Detection of masses and microcalcifications in digital mammogram images using fuzzy logic

Mammograms are difficult images to interpret, and a preprocessing phase is necessary to improve the quality of the images and make the feature extraction phase more reliable. Two techniques were applied to the images: a cropping operation and an image filtering operation. The second technique used was 3 by 3 median filtering. The median filter is the best filter to reduce noise in digital mammogram images [9, 10]. Finally, the pectoral muscle was automatically detected using a region growing algorithm.

Texture is a property that describes the surface of an object based on its attributes such as shape and size. Texture analysis is used to explore useful information based on local variations in image pixel values. The goal of texture analysis is to quantify the relationship between pixels in a particular image.

Computer algorithms and techniques are not exactly the same as the human interpretation of textures. However, computers are able to help as a “second reader” for radiologists. Computers may also provide additional quantitative information from textures, while human interpretation may not. Although there are various methods for statistical texture, the gray-level co-occurrence matrix (GLCM) is a better choice than the others because more features are accessible. Moreover, it is useful for detecting small objects [11]. Therefore, the GLCM was a consideration in this study. One co-occurrence matrix implies that the relationships between neighboring pixels occur in both the forward and backward directions. There are a total of 8 directions: 0, 45°, 90°, 135°, 180°, 225°, 270°, and 315° [11]. The most important point is that opposite directions yield the same co-occurrence matrix. Therefore, in the present study, 4 directions, which were suggested by Haralick [11] were employed to compute co-occurrence matrices at distance of d = 1 · Fourteen statistical measurements such as contrast, correlation, and inverse difference moment were derived from the four GLCM matrices. In addition, the mean, median, mode, standard deviation, skewness, and kurtosis are also calculated.

Because the final aim of the fuzzy system was classification of different tissues, namely fat, dense, mass, and microcalcifications, small 8 by 8 view masks were defined. We extracted 18000 samples (8 pixels x 8 pixels) from various breast tissues. The method applied takes the small samples and calculates the co-occurrence matrices at distance d = 1. The angles used are 0, 45°, 90°, and 135°, with a 5th matrix being the mean of the 4 directions.

In the present study, to select the best features, data mining techniques were employed using Waikato Environment for Knowledge Analysis (WEKA) machine learning software (https://svn.cms.waikato.ac.nz/svn/weka/ and http://www.cs.waikato.ac.nz/~ml/weka/). The attribute selection was run and 7 features were selected, namely, mean, median, standard deviation, entropy, correlation, energy, and contrast.

The suggested system was designed and implemented using data mining and fuzzy tools. There are different steps in this method i.e. fuzzification, process, and defuzzification. These steps are explained in detail in the following subsections.

The fuzzy set theory has been proven useful in many areas of image processing [12]. It is well known that mammographic images have some degrees of fuzziness, such as indistinct borders, ill-defined shapes, and different densities. Because of the nature of mammography and breast structure, fuzzy logic is a better choice to handle the fuzziness of mammograms than traditional methods.

Because the crisp data were not suitable for a fuzzy inference (classifier) system, for each selected feature (which were specified earlier), a membership function was defined. The MatLab fuzzy tool box was employed for this purpose. The bell shape (Gaussian) membership function is more suitable because of the symmetric shape of this function. The Gaussian curve is given by:

f(x)=exp⁡(−0.5(x−c)2σ2)$$f\left( x \right) = \exp \left( {{{ - 0.5{{\left( {x - c} \right)}^2}} \over {{\sigma ^2}}}} \right)$$(1)

A knowledge base including more than a hundred rules was prepared. The rules were developed based on the decision tree which was built using the WEKA software.

The output of the rules would be the defuzzificated output images. Output membership function included 4 triangular members as different tissue types. Upon the “if-then” rules and membership weights the output in one of these 4 classes. The centroid aggregation method chooses the center of an output as the final fuzzy inference output. The centroid position could be calculated using following equation [13]:

X¯=13(a+xmax+b)$$\overline X = {1 \over 3}\left( {a + {x_{\max }} + b} \right)$$(2)

After approval by the Medical Ethics Committee of the Faculty of Medicine and Health Sciences of the University Putra Malaysia (approval No. F01 (JIAPR (OB) 07)) and National Cancer Society of Malaysia (NCSM), the suggested system was implemented on 326 standard mammogram images that were obtained from the NCSM database, which included 194 normal cases and 132 abnormal cases.

To interpret images, 3 expert radiologists from the Department of Medical Imaging, University Malaya, Department of Imaging, University Putra Malaysia and Hospital Serdang with at least 5 years’ experience of digital mammogram reading and interpretation were invited to read the images and select the area of lesions.

PASW Statistics for Windows (version 18; SPSS Inc., Chicago, IL, USA) was used for data analysis. The results were obtained were based on the appropriate statistical approaches, and sensitivity and specificity as descriptive statistics, and a kappa statistic as inferential statistics. In addition, a receiver operating characteristic (ROC) curve was used.