Breast masses in mammography classification with local contour features
 Haixia Li^{1, 2},
 Xianjing Meng^{3},
 Tingwen Wang^{3},
 Yuchun Tang^{4} and
 Yilong Yin^{1, 3}Email author
DOI: 10.1186/s1293801703320
© The Author(s) 2017
Received: 11 September 2016
Accepted: 20 March 2017
Published: 14 April 2017
Abstract
Background
Mammography is one of the most popular tools for early detection of breast cancer. Contour of breast mass in mammography is very important information to distinguish benign and malignant mass. Contour of benign mass is smooth and round or oval, while malignant mass has irregular shape and spiculated contour. Several studies have shown that 1D signature translated from 2D contour can describe the contour features well.
Methods
In this paper, we propose a new method to translate 2D contour of breast mass in mammography into 1D signature. The method can describe not only the contour features but also the regularity of breast mass. Then we segment the whole 1D signature into different subsections. We extract four local features including a new contour descriptor from the subsections. The new contour descriptor is root mean square (RMS) slope. It can describe the roughness of the contour. KNN, SVM and ANN classifier are used to classify benign breast mass and malignant mass.
Results
The proposed method is tested on a set with 323 contours including 143 benign masses and 180 malignant ones from digital database of screening mammography (DDSM). The best accuracy of classification is 99.66% using the feature of root mean square slope with SVM classifier.
Conclusion
The performance of the proposed method is better than traditional method. In addition, RMS slope is an effective feature comparable to most of the existing features.
Keyword
Breast mass 1D signature contour subsection RMS slopeBackground
Researchers proposed many methods to describe the shape and texture in the system of CAD. Shape descriptor is compactness, eccentricity, moment, Fourier transformation descriptor, statistical marginal characteristics [7–11]. Texture descriptions gray level cooccurrence matrix and fractal dimension and so on [5, 12–14]. Pohlman et al. [15] proposed a method to transform 2D contour of breast mass to 1D signature. The signature of a contour is obtained by a function of radial distance from the centroid to the contour versus the angle of the radial line over the range (0°–360°). In this way, a signature of small fluctuation is obtained if the contour of breast mass is benign. Otherwise, if it is a malignant mass, a signature of large fluctuation is obtained. Fractal character can describe the fluctuation. So in literature [16] the breast mass is classified with the fractal analysis and the classification accuracy is greater than 80%. However, the function of radial versus degree could lead to a multivalue function in the case of an irregular or speculated margin [17]; the signature computed in this manner would also have ranges of undefined values in the case of a contour for which the centroid falls outside the region enclosed by the contour. Rangaraj et al. [16] improved the method. They transformed the 2D contour of breast mass to 1D signature by polygonal modeling of contours of breast masses using the turning angle function. Rangayyan and Nguyen [2] demonstrated the usefulness of fractal analysis for the classification of breast masses with the boxcounting and ruler methods for the derivation of the FD of the twodimensional 2D contours of masses as well as their onedimensional 1D signatures. Some literatures [2, 9, 18–20] revealed that the regular extent is also very important to make a distinction between benign and malign breast mass. If the shape of mass is circular or oval then its probability to be benign is larger than to be malign mass.
The remainder of this paper is organized as follows. The new method for translating 2D contour to 1D signature is proposed in “Methods”. In “Features”, we extract fractal dimension FD, \( w \), \( \mu_{R} /\sigma_{R} \) (where \( \mu_{R} \) means mean radial distance of tumor boundary, and \( \sigma_{R} \) means standard deviation), and root mean square slope features describing the contour characteristic. Then in the next Section, experimental results and analysis are introduced. The last is the summary of our work and the prospect of future work.
Methods
In this part, the database is firstly introduced. Second, the method of 2D contour to 1D signature is illustrated in some detail. Finally, we explain how to segment 1D signature into subsections and how to reorganize these subsections.
Database
In this paper, digital database for screening mammography (DDSM) has been utilized to provide the mammography images. This database is provided by the Massachusetts General Hospital, the University of South Florida, and Sandia National Laboratories [21, 22]. This database includes about 2620 cases. Each case has 4 mammography images composed of two view images of each breast, along with some associated patient information. Images containing suspicious areas have associated pixellevel ground truth information about the locations and types of suspicious regions. This information is saved as an overlay file. Each overlay file may specify multiple abnormalities. Each abnormality has information on the lesion type, the assessment, the subtlety, the pathology and at least one outline. Each boundary is specified as a chain code. The details about the DDSM database can be found in literature [23] or availability of data and materials at the end of this article. The database includes Normal, benign and cancer volumes. The research object in this article is the contour of benign and malignant mass. So we choose 323 contours of mammography images from DDSM database including 143 contours of benign images and 180 contours of malign images. In order to simplicity and convenience of experiment, we choose some mammography images including single abnormality. The numbers of the images of we used are listed on the Additional file 1: Appendix S1. Among 143 benign images, most contours are similar ellipse. These benign mass is prone to classify wrongly using existing method. All images are from the different patient.
