*2.1.3 Localization and extraction of the pectoral muscle*

In the mammogram preprocessing, the identification and extraction of the pectoral muscle is one of the major challenges in Medio lateral Oblique (MLO) view. It could be noticed here, that this step is important to improve the diagnostic accuracy of the CAD system. The difficulty in removing the pectoral muscle is due to the following reasons [27]:


*Medical Image Classification Using the Discriminant Power Analysis (DPA) of Discrete Cosine… DOI: http://dx.doi.org/10.5772/intechopen.94026*

In this chapter, we present a new algorithm for pectoral muscle suppression, this operation is based on the Localization of the triangular region that contains the Pectoral Muscle, where the Seeded Region Growing (SRG) algorithm is invoked in this operation.


Seeded Region Growing (SRG) is a useful image segmentation technique for medical images that is initially proposed by R. Adams et *al.* [28]. This technique is robust, fast and consists of three major steps: seed selection, region growing, and region merging.

The advantage of applying the (SRG) method into the localized triangular ABC region (**Figure 3**) is to remove only the pectoral muscle, without completely suppressing the triangular region as in some other methods. **Figures 3**–**5** show a visual scheme of the proposed algorithm.

The Seed point is selected automatically by considering the results obtained from step (4) of algorithm 1.

**Figure 5(a)** shows the cropped image, where **Figure 5(b)** shows the selected region of interest (ROI). All obtained (ROI) images are resized in order to get the same dimension.

**Figure 3.** *Localization of the ABC triangle in the left upper quadrant.*

Step (2) Mark all regions in the thresholded image (i.e., Artifacts, labels, … ).

*The preprocessing steps of mammogram image: (a) original image, (b) noise removed image, (c) binary image,*

In the mammogram preprocessing, the identification and extraction of the pectoral muscle is one of the major challenges in Medio lateral Oblique (MLO) view. It could be noticed here, that this step is important to improve the diagnostic accuracy of the CAD system. The difficulty in removing the pectoral muscle is due to the

• Homogeneous area situated in the top left/right corner contains the brightest

• The pectoral muscle boundary shape is concave, convex or a mixture of both of

• The density of the pectoral muscle area appears at approximately with similar

• Varying position, size, shape and texture from image to image.

Step (3) Calculate the area of each region, and select the largest one. Step (4) The result of the step (3) is then used as a mask of the original

*Real Perspective of Fourier Transforms and Current Developments in Superconductivity*

grayscale mammography image.

following reasons [27]:

them.

**52**

**Figure 2.**

pixels in the image.

density as the dense tissues.

*2.1.3 Localization and extraction of the pectoral muscle*

*(d) largest area, (e) image right flipped, (f) parenchyma of the breast.*

coefficients, while these coefficients do not have the same aptitude to discriminate between the different classes. However, the use of the standard approaches to select these coefficients are not always efficient in selecting the most discriminative coefficients. In this chapter, we present a novel features extraction technique that is composed of two phases. In the first one, the discrete cosine transforms (DCT) is applied on all the obtained regions of interest (ROI), and then the low frequency coefficients in the upper left corner (ULC) are retained. In the second phase, a combination of the retained frequency coefficients with the discriminative power coefficients algorithm [24] is proposed to calculate the discrimination power matrix, which is given by the ratio between the two variances, the between-class variance and the within-class variance. Where, high classification accuracies are

*Medical Image Classification Using the Discriminant Power Analysis (DPA) of Discrete Cosine…*

This mathematical tool transforms any signal or image from the spatial domain to frequency domain. It has been widely used in digital signal and image

processing, where its major advantages over the FFT reside in giving real coefficients. In addition, it concentrates the information in the low frequency region. Fast implementation can be obtained by using the FFT algorithm [29] which make the use of this transform very simple in real-time applications. It is

> *M* X�1 *i*¼0

X *N*�1

*I i*ð Þ , *<sup>j</sup> cos* ð Þ <sup>2</sup>*<sup>i</sup>* <sup>þ</sup> <sup>1</sup> *<sup>u</sup><sup>π</sup>*

1 ffiffi 2 p *u* ¼ 0

1 ffiffi 2 p *v* ¼ 0

After the calculation of the DCT coefficients, we retain only the 512x512 region in the upper left corner (ULC coefficients). In the feature's selection step, a new most discriminative power analysis (DPA) algorithm has been proposed to select the most significant features that have the high discrimination power (DP) values.

