Keywords

1 Introduction

Cancer comes under a class of diseases that are characterized by uncontrolled growth of cells resulting in formation of tissue masses called tumors at any location in the body [1]. The malignant tumor can destroy other healthy tissues in the body and often travels to other parts of the body to form new tumors. This process of invasion and destruction of healthy tissues is called metastasis [2]. Breast cancer is the type of cancer that develops form breast cells. It is considered to be a major health problem nowadays and is the most common form of cancer found in women [3]. For the women in United Kingdom, the lifetime risk of being diagnosed with breast cancer is 1 in 8 [4]. The study in [5] reported 1.67 million new incidences of breast cancer worldwide in the year 2012. There are various risk factors associated with cancer development: (a) Age, (b) History of breast cancer, (c) Formation of certain lumps in the breasts (d) Higher breast density, (e) Obesity, (f) Alcohol consumption, (g) Cosmetic implants.

It has been strongly advocated by many researchers in their study that high breast density is strongly correlated with the risk of developing breast cancer [6–14]. The association between increased breast density and breast cancer risk can be explained on the basis of effects due to the hormones mitogens and mutagens. The size of the cell population in the breast and cell proliferation is affected by mitogens while the likelihood of damage to these cells is due to mutagens. Due to increased cell population, there is an increase in reactive oxygen species (ROS) production and lipid peroxidation. The products of lipid peroxidation; malondialdehyde (MDA) and isoprostanes catalyze the proliferation of cells [15].

Even though breast cancer is considered to be a fatal disease with a high mortality rate, the chances of survival are improved significantly if it can be detected at an early stage. Various imaging modalities like ultrasound, MRI, computerized tomography, etc. can be used for diagnosis of breast abnormalities but mammography is considered to be the best choice for detection due to its higher sensitivity [16–23]. Mammography is an X-ray imaging technique used to detect the breast abnormalities. Mammograms display the adipose (fatty) and fibroglandular tissues of the breast along with the present abnormalities.

On the basis of density, breast tissue can be classified into the following categories:

  1. (a)

    Fatty (F)/Dense (D) (Two-class classification)

  2. (b)

    Fatty (F)/Fatty-glandular (FG)/Dense-glandular (DG) (Three-class classification)

  3. (c)

    Almost entirely fatty (B-I)/Some fibro-glandular tissue (B-II)/Heterogeneously dense breast (B-III)/Extremely dense breast (B-IV) (Four-class BI-RADS classification)

The typical fatty tissue being translucent to X-rays appears dark on a mammogram where as the dense tissues appear bright on the mammograms. The fatty-glandular breast tissue is an intermediate stage between fatty and dense tissues therefore a typical fatty-glandular breast tissue appears dark with some bright streaks on the mammogram. The mammographic appearances of the typical breast tissues based on density are depicted in Fig. 1.

Fig. 1
figure 1

Sample mammographic images depicting typical cases. a Typical fatty tissue ‘mdb012’. b Typical fatty-glandular tissue ‘mdb014’. c Typical dense-glandular tissue ‘mdb108’

Full size image

The discrimination between different density patterns by visual analysis is highly subjective and depends on the experience of the radiologist. The participating radiologist i.e. one of the co-author of this work, opined that, in case of atypical cases where there is a high overlap in appearances of the different density patterns, a clear discrimination cannot be made by visual analysis easily. The sample mammographic images depicting the atypical cases are shown in Fig. 2.