2D contour to 1D signature
Subsection and integration
The method which 2D contour transforms into 1D signature can describe the feature of the whole contour. Sometimes the local feature is also very important to classify the benign and malignant breast mass. In Fig. 1b, for example, the \( 2/3 \) contour in the left is smooth and regular but subsection in the right is microlobulated. It is not precise if we extract the feature on whole contour. So we propose a method that a whole signature is divided into \( C \in \{ 1,\;2,\;4,\;6,\;8,\;10,\;12,\;14,\;16,\;18,\;20\} \) subsections respectively. If C = 1, the signature is whole one. The feature is a value. Otherwise, the feature of each subsection is extracted respectively. Then segments are ranked by the value of each subsection feature. Finally these subsections are integrated into a whole signature in sequential order according to the value of feature. That is to say the feature of each contour of breast mass is a vector of C dimension. The number of subsections affects the accuracy of classification. Because the optimized amounts of subsections are relevant to the size of mass contour and features, we divide each contour into C subsections and choose the average accuracy of all kinds of subsections as the final performance of each feature. For example, if C = 4, each contour is segmented into 4 subsections. The feature is a vector of 4 dimensions. Then we feed 323 feature vectors into classifiers. After the whole set C is ergodic, we obtain 11 results. The average of 11 results is as the final performance.
Features
In this part, four features are introduced. Among them, RMS \( s \) is first proposed by us. It can describe the variation of 1D signature in vertical direction well.
Root mean square roughness w
Root mean square roughness describes the irregular degree of 1D signature. The root mean square roughness is defined as: \( w \) is root mean square roughness defined as \( w = \sqrt { \langle h^{2}\rangle  \langle h \rangle ^{2} } \). Among the equation, 〈 〉 expresses the statistical average, \( w \) expresses the fluctuation degree of \( h \) in vertical direction. The shape is more regular with the value of more small. That is to say that the margin is more close to a circle or ellipse. The mass will more probably be benign than malign. So root mean square roughness may be used as a feature to classify the benign or malign breast mass.
The \( \mu_{R} /\sigma_{R} \) ratio
The \( \mu_{R} /\sigma_{R} \) ratio (where \( \mu_{R} \) means mean radial distance of tumor boundary, and \( \sigma_{R} \) means standard deviation), describes the circularity of the breast mass contour. Malignant mass should have smaller values of circularity than benign mass. Haralick [24] proved that the \( \mu_{R} /\sigma_{R} \) ratio is a good feature in classifying malignant mass and benign mass. Polhman [15] applied this feature in his 1D signature and acquired the good result.
Fractal dimension
Here, \( \rho = i_{2}  i_{1}  \) is the interval between two points on signature. The autocorrelation function \( R \) has some characteristics such as: (1) If the signal is the smooth and steady random process, \( R(i + \rho ) \) is irrelevant to \( n \) and relevant to only \( o \) i.e. \( R(i + \rho ) = R(\rho ) \). With the increment of correlation interval \( \rho \), \( R(\rho ) \) decreases little by little and tends to be zero. The rate of decrease is decided by the distance between two points irrelevant to each other. The correlation length is defined by the value of correlation interval at the point that the autocorrelation function \( R(\rho ) \) decreases to \( e^{  1} \) of the maximum. The correlation length \( \xi \) expresses the speed that \( R(\rho ) \) decreasing with \( \rho \).If the interval between two points is less than \( \xi \), the two points are correlated. Otherwise, the two points are independent. The fluctuation in the horizontal direction is expressed with \( \xi \) and the fluctuation in the vertical direction is expressed with \( w \).
RMS slope \( s \)
We can see from the Fig. 4 and Eq. (6) that the slope of benign mass has small value and the fluctuation is gentle. While the slope of malignant mass has big value and the fluctuation is violent. The variation range of the RMS \( s \) for malignant mass is wider than benign mass.
Classification
KNearestneighbor (KNN), support vector machine (SVM) and artificial neural network (ANN) are used as classifiers in this paper to differ benign mass from malign mass of breast. We choose K = 1 in KNN classifier and use a linear support vector machine classifier. The NNet classier is configured with 10 nodes in the hidden layer. The internal weight is initialized with randomly chosen values. 323 contours are divided into two subsets 300 contours for training and 23 for testing. The software we use is Matlab R2015b on a Win10 Operating System.
Experimental results and analysis
In this part, the performance of the proposed method is reported. Then, performance of four features is compared. Third, the effect of subsections is analyzed. And finally, classifier performance is shown.
Performance evaluation for 2D contour to 1D signature
The accuracy comparison of our work \( h(i) \) with traditional one \( h_{p} (i) \)
Feature  Method  KNN (%)  SVM (%)  ANN (%) 