The calculation of the (DP) for each transformed coefficient is shown in the (DCT-DPA) algorithm shown below. Considering an image *Iij* of size N � M. *Fuv* are the transformed coefficient by the 2D-DCT. The used database has C classes each is composed of S training images. Consequently, a total of C � S training images are

1 *otherwise*

1 *otherwise*

2*M*

� � *cos* ð Þ <sup>2</sup>*<sup>j</sup>* <sup>þ</sup> <sup>1</sup> *<sup>v</sup><sup>π</sup>*

2*N* � � (1)

(2)

(3)

*j*¼0

αð Þ¼ *u*

αð Þ¼ *v*

and *F u*ð Þ , *v* is the DCT coefficient matrix of the image *I i*ð Þ , *j* .

*2.2.2 Discriminative power analysis of DCT coefficients*

with 0 ≤*u*≤ M, 0 ≤*v*≤ *N*, and αð Þ *u* , αð Þ*v* are defined by Eq. (2), Eq. (3)

8 ><

>:

8 ><

>:

represented by high rate values.

1 ffiffiffiffiffiffiffiffiffi *MN* <sup>p</sup> *<sup>α</sup>*ð Þ *<sup>u</sup> <sup>α</sup>*ð Þ*<sup>v</sup>*

defined by Eq. (1):

*F u*ð Þ¼ , *v*

used.

**55**

*2.2.1 Discrete cosine transform (DCT)*

*DOI: http://dx.doi.org/10.5772/intechopen.94026*

**Figure 4.**

*Pectoral muscle segmentation steps: (a) mammogram top left quadrant, (b) triangular mask, (c) masked top left quadrant, (d) suppression of the pectoral muscle, (e) cropped top left quadrant without pectoral muscle.*

**Figure 5.**

*Identification of the region of interest (ROI). (a) Cropped image, and (b) Selected region of Interest (ROI).*

### **2.2 Frequency domain features extraction and selection**

Features extraction plays an essential role, and a challenging step in the accurate classification and diagnostic rate of mammograms. In this chapter, we have used features extracted from the image in the frequency domain representation. The most used transform to this domain is the discrete Fourier transform with its fast algorithm (FFT) [29]. In classification problems, for example, Fourier descriptors have been used for pattern recognition [30, 31]. Another interesting transform is the discrete cosine transform (DCT) which decomposes the image on a set of cosine functions. It provides a real representation of the image contrary to the FFT, which give complex coefficients.

The frequency domain features are very used in the classification and pattern recognition field. However, the hard task is the selection of the transformed

*Medical Image Classification Using the Discriminant Power Analysis (DPA) of Discrete Cosine… DOI: http://dx.doi.org/10.5772/intechopen.94026*

coefficients, while these coefficients do not have the same aptitude to discriminate between the different classes. However, the use of the standard approaches to select these coefficients are not always efficient in selecting the most discriminative coefficients. In this chapter, we present a novel features extraction technique that is composed of two phases. In the first one, the discrete cosine transforms (DCT) is applied on all the obtained regions of interest (ROI), and then the low frequency coefficients in the upper left corner (ULC) are retained. In the second phase, a combination of the retained frequency coefficients with the discriminative power coefficients algorithm [24] is proposed to calculate the discrimination power matrix, which is given by the ratio between the two variances, the between-class variance and the within-class variance. Where, high classification accuracies are represented by high rate values.

### *2.2.1 Discrete cosine transform (DCT)*

This mathematical tool transforms any signal or image from the spatial domain to frequency domain. It has been widely used in digital signal and image processing, where its major advantages over the FFT reside in giving real coefficients. In addition, it concentrates the information in the low frequency region. Fast implementation can be obtained by using the FFT algorithm [29] which make the use of this transform very simple in real-time applications. It is defined by Eq. (1):

$$F(u,v) = \frac{1}{\sqrt{MN}} \, a(u)a(v) \sum\_{i=0}^{M-1} \sum\_{j=0}^{N-1} I(i,j) \cos\left(\frac{(2i+1)u\pi}{2M}\right) \cos\left(\frac{(2j+1)v\pi}{2N}\right) \tag{1}$$

with 0 ≤*u*≤ M, 0 ≤*v*≤ *N*, and αð Þ *u* , αð Þ*v* are defined by Eq. (2), Eq. (3)

$$\alpha(u) = \begin{cases} \frac{1}{\sqrt{2}}u = 0\\ 1 \, otherwise \end{cases} \tag{2}$$

$$a(v) = \begin{cases} \frac{1}{\sqrt{2}}v = 0\\ 1 \, \text{otherwise} \end{cases} \tag{3}$$

and *F u*ð Þ , *v* is the DCT coefficient matrix of the image *I i*ð Þ , *j* .