Fig. 2
figure 2

Sample mammographic images depicting atypical cases a Atypical fatty tissue ‘mdb088’. b Atypical fatty-glandular tissue ‘mdb030’. c Atypical dense-glandular tissue ‘mdb100’

Full size image

In order to correctly identify and analyze these atypical cases various computer aided diagnostic (CAD) systems have been developed for breast tissue density classification. These proposed CAD systems can be categorized as: (a) CAD system designs based on segmented breast tissue versus CAD system designs based on Regions of Interest (ROIs). (b) CAD system designs for two class classification (fatty/dense) versus CAD system designs for three class classification (fatty/fatty-glandular/dense-glandular) versus CAD system designs for four class classification based on BI-RADS (B-I: almost entirely fatty/B-II: some fibro-glandular tissue/B-III: heterogeneously dense breast/B-IV: extremely dense breast). (c) CAD system designs using standard benchmark dataset (Mammographic image analysis society (MIAS), Digital database of screening mammograms (DDSM), Oxford, Nijmegen) versus CAD system designs using data collected by individual research groups. A brief description of the related studies is given in Tables 1, 2 and 3.

Table 1 Summary of studies carried out for two-class breast tissue density classification
Full size table
Table 2 Summary of studies carried out for three-class breast tissue density classification
Full size table
Table 3 Summary of studies carried out for four-class breast tissue density classification
Full size table

From the above tables, it can be observed that most of the researchers have used a subset of MIAS and DDSM databases and have worked on the segmented breast tissue. It is also observed that only a few studies report CAD systems based on ROIs extracted from the breast [26, 28–32, 39] even though it has been shown that the ROIs extracted from the center of the breast result in highest performance as this region of the breast is densest and extraction of ROIs also eliminates an extra step of preprocessing included in obtaining the segmented breast tissue for pectoral muscle removal [44].

The chapter is organized into three sections. Section 2 presents the methodology adopted for present work, i.e. (a) description of the dataset on which the work has been carried out (b) description of texture features extracted from each ROI image and (c) description of the classification module. Section 3 describes the various experiments carried out in the present work for two-class and three-class breast tissue density classification using statistical texture features. Finally, Sect. 4 reports the conclusions drawn from the exhaustive experiments carried out in the present work for two-class and three-class breast tissue density classification.

2 Methodology

2.1 Dataset Description

In the present work a publicly available database, mini-MIAS has been used. This database consists of the Medio Lateral Oblique (MLO) views of both the breasts of 161 women i.e. a total of 322 mammographic images. These images are selected from the UK National Breast Screening Programme and were digitized using The Joyce-Loebl scanning microdensitometer. The images in the database are categorized into three categories as per their density namely fatty (106 images), fatty-glandular (104 images) and dense-glandular (112 images). Each image in the database is of size 1024 \(\times \) 1024 pixels, with 256 gray scale tones and a horizontal and vertical resolution of 96 dpi. The database also includes location of abnormality, the radius of the circle enclosing the abnormality, its severity and nature of the tissue [45]. In the present work CAD system designs have been proposed for (a) two-class breast tissue density classification i.e. (fatty and dense class) and (b) three-class breast tissue density classification i.e. (fatty, fatty-glandular and dense-glandular classes). For implementing CAD systems for two-class breast tissue density classification, the fatty-glandular and dense-glandular classes are combined and considered as dense class resulting in 106 mammograms belonging to fatty class and 216 mammograms belonging to dense class. The description of the dataset, used for two-class and three-class CAD system designs is shown in Fig. 3.

2.2 Region of Interest (ROI) Selection

The ROI size is selected carefully considering the fact that it should provide a good population of pixels for computing texture features [44]. Different ROI sizes that have been selected in the literature for classification are 256 \(\times \) 256 pixels [26], 512 \(\times \) 384 pixels [28], 200 \(\times \) 200 pixels [29–32] and 300 \(\times \) 300 pixels [39]. Other researchers have pre-processed the mammograms by removal of the pectoral muscle and the background using segmented breast tissue for feature extraction [24, 25, 27, 33–38, 40–43]. The participating radiologist, one of the coauthors opined that for accessing the breast tissue density patterns, visual analysis of texture patterns of the center of the breast tissue is carried out during routine practice. Accordingly, for the present work, ROIs of size 200 \(\times \) 200 pixels are manually extracted from each mammogram. The ROIs are selected from the center of the breast tissue as it has also been asserted by many researchers in their research that the center region of the breast tissue is the densest region and selecting ROI from this part of the breast results in highest performance of the proposed algorithms [29–32, 44]. The selection and extraction of ROI from the breast tissue is shown in Fig. 4.

