaling of linear pixel values ​​using the entire grayscale level range to get a sharper image. Contrast represents light and dark spread in the image. Images are grouped into 3 contrast categories, ie low contrast, normal contrast, and high contrast. This category is usually distinguished intuitively. The normalization process of the histogram is as follows:

  • Calculate the maximum grayscale (max_f) and the minimum grayscale (min_f) of the image.
  • The absolute difference between minimum and maximum grayscale is calculated based on (1)

= normalization image

2)   Speckle Reduction Anisotropic Diffusion (SRAD) Filter

Speckle noise is noise that occurs during image acquisition that’s multiplicative and locally correlated noise. Filtering reduces the speckle noise  without damaging the important features. SRAD filter is proposed by Yu, et al [15] combine anisotropic diffusion (AD) method proposed by Frost and Adaptive Mean Filter proposed by Lee. this technique based on Partial Differential Equation (PDE) and Minimum Mean Square Error (MMSE) [16].

The gradient based edge detector in the original anisotropic diffusion with the instantaneous coefficient  of variation is replaced by SRAD filter method to be suitable for speckle filtering [17]. Gradient magnitude and Laplacian operators as edge detection are instantaneous coefficient functions.

If the pixel of the image is represented as

To control how much smoothing performed on a pixel using instantaneous coefficient in the diffusion function is given by (4) [17].

of d-dimensional measured data. 

In this neutrosophic approach, fuzzy c-means method is used to segment the image with the following steps [11]:

  • Map and decide {T,F}.
  • Enhancement.
  • Find the threshold in T and F.
  • Define homogeneity in intensity domain and decide {I}.
  • Convert the image to a binary image based on {T, I, F}.
  • Apply the fuzzy c-means clustering to the converted binary image.

C.    Evaluation performance

1)   Area metrics can assess how much the nodule area is covered by the generated nodule area correctly and how much is covered wrongly evaluated. The false positive (FP), the false negative (FN) and dice coefficient (Dice) are calculated based on (10), (11) and (12), respectively

HD evaluate the defective possible disagreement between two contours whilst MDSS evaluate the disagreement averaged over two boundaries.

III.   Evaluation and Result

This research uses 62 breast ultrasound images which are obtained from 3 hospital databases and completed with anatomical pathology results. The examples of  breast nodule is shown in Fig. 1

j12_ROI g2_ROI

Fig. 1.  Breast nodule ultrasound

A.    Pre-processing

RoI is the process of determining an area containing nodule based on mark from radiologist. Several ultrasound images contain label and marker, therefore important to be eliminated. Adaptive median filtering affective to solve it without causing any blur effect. The results of these processes is shown in Fig. 2

D:Backup S2paperDATA RENIData uji fix17.bmp
(a) (b)
(c) (d)

Fig. 2. (a) Original image (b) RoI image (c) Gray scale image (d) Unmark image

The purpose of image normalization is to increase image contrast. SRAD filter can reduce the noise speckle without damaging edge of the object. Fig. 3 shows the results of the normalization process and the SRAD filter.

(a) (b) (c)

Fig. 3. (a) Original image (b) SRAD image (c) SRAD image with normalization

B.    Segmentation

A hybrid technique based on neutrosophic set and FCM clustering method algorithm to breast ultrasound image segmentation is proposed. In this paper, objects are T and background is F. The blurry edges are gradually changed from objects to background, and there are no clear boundaries between the objects and edges or between the background and edges. The blurry boundaries are defined in I. Fig. 4 shows the result of neutrosophic algorithm based on FCM clustering for nodule segmentation.

Fig. 5 shows the example of segmented nodule regions by two methods. From the segmentation results, the proposed methods can separate the nodule area appropriately and preserved the important area of diagnosis, i.e. edges and the boundary area of nodule. The red lines on original image represent the nodule boundaries that are obtained with the different pre-processing methods. The results of neutrosophic based on FCM with normalization methods are more exactly and more appropriate to the gold standard than neutrosophic based on FCM without normalization..

There are five measurement parameters used to evaluate quantitatively. It compares the segmentation results of the proposed method with the segmentation results by the radiologist. The radiologist manually outline the nodule boundaries as a gold standard for evaluation of nodule area.

Total 62 images were selected from 2 cases. The nodule boundaries were manually outlined by the researcher based on the gold standard from the radiologist. it was used as a performance evaluation for segmentation results. All data represent breast cancer characteristics on our data set. The corresponding images calculated by the parameters Dice, FN, FP, HD, and MSSD.

As shown in TABLE I Dice, FP, HD and MSSD were improved from 82.0%, 43.7%, 47.5 pixel and 334.0 using neutrosophic based on FCM without normalization to 87.0%, 25.4%, 37.9 pixel, and 160.5 pixel using neutrosophic based on FCM with normalization, respectively. But On the contrary, FN was degraded performance from 1.4% using neutrosophic based on FCM without normalization to 4.0% using neutrosophic based on FCM with normalization. However, performance degradation in FN is offset by improved FP performance.

The comparison demonstrates that the neutrosophic based on FCM with normalization method can achieve better performance than neutrosophic based on FCM without normalization method. We can draw a conclusion that neutrosophic based on FCM clustering with normalization method is decent to segment nodule in the breast ultrasound images.

(a) (b) (c)
(d) (e) (f)
(g) (h) (i)

Fig. 4. (a) preprocessing image (b) T-domain (c) F-domain (d) indeterminate image (e) FCM for T-domain (f) FCM for F-domain (g) binary image based on T,I,F (h) binary segmentation (i) nodule segmentation

D:Backup S2Semester 4Neutrohasilsegmentdatabaru58 dataoundary 58 fcm SRADj25_ROI_filt_watershed.bmp D:Backup S2Semester 4Neutrohasilsegmentdatabaru58 dataoundary 58 fcm NSRADj25_ROI_normfilt_fcm.bmp
D:Backup S2Semester 4Neutrohasilsegmentdatabaru102 dataoundary 102 fcm SRADunMark_T_ROI_N Sumiyati  jinak  oval tegas hipo  posterior enhancement paralel_filt_fcm.bmp D:Backup S2Semester 4Neutrohasilsegmentdatabaru102 dataoundary 102 fcm NSRADSRAD_unMark_T_ROI_N Sumiyati  jinak  oval tegas hipo  posterior enhancement paralel_fcmnlm.bmp
(a) (b) (c)

Fig. 5. Example of nodule segmentation with different methods: (a) radiologist’s (b) result by neutrosophic based on FCM without normalization (c) ) result by neutrosophic based on FCM with normalization

  1. Performance Evaluation of Segmentation Methods
Methods Average area  metrics Average boundary metrics
Dice (%) FN (%) FP (%) HD (pixel) MSSD (pixel)
Neutrosophic FCM without normalization 82.0 1.4 43.7 47.5 334.0
Neutrosophic FCM with normalization 87.0 4.0 25.4 37.9 160.5

IV.   Conlusion

This research demonstrated that neutrosophic based on FCM clustering method with normalization improved the nodule segmentation. Automatic and exactly segmentation is a crucial step for many image processing and CAD application in breast ultrasound, and the proposed methods will find more implementations in this area.


We would like to express our gratitude to the department of Radiology RSUP Sardjito for the data set, the radiologists for the very helpful discussion and colleagues in Intelligent System research group at the Department of Electrical Engineering and Information Technology, Universitas Gadjah Mada.


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