After the calculation of the DCT coefficients, we retain only the 512x512 region in the upper left corner (ULC coefficients). In the feature's selection step, a new most discriminative power analysis (DPA) algorithm has been proposed to select the most significant features that have the high discrimination power (DP) values.

### *2.2.2 Discriminative power analysis of DCT coefficients*

The calculation of the (DP) for each transformed coefficient is shown in the (DCT-DPA) algorithm shown below. Considering an image *Iij* of size N � M. *Fuv* are the transformed coefficient by the 2D-DCT. The used database has C classes each is composed of S training images. Consequently, a total of C � S training images are used.

**2.2 Frequency domain features extraction and selection**

give complex coefficients.

**Figure 5.**

**54**

**Figure 4.**

Features extraction plays an essential role, and a challenging step in the accurate classification and diagnostic rate of mammograms. In this chapter, we have used features extracted from the image in the frequency domain representation. The most used transform to this domain is the discrete Fourier transform with its fast algorithm (FFT) [29]. In classification problems, for example, Fourier descriptors have been used for pattern recognition [30, 31]. Another interesting transform is the discrete cosine transform (DCT) which decomposes the image on a set of cosine functions. It provides a real representation of the image contrary to the FFT, which

*Identification of the region of interest (ROI). (a) Cropped image, and (b) Selected region of Interest (ROI).*

*Pectoral muscle segmentation steps: (a) mammogram top left quadrant, (b) triangular mask, (c) masked top left quadrant, (d) suppression of the pectoral muscle, (e) cropped top left quadrant without pectoral muscle.*

*Real Perspective of Fourier Transforms and Current Developments in Superconductivity*

The frequency domain features are very used in the classification and pattern

recognition field. However, the hard task is the selection of the transformed

**2.3 Classification**

extraction.

advantages and disadvantages.

boundary is given by [33]:

clear.

**57**

*2.3.2 Artificial neural network (ANN)*

*2.3.1 The support vector machine (SVM)*

*DOI: http://dx.doi.org/10.5772/intechopen.94026*

The classification is the last step to identify if the breast tumor is benign or malignant. It plays a vital role in the medical image diagnosis field. Therefore, the images need to be classified with maximum accuracy. As a result, some automated classification methods have been proposed. In this part, we presented some of these classifiers including NB, SVM, ANN, and KNN that are used for breast cancer detection. A brief description of these algorithms will be presented as well as their

*Medical Image Classification Using the Discriminant Power Analysis (DPA) of Discrete Cosine…*

SVMs are a set of machine learning algorithms that help solve problems associated with classification, regression, and fault detection. They are considered to be among the algorithms that are distinguished by their strong theoretical guarantee and their great flexibility. They are also considered among the easiest algorithms in terms of ease of use even in cases where there is a little knowledge of data

The SVMs use increases widely in medical imaging field especially for breast cancer diagnosis [32]. The basic principle of SVM in this chapter is to separate and classify images into two categories malignant and benign using a hyperplane decision boundary, ensuring a maximum distance between different data sets and the boundary separating them. For linearly separable data, the hyperplane decision

*<sup>x</sup>* <sup>þ</sup> *<sup>b</sup>* <sup>¼</sup> <sup>X</sup>*<sup>n</sup>*

where *x* is the input data set vector *w* is (*n*) dimensional and b is a bias. The main

2. It works very well in cases where the separation margin between data sets is

3. It can also solve any complex problem by specifying different kernel function.

The main disadvantages of the SVM algorithm are the difficulty of choosing the

The artificial neural networks are feed-forward networks that can be trained to classify inputs according to target classes. Generally, a neural network is composed of three layers: an input layer, a hidden layer and an output layer [34]. Usually, only the input and output signals of the network are already known [17]. The process of training an artificial neural network before setting it up represents a serious operation and affects directly the final obtained results. This operation depends on some constraints like the initial parameters setting, the use weights, bias and finally the used algorithm learning rate. To adjust the weights of the ANN, one can use some

*i*¼1 *wt i*

*xi* þ *b* (5)

*g x*ð Þ¼ *<sup>w</sup><sup>t</sup>*

advantages of the (SVM) classifier can generally be listed as follows [15]:

appropriate kernel function and the long training time for large datasets.