Fig. 3
figure 3

Dataset description. a Two-class breast tissue density classification. b Three-class breast tissue density classification

Full size image
Fig. 4
figure 4

Sample mammographic image with ROI marked

Full size image

The sample images of ROIs extracted from the mammographic images are shown in Fig. 5.

Fig. 5
figure 5

Sample ROI images. a Fatty tissue ‘mdb012’, b Fatty-glandular tissue ‘mdb014’, c Dense-glandular tissue ‘mdb108’

Full size image

2.3 Experimental Workflow for Design of CAD System for Two-Class and Three-Class Breast Tissue Density Classification

With the advancement in computer technology and artificial intelligence techniques there has been a substantial increase in the opportunities for researchers to investigate the potential of CAD systems for texture analysis and tissue characterization of radiological images [46–58]. Tissue characterization refers to quantitative analysis of the tissue imaging features resulting in accurate distinction between different types of tissues. Thus, the result of tissue characterization is interpreted using numerical values. The overall aim of developing a computerized tissue characterization system is to provide additional diagnostic information about the underlying tissue which cannot be captured by visual inspection of medical images.

Fig. 6
figure 6

Experimental workflow for design of CAD systems for two-class and three class breast tissue density classification

Full size image

The CAD systems are used in the medical imaging as a second opinion tool for the radiologists to gain confidence in their diagnosis. In radiology, CAD systems improve the diagnostic accuracy for medical image interpretation helping the radiologists in detecting the lesions present in the images which might be missed by them.

In general, CAD system design consists of feature extraction module, feature space dimensionality reduction module and classification module. For implementing the proposed CAD system design for breast density classification, 322 ROIs are extracted from 322 images of the MIAS database. The block diagram of experimental workflow followed in the present work is shown in Fig. 6.

For the present CAD system design, ROIs are manually extracted from the mammograms of the MIAS database. In feature extraction module statistical features are extracted from the ROIs. In feature space dimensionality reduction module, PCA is applied to the feature set (training data) to derive its principal components (PCs). The reduced testing dataset is obtained by projecting the data points of feature set (testing data) in the direction of the PCs of feature set (training data). In feature classification module 4 classifiers i.e. k-nearest neighbor (kNN) classifier, probabilistic neural network (PNN) classifier, support vector machine (SVM) classifier and smooth support vector machine (SSVM) classifier are used for the classification task. These classifiers are trained and tested using the reduced texture feature vectors (RTFVs) i.e. set of optimal PCs obtained after applying PCA.

2.3.1 Feature Extraction Module

The feature extraction is the process used to transform the visually extractable and non-extractable features into mathematical descriptors. These descriptors are either shape-based (morphological features) or intensity distribution based (textural features). There are a variety of methods to extract the textural features including statistical, signal processing based and transform domain methods. The different methods of feature extraction are depicted in Fig. 7.

In the present work, the statistical methods are used to extract the texture features from an image based on the gray level intensities of the pixels of that image.

Fig. 7
figure 7

Different feature extraction methods. Note: GLCM: Gray level co-occurrence matrix, GLRLM: Gray level run length matrix, NGTDM: Neighborhood gray tone difference matrix, SFM: Statistical feature matrix, FPS: Fourier power spectrum

Full size image
2.3.1.1 First Order Statistics (FOS) Features

Six features namely average gray level, standard deviation, smoothness, kurtosis and entropy are computed for each ROI [59].

