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;
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 .
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 . 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 .
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 .
In the last decades, the segmentation methods in breast ultrasound images have been proposes whether automatically, semi-automatically or manually. Huang et al  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  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  used neutrosophic and K-means algorithm, Cheng et al  used neutrosophic and fuzzy c-means (FCM) clustering algorithm and Zhang et al used neutrosophic and watershed method . All of them used non-medical images. Meanwhile Anter et al  used neutrosophic and FCM clustering , Shan et al used neutrosophic and l-means clustering  and Guo  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.
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
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  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) .
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 . 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) .