1.SVM generally gives good accuracy with less memory use.


The *Dp i*ð Þ , *j* matrix is defined as the ratio of between-class variance and withinclass variance. Large values of DP imply a large discrimination power of the coefficients. The selection of the DCT coefficients is made in an adaptive way according to their corresponding DP values, where the DCT coefficients with higher DP are preserved [24]. The *Dp i*ð Þ , *j* matrix is then transformed into a column vector that will be sorted in descending order. Therefore, the number *k* selected among the highest values, defines the number of the features to be used by the classifier. By setting the positions of selected features as ones and the others as zeros, we create a mask that can be used later in the selection process of the classification step. Alternatively, we can use a thresholding step of the *DP* matrix to create a mask that contain *k* elements as follows:

$$\text{Mask}(i, j) = \begin{cases} 1 & \text{D}p(i, j) \ge T \\ 0 & \text{otherwise} \end{cases} \tag{4}$$

with 1≤ *k*≤ Mx*N* and *T* is the *kth* highest value in the *DP* matrix.

*Medical Image Classification Using the Discriminant Power Analysis (DPA) of Discrete Cosine… DOI: http://dx.doi.org/10.5772/intechopen.94026*

## **2.3 Classification**

The classification is the last step to identify if the breast tumor is benign or malignant. It plays a vital role in the medical image diagnosis field. Therefore, the images need to be classified with maximum accuracy. As a result, some automated classification methods have been proposed. In this part, we presented some of these classifiers including NB, SVM, ANN, and KNN that are used for breast cancer detection. A brief description of these algorithms will be presented as well as their advantages and disadvantages.

### *2.3.1 The support vector machine (SVM)*

SVMs are a set of machine learning algorithms that help solve problems associated with classification, regression, and fault detection. They are considered to be among the algorithms that are distinguished by their strong theoretical guarantee and their great flexibility. They are also considered among the easiest algorithms in terms of ease of use even in cases where there is a little knowledge of data extraction.

The SVMs use increases widely in medical imaging field especially for breast cancer diagnosis [32]. The basic principle of SVM in this chapter is to separate and classify images into two categories malignant and benign using a hyperplane decision boundary, ensuring a maximum distance between different data sets and the boundary separating them. For linearly separable data, the hyperplane decision boundary is given by [33]:

$$\log(\mathbf{x}) = w^t \mathbf{x} + b = \sum\_{i=1}^{n} w\_i^t \mathbf{x}\_i + b \tag{5}$$

where *x* is the input data set vector *w* is (*n*) dimensional and b is a bias. The main advantages of the (SVM) classifier can generally be listed as follows [15]:

1.SVM generally gives good accuracy with less memory use.


The main disadvantages of the SVM algorithm are the difficulty of choosing the appropriate kernel function and the long training time for large datasets.

### *2.3.2 Artificial neural network (ANN)*

The artificial neural networks are feed-forward networks that can be trained to classify inputs according to target classes. Generally, a neural network is composed of three layers: an input layer, a hidden layer and an output layer [34]. Usually, only the input and output signals of the network are already known [17]. The process of training an artificial neural network before setting it up represents a serious operation and affects directly the final obtained results. This operation depends on some constraints like the initial parameters setting, the use weights, bias and finally the used algorithm learning rate. To adjust the weights of the ANN, one can use some

The *Dp i*ð Þ , *j* matrix is defined as the ratio of between-class variance and withinclass variance. Large values of DP imply a large discrimination power of the coefficients. The selection of the DCT coefficients is made in an adaptive way according to their corresponding DP values, where the DCT coefficients with higher DP are preserved [24]. The *Dp i*ð Þ , *j* matrix is then transformed into a column vector that will be sorted in descending order. Therefore, the number *k* selected among the highest values, defines the number of the features to be used by the classifier. By setting the positions of selected features as ones and the others as zeros, we create a mask that can be used later in the selection process of the classification step. Alternatively, we can use a thresholding step of the *DP* matrix to create a mask that

*Real Perspective of Fourier Transforms and Current Developments in Superconductivity*

1 *Dp i*ð Þ , *j* ≥ *T* 0 *otherwise:*

(4)

*Mask i*ð Þ¼ , *j*

with 1≤ *k*≤ Mx*N* and *T* is the *kth* highest value in the *DP* matrix.