2.3.1.2 Second Order Statistics-Gray Level Co-occurrence Matrix (GLCM) Features

To derive the statistical texture features from GLCM, spatial relationship between two pixels is considered. The GLCM tabulates the number of times the different combinations of pixel pairs of a specific gray level occur in an image for various directions \(\theta = 0^{\circ }, 45^{\circ }, 90^{\circ }, 135^{\circ }\) and different distances d = 1, 2, 3 etc. A total of 13 GLCM features namely angular second moment (ASM), correlation, contrast, variance, inverse difference moment, sum average, sum variance, difference variance, entropy, sum entropy, difference entropy, information measures of correlation-1 and information measures of correlation-2 are computed from each ROI [60–62].

2.3.1.3 Higher Order Statistics-Gray Level Run Length Matrix (GLRLM) Features

To derive the statistical texture features from the GLRLM, spatial relationship between more than two pixels is considered. In a given direction, GLRLM measures the number of times there are runs of consecutive pixels with the same value. Total of 11 GLRLM features namely short run emphasis, long run emphasis, low gray level run emphasis, high gray level run emphasis, short run low gray level emphasis, short run high gray level emphasis, long run low gray level emphasis, long run high gray level emphasis, gray level non uniformity, run length non-uniformity and run percentage are computed from each ROI [63, 64].

2.3.1.4 Edge Features (Absolute Gradient)

The edges in an image contain more information about the texture than other parts of the image. The gradient of an image measures the spatial variation of gray levels across an image. At an edge, there is an abrupt change in gray level of the image. If the gray level variation at some point is abrupt then that point is said to have a high gradient and if the variation is smooth the point is at low gradient. Absolute gradient is used to judge whether the gray level variation in an image is smooth or abrupt. The texture features computed are absolute gradient mean and absolute gradient variance [65].

2.3.1.5 Neighborhood Gray Tone Difference Matrix (NGTDM) Features

NGTDM represents a difference in grayscale between pixels with a certain gray scale and the neighboring pixels. Features extracted from NGTDM are: coarseness, contrast, business, complexity and strength [26, 66].

2.3.1.6 Statistical Feature Matrix (SFM) Features

SFM is used to measure the statistical properties of pixels at several distances within an image. The features computed from SFM are coarseness, contrast, periodicity and roughness.

2.3.1.7 Gray Level Difference Statistics (GLDS)

These features are based on the co-occurrence of a pixel pair having a given absolute difference in gray-levels separated by a particular distance. The extracted features are: homogeneity, contrast, energy, entropy and mean [67, 68].

2.3.2 Feature Space Dimensionality Reduction Module

The texture feature vector (TFV) formed after computing the texture features in the feature extraction module may contain some redundant and correlated features which when used in the classification task can degrade the performance of the proposed CAD system. These redundant features give no extra information that proves to be helpful in discriminating the textural changes exhibited by different density patterns. Hence, to remove these redundant features and obtain the optimal attributes for the classification task, PCA is employed [69–71]. Steps used in the PCA algorithm are:

  1. (1)

    Normalize each feature in dataset to zero mean and unity variance.

  2. (2)

    Obtain co-variance matrix of the training dataset.

  3. (3)

    Obtain Eigen values and Eigen vectors from the co-variance matrix. Eigen vectors give the directions of the PCs.

  4. (4)

    Project the data points in testing dataset in the direction of the PCs of training dataset.

The obtained PCs are uncorrelated to each other and the 1st PC has the largest possible variance out of all the successive PCs. The optimal number of PCs is determined by performing repeated experiments by going through first few PCs i.e. by first considering the first two PCs, then first three PCs and so on, and evaluating the performance of the classifier for each experiment.