\( w \)  \( h_{p} (i) \)  76.68  82.21  79.84 
\( h(i) \)  81.82  88.14  88.54  
\( \mu_{R} /\sigma_{R} \)  \( h_{p} (i) \)  76.68  84.51  79.45 
\( h(i) \)  81.82  90.57  88.54  
\( \alpha \)  \( h_{p} (i) \)  83.00  87.21  83.79 
\( h(i) \)  86.17  91.92  89.33  
\( s \)  \( h_{p} (i) \)  92.09  99.33  94.86 
\( h(i) \)  92.47  99.66  99.60 
Performance evaluation for four features with three classifiers
Performance evaluation for subsection
Conclusion and future work
It is very important for contour to distinguish the benign breast mass from malign one. In this paper, we propose three shape features of broken line for contour to classify the benign and malign breast mass. The accuracy rate attains 99.66% with the RMS slope feature. In addition, we compute fractal dimension by another method of heightheight correlation function in log–log coordinate. The accuracy rate attains 99.33%. It is higher than \( \mu_{R} /\sigma_{R} \) and \( w \). For further researches, the selection of N and some texture features could be studied for improving the classification performances. We can choose more cases in order that our study has a wider application range. Also, more advanced classification methods such as deep neural network can be used to improve the classification accuracy.
Abbreviations
 RMS:

root mean square
 KNN:

Knearest neighbor
 SVM:

support vector machine
 ANN:

artificial neural network
 DDSM:

digital database of screening mammography
 FD:

fractal dimension
 ROI:

region of interest
Declarations
Authors’ contributions
HL designed the study and drafted the manuscript. YY and XM designed the study and revised the manuscript significantly. TW and YT oversaw the study and revised the manuscript. All authors read and approved the final manuscript.
Acknowledgements
This research is supported by National Natural Science Foundation of China (Grant No. 61573219); NSFC Joint Fund with Guangdong under Key Project (Grant No. U1201258); Shandong Natural Science Funds for Distinguished Young Scholar (Grant No. JQ201316); Fundamental Research Funds of Shandong University (2014JC028); the Fostering Project of Dominant Discipline and Talent Team of Shandong Province Higher Education Institutions. Colleges and universities of Shandong province science and technology plan projects (J16LN19).
Competing interests
The authors declare that they have no competing interests.
Availability of data and materials
The dataset analyzed during the current study was derived from the following public domain resources: http://marathon.csee.usf.edu/Mammography/Database.html
Ethics approval
All human data used in this study were obtained from public dataset DDSM. This experiment was approved by the hospital’s ethical research committee.
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Authors’ Affiliations
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