(

contain *k* elements as follows:

**56**

learning methods like the back-propagation or an optimization algorithm. In this work, the input layer is based on the number of the features selected, the hidden layer contains 10 neurons, and finally the out layer.

### *2.3.3 Naive Bayes classifier (NB)*

Naive Bayes is becoming increasingly popular in many areas, it has shown excellent performances for classification tasks. It is a simple probabilistic classifier based on Bayes' theorem, which is based on conditional probabilities [35]. A Naive Bayes classifier assigns a new observation to the most probable class, assuming the features are conditionally independent for a given the class value. It is easy and fast to predict the class of the test data set, but their biggest disadvantage is its requirement to an independent predictor [15].

### *2.3.4* K*-nearest neighbors (KNN)*

*K*-nearest neighbors' classifier is a statistical non-parametric method that is used for both classification and regression [36]. In its simplest version, the *K*NN takes an arbitrary number (*k*) of neighbors nearer from the training set, and for each test point we start by determining all of its *k*-nearest neighbors among the learning points. The class that we assign to the new point is then the more frequent. In the KNN the Euclidean distance metric is used and it is given by:

$$d(\mathbf{x}, y) = \sqrt{\sum\_{i=1}^{k} \left(\mathbf{x}\_i - y\_i\right)^2} \tag{6}$$

Where:

*DOI: http://dx.doi.org/10.5772/intechopen.94026*

the average of ten runs.

*neighbors.*

**Table 1.**

**Table 2.**

**59**

*represented by bold values.*

*TN* (True Negative) is the number of a benign classified as benign. *TP* (True Positive) is the number of a malignant classified as malignant. *FN* (False Negative) is the number of a benign classified as malignant. *FP* (False Positive) is the number of a malignant classified as benign.

In this test, we have calculated the *Dp* matrix using a set of 50 images of benign mammograms and another 50 images of malignant mammograms. These images are randomly selected as shown in the DCT-DPA algorithm. It is very important to select an equal number of samples from each class. The increase of the number of samples implies an increase of the efficiency of the performance of the classifier. However, the best results in this test are obtained using 50–50 mammogram images. Then, the database is randomly divided into train and test data sets. We have taken 113 (ROIs) divided into 70% for training and 30% for testing. The given results are

*Medical Image Classification Using the Discriminant Power Analysis (DPA) of Discrete Cosine…*

**Table 1** shows a comparison of the measured performances of the SVM, ANN, NB and KNN classifiers. It is observed that the classification accuracy can reach 100% for the (ANN) classifier, is 98.8, 96.7%, 87.3% for SVM, NB and KNN

**Classifiers Sensitivity (%) Specificity (%) Accuracy (%)** KNN 91.05 82.67 87.3 NB 97.9 97.3 96.7 SVM 99.5 98.1 98.8 ANN **100 100 100**

*Abbreviations: ANN, artificial neural network; SVM, support vector machines; NB, Naive Bayes, KNN, K-nearest*

128x128 60 95.6 86.76 90.6 77.9

256x256 60 98.2 91.2 93.2 75.0

512x512 60 98.2 92.1 93.8 77.0

1024x1024 60 98.2 92.6 93.1 82.6

*Abbreviations: ANN, artificial neural network; SVM, support vector machines; NB, Naive Bayes, KNN, K-nearest neighbors.*

*Classification accuracy with various sizes of ULC and different numbers of features. Where the best results are*

**ANN SVM NB KNN**

80 96.5 90.3 92.3 78.5 100 98.2 94.7 92.6 79.7

80 97.3 91.7 95.3 75.8 100 98.2 93.8 93.8 76.1

80 99.1 97.3 97.3 79.1 100 **100 98.8 97.6 87.3**

80 96.5 88.5 93.2 83.5 100 97.3 91.7 94.1 85.6

*Classification performance using ANN, SVM, NB and KNN classifiers.*

**ULC size N. of Features Accuracy (%)**

where *xi* is the test sample with *k* features and *yi* specified the training samples with *k* features. The Advantages of using KNN are that it is robust to noisy training data, and it is effective when used with large training data. On the other hand, it needs to determine the number of nearest neighbors (*k*) and the distance-based learning.