2.3.3 Feature Classification Module

Classification is a machine learning technique, used to predict the class membership of unknown data instances based on the training set of data containing instances whose class membership is known. In this module, different classifiers like kNN, PNN, SVM and SSVM are employed to classify the unknown testing instances of mammographic images. The extracted features are normalized in the range [0, 1] by using min-max normalization procedure to avoid any bias caused by unbalanced feature values. The different classifiers employed in the present work are described as below:

2.3.3.1 k-Nearest Neighbor (kNN) Classifier

The kNN classifier is based on the idea of estimating the class of an unknown instance from its neighbors. It tries to cluster the instances of feature vector into disjoint classes with an assumption that instances of feature vector lying close to each other in feature space represent instances belonging to the same class. The class of an unknown instance in testing dataset is selected to be the class of majority of instances among its k-nearest neighbors in the training dataset. The advantage of kNN is its ability to deal with multiple class problems and is robust to noisy data as it averages the k-nearest neighbors [71–74]. Euclidean distance is used as a distance metric. The classification performance of kNN classifier depends on the value of k. In the present work, the optimal value of k and number of PCs to be retained is determined by performing repeated experiments for the values of \(k \in \{1,2, \ldots ,9,10\}\) and number of PCs \(\in \{1,2, \ldots , 14,15\}\). If same accuracy is obtained for more than one value of k, smallest value of k is used to obtain the result.

2.3.3.2 Probabilistic Neural Network (PNN) Classifier

The PNN is a supervised feed-forward neural network used for estimating the probability of class membership [75–77]. The architecture of PNN has four layers: input layer, pattern layer, summation layer and output layer. Primitive values are passed to the ‘n’ neurons in the input unit. Values from the input unit are passed to the hidden units in the pattern layer where responses for each unit are calculated. There are ‘p’ number of neurons in the pattern layer, one for each class. In the pattern layer a probability density function for each class is defined based on the training dataset and optimized kernel width parameter. Values of each hidden unit are summed in the summation layer to get response in each category. Maximum response is taken from all categories in the decision layer to get the class of the unknown instance. The optimal choice of spread parameter (Sp) i.e. the kernel width parameter is critical for the classification using PNN. In the present work, the optimal values used for Sp and optimal number of PCs to design a PNN classifier are determined by performing repeated experiments for values of Sp \(\in \{1,2, \ldots ,9,10\}\) and number of PCs \(\in \{1,2, \ldots , 14,15\}\).

2.3.3.3 Support Vector Machine (SVM) Classifier

The SVM classifier belongs to a class of supervised machine learning algorithms. It is based on the concept of decision planes that define the decision boundary. In SVM, kernel functions are used to map the non-linear training data from input space to a high dimensionality feature space. Some common kernels are polynomial, Gaussian radial basis function and sigmoid. In the present work, SVM classifier is implemented using LibSVM library [78] and the performance of the Gaussian Radial Basis Function kernel is investigated. The critical step for obtaining a good generalization performance is the correct choice of regularization parameter C and kernel parameter \(\gamma \). The regularization parameter C tries to maximize the margin while keeping the training error low. In the present work, ten-fold cross validation is carried out on the training data, for each combination of (C, \(\gamma \)) such that, C \(\in \{2^{-4},2^{-3} , \ldots , 2^{15}\}\) and \(\gamma \in \{2^{-12},2^{-11} , \ldots , 2^{4}\}\). This grid search procedure in parameter space gives the optimum values of C and \(\gamma \) for which training accuracy is maximum [79–83].

2.3.3.4 Smooth Support Vector Machine (SSVM) Classifier

To solve important mathematical problems related to programming, smoothing methods are extensively used. SSVM works on the idea of smooth unconstrained optimization reformulation based on the traditional quadratic program which is associated with SVM [84, 85]. For implementing SSVM classifier, the SSVM toolbox developed by Laboratory of Data Science and Machine Intelligence, Taiwan was used [86]. Similar to SVM implementation in case of SSVM also, ten-fold cross validation is carried out on training data for each combination of (C, \(\gamma \)) such that, C \(\in \{2^{-4},2^{-3} , \ldots , 2^{15}\}\) and \(\gamma \in \{2^{-12},2^{-11} , \ldots , 2^{4}\}\). This grid search procedure in parameter space gives the optimum values of C and \(\gamma \) for which training accuracy is maximum.

2.3.3.5 Classifier Performance Evaluation Criteria

The performance of the CAD system for two-class and three class breast tissue density classification can be measured using overall classification accuracy (OCA) and individual class accuracy (ICA). These values can be calculated using the confusion matrix (CM).

$$\begin{aligned} \mathrm{{OCA}} = \frac{\Sigma \text { No. of correctly classified images of each class}}{\text {Total images in testing dataset}} \end{aligned}$$
(1)
$$\begin{aligned} {\text {ICA}} = \frac{{{\text {No. of correctly classified images of one class}}}}{{{\text {Total no. of images in the testing dataset for that class}}}} \end{aligned}$$
(2)

3 Results

Rigorous experimentation was carried out in the present work to characterize the mammographic images as per breast tissue density. The experiments carried out in the present work are described in Tables 4 and 5, respectively for two-class and three-class breast tissue density classification.

Table 4 Description of experiments carried out for two-class breast tissue density classification
Full size table
Table 5 Description of experiments carried out for three-class breast tissue density classification
Full size table

3.1 Experiments Carried Out for Two-Class Breast Tissue Density Classification

3.1.1 Experiment 1: To Obtain the Classification Performance of Statistical Features for Two-Class Breast Tissue Density Classification Using kNN, PNN, SVM and SSVM Classifiers

In this experiment, classification performance of TFV containing different statistical features is evaluated for two-class breast tissue density classification using different classifiers. The results of the experiment are shown in Table 6. It can be observed from the table that for statistical features, the overall classification accuracy of 92.5, 91.3, 90.6 and 92.5 % is achieved using kNN, PNN, SVM and SSVM classifiers, respectively. It can also be observed that the highest in individual class accuracy for fatty class is 83.0 % with SSVM classifier and highest individual class accuracy for dense class is 100 %, using PNN classifier. Out of total 161 testing instances, 12 instances (12/161) are misclassified in case of kNN, 14 instances (14/161) are misclassified in case of PNN, 16 instances (16/161) are misclassified in case of SVM and 12 instances (12/161) are misclassified in case of SSVM classifier.

Table 6 Classification performance of statistical features using kNN, PNN, SVM and SSVM classifiers for two-class breast tissue density classification
Full size table

3.1.2 Experiment 2: To Obtain the Classification Performance of Statistical Features for Two-Class Breast Tissue Density Classification Using PCA-kNN, PCA-PNN, PCA-SVM and PCA-SSVM Classifiers

In this experiment, classification performance of reduced texture feature vector (RTFV) derived by applying PCA to TFV containing different statistical features is evaluated for two-class breast tissue density classification using different classifiers. The results are shown in Table 7.

Table 7 Classification performance of statistical features using PCA-kNN, PCA-PNN, PCA-SVM and PCA-SSVM classifiers for two-class breast tissue density classification
Full size table

It can be observed from the table that the overall classification values of 91.9, 91.3, 93.7 and 94.4 % have been achieved using the PCA-kNN, PCA-PNN, PCA-SVM and PCA-SSVM classifiers, respectively. It can also be observed that the highest individual class accuracy for fatty class is 88.6 % using PCA-SSVM classifier and that for dense class is 100 % using PCA-PNN and PCA-SVM classifiers. Out of total 161 testing instances, 13 instances (13/161) are misclassified in case of PCA-kNN, 14 instances (14/161) are misclassified in case of PCA-PNN, 10 instances (10/161) are misclassified in case of PCA-SVM and 9 instances (9/161) are misclassified in case of PCA-SSVM classifier.

From the results obtained from the above experiments, it can be observed that for two-class breast tissue density, PCA-SSVM classifier achieves highest classification accuracy of 94.4 % using first 10 PCs.

3.2 Experiments Carried Out for Three-Class Breast Tissue Density Classification

3.2.1 Experiment 1: To Obtain the Classification Performance of Statistical Features for Three-Class Breast Tissue Density Classification Using kNN, PNN, SVM and SSVM Classifiers

In this experiment, the classification performance of TFV containing different statistical features is evaluated for three-class breast tissue density classification using different classifiers. The results are shown in Table 8.

Table 8 Classification performance of statistical features using kNN, PNN, SVM and SSVM classifiers for three-class breast tissue density classification
Full size table
Table 9 Classification performance of statistical features using PCA-kNN, PCA-PNN, PCA-SVM and PCA-SSVM classifiers for three-class breast tissue density classification
Full size table

It can be observed from the table that the overall classification accuracy of 86.9, 85.0, 83.8 and 82.6 % is achieved using kNN, PNN, SVM and SSVM classifiers, respectively. The highest individual class accuracy for fatty class is 94.3 % using SVM classifier, for fatty-glandular class the highest individual class accuracy achieved is 88.4 % using SSVM classifier and for the dense-glandular class, highest individual class accuracy achieved is 96.4 % using kNN classifier. Out of total 161 testing instances, 21 instances (21/161) are misclassified in case of kNN, 24 instances (24/161) are misclassified in case of PNN, 26 instances (26/161) are misclassified in case of SVM and 28 instances (28/161) are misclassified in case of SSVM classifier.

3.2.2 Experiment 2: To Obtain the Classification Performance of Statistical Features for Three-Class Breast Tissue Density Classification Using PCA-kNN, PCA-PNN, PCA-SVM and PCA-SSVM Classifiers

In this experiment, the classification performance of RTFV derived by applying PCA to TFV containing different statistical features is evaluated for three-class breast tissue density classification using different classifiers. The results are shown in Table 9. It can be observed from the table that the overall classification of 85.0, 84.4, 86.3 and 85.0 % is achieved using PCA-kNN, PCA-PNN, PCA-SVM and PCA-SSVM classifiers, respectively. The highest individual class accuracy for fatty class is 88.6 % using PCA-SVM classifier, for fatty-glandular class the highest individual class accuracy achieved is 84.6 % using PCA-PNN and PCA-SSVM classifiers and for the dense-glandular class, highest individual class accuracy achieved is 98.2 % using PCA-kNN classifier. Out of total 161 testing instances, 24 instances (24/161) are misclassified in case of PCA-kNN, 25 instances (25/161) are misclassified in case of PCA-PNN, 22 instances (22/161) are misclassified in case of PCA-SVM and 24 instances (24/161) are misclassified in case of PCA-SSVM classifier.

Fig. 8
figure 8

Proposed SSVM based CAD system design for two-class breast tissue density classification

Full size image

For three-class breast tissue density classification, it can be observed from the above experiments that highest classification accuracy of 86.9 % is achieved using the kNN classifier, however it should also be noted that PCA-SVM classifier achieves the highest classification accuracy of 86.3 % by using only the first 4 PCs obtained by applying PCA to the TFV of statistical features. Thus CAD system design based on PCA-SVM classifier can be considered to be the best choice for three-class breast tissue density classification.

4 Conclusion

Fig. 9
figure 9

Proposed CAD system design for three-class breast tissue density classification

Full size image

From the rigorous experiments carried out in the present work, it can be observed that for two-class breast tissue density, PCA-SSVM based CAD system using first 10 PCs obtained by applying PCA to the TFV derived using statistical features yields highest OCA of 94.4 % using mammographic images. It could also be observed that the PCA-SVM based CAD system using first 4 PCs obtained by applying PCA to the TFV derived using statistical features yields highest OCA of 86.3 % for three-class breast tissue density classification using mammographic images. It can be concluded that statistical features are significant to account for the textural changes exhibited by the fatty and dense breast tissues. The proposed CAD system designs derived using the above results are shown in Figs. 8 and 9 for two-class and three-class breast tissue density classification, respectively.

The promising results obtained by the proposed CAD system designs indicate their usefulness to assist radiologists for characterization of breast tissue density during routine clinical practice.