### **3. Results and discussions**

To validate the proposed system, experiments were performed on the digital mammography images from the Mammographic Image Analysis Society (MIAS) database [25]. The MIAS database is a standard and publicly available database of digital mammogram images. Each mammogram is 1024 � 1024 pixels of size with a resolution of 200 microns. MIAS contains 322 mammograms for right and left breast of 161 patients in the mediolateral oblique (MLO) view, 61 mammograms were diagnosed as benign, 54 as malignant and 207 normal. The performance of the proposed method has been tested based on algorithms' accuracy, sensitivity and specificity using the following expressions:

$$\text{Sensitivity} = \frac{\text{TP}}{\text{TP} + \text{FN}} \times \text{100 } (\text{\%}) \tag{7}$$

$$\text{Specificity} = \frac{\text{TN}}{\text{TN} + \text{FP}} \times \mathbf{100} \text{ (\%)}\tag{8}$$

$$\text{Accuracy} = \frac{\text{TN} + \text{TP}}{\text{TN} + \text{FN} + \text{FP} + \text{TP}} \times \mathbf{100} \ (\text{\%}) \tag{9}$$

*Medical Image Classification Using the Discriminant Power Analysis (DPA) of Discrete Cosine… DOI: http://dx.doi.org/10.5772/intechopen.94026*

### Where:

learning methods like the back-propagation or an optimization algorithm. In this work, the input layer is based on the number of the features selected, the hidden

*Real Perspective of Fourier Transforms and Current Developments in Superconductivity*

Naive Bayes is becoming increasingly popular in many areas, it has shown excellent performances for classification tasks. It is a simple probabilistic classifier based on Bayes' theorem, which is based on conditional probabilities [35]. A Naive Bayes classifier assigns a new observation to the most probable class, assuming the features are conditionally independent for a given the class value. It is easy and fast to predict the class of the test data set, but their biggest disadvantage is its require-

*K*-nearest neighbors' classifier is a statistical non-parametric method that is used for both classification and regression [36]. In its simplest version, the *K*NN takes an arbitrary number (*k*) of neighbors nearer from the training set, and for each test point we start by determining all of its *k*-nearest neighbors among the learning points. The class that we assign to the new point is then the more frequent. In the

> X*<sup>k</sup> i*¼1

where *xi* is the test sample with *k* features and *yi* specified the training samples with *k* features. The Advantages of using KNN are that it is robust to noisy training data, and it is effective when used with large training data. On the other hand, it needs to determine the number of nearest neighbors (*k*) and the distance-based

To validate the proposed system, experiments were performed on the digital mammography images from the Mammographic Image Analysis Society (MIAS) database [25]. The MIAS database is a standard and publicly available database of digital mammogram images. Each mammogram is 1024 � 1024 pixels of size with a resolution of 200 microns. MIAS contains 322 mammograms for right and left breast of 161 patients in the mediolateral oblique (MLO) view, 61 mammograms were diagnosed as benign, 54 as malignant and 207 normal. The performance of the proposed method has been tested based on algorithms' accuracy, sensitivity and

*TP* þ *FN*

*TN* þ *FP*

*TN* þ *FN* þ *FP* þ *TP*

� 100 %ð Þ (7)

� 100 %ð Þ (8)

� 100 %ð Þ (9)

*Sensitivity* <sup>¼</sup> *TP*

*Specificity* <sup>¼</sup> *TN*

*Accuracy* <sup>¼</sup> *TN* <sup>þ</sup> *TP*

r

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

*xi* � *yi* � �<sup>2</sup>

(6)

KNN the Euclidean distance metric is used and it is given by:

*d x*ð Þ¼ , *y*

layer contains 10 neurons, and finally the out layer.

*2.3.3 Naive Bayes classifier (NB)*

ment to an independent predictor [15].

*2.3.4* K*-nearest neighbors (KNN)*

**3. Results and discussions**

specificity using the following expressions:

learning.

**58**

*TN* (True Negative) is the number of a benign classified as benign.

*TP* (True Positive) is the number of a malignant classified as malignant.

*FN* (False Negative) is the number of a benign classified as malignant.

*FP* (False Positive) is the number of a malignant classified as benign.

In this test, we have calculated the *Dp* matrix using a set of 50 images of benign mammograms and another 50 images of malignant mammograms. These images are randomly selected as shown in the DCT-DPA algorithm. It is very important to select an equal number of samples from each class. The increase of the number of samples implies an increase of the efficiency of the performance of the classifier. However, the best results in this test are obtained using 50–50 mammogram images. Then, the database is randomly divided into train and test data sets. We have taken 113 (ROIs) divided into 70% for training and 30% for testing. The given results are the average of ten runs.

**Table 1** shows a comparison of the measured performances of the SVM, ANN, NB and KNN classifiers. It is observed that the classification accuracy can reach 100% for the (ANN) classifier, is 98.8, 96.7%, 87.3% for SVM, NB and KNN


*Abbreviations: ANN, artificial neural network; SVM, support vector machines; NB, Naive Bayes, KNN, K-nearest neighbors.*

### **Table 1.**

*Classification performance using ANN, SVM, NB and KNN classifiers.*


### **Table 2.**

*Classification accuracy with various sizes of ULC and different numbers of features. Where the best results are represented by bold values.*

**Figure 6.** *Classification accuracy performances vs. the ULC sizes with 100 features.*

respectively. We have evaluated the classification performances of the proposed algorithm according to the number of the used features in the classification.

The SVM, ANN, NB and KNN classifiers are used to classify input images into benign or malignant. The sensitivity, accuracy and specificity are shown in **Table 2**. According to the results in **Table 2**, we can see that small number of features (100 features in this case) can achieve best performances in the case of 512x512 ULC size. In addition, we have studied the effect of the ULC size on the obtained results. The accuracy curve of the classification accuracy versus the ULC size is shown in **Figure 6**. The number of used features is 100 features.

**Figure 7** represents the variation of the classification accuracy according to different features' number with a fixed ULC size of 512x512. **Figure 8** demonstrates the classification performance of ANN using the confusion matrix for training, test and validation data.

**Figure 8.**

**61**

*Confusion matrix for training, test and validation data.*

*DOI: http://dx.doi.org/10.5772/intechopen.94026*

**Authors Year Database Classifier Classes Accuracy (%)** Lima [12] 2016 MIAS SVM 2 94.1 Singh [37] 2017 MIAS RF 2 97.3 Elmoufidi [38] 2017 MIAS SVM 2 94.4

*Medical Image Classification Using the Discriminant Power Analysis (DPA) of Discrete Cosine…*

Benzebouchi [22] 2019 MIAS SVM 2 94.0

Taifi [18] 2020 MIAS SVM 2 94.1

SVM NB

SVM RF NB

2

3

KNN 2 88.8

98.5 95

94.1 92.6

92.5 90.0

99.4 98.2 97.7

2 100

2 99.1

Mughal [20] 2018 MIAS NNB 2

El-Sokary [39] 2019 MIAS SVM 2

Benhassine [15] 2019 MIAS ANN

Benhassine [17] 2020 MIAS ANN

To show the efficiency of the presented technique, **Table 3** shows a comparison between the results of the proposed algorithm with previous results, which are reported in the literature. We can see that the proposed CAD system gives better accuracy results compared to those obtained using the other methods.

**Figure 7.** *Classification performances vs. the number of features. (ULC size of 512x512).*

*Medical Image Classification Using the Discriminant Power Analysis (DPA) of Discrete Cosine… DOI: http://dx.doi.org/10.5772/intechopen.94026*

**Figure 8.** *Confusion matrix for training, test and validation data.*


respectively. We have evaluated the classification performances of the proposed algorithm according to the number of the used features in the classification.

*Real Perspective of Fourier Transforms and Current Developments in Superconductivity*

**Figure 6**. The number of used features is 100 features.

*Classification accuracy performances vs. the ULC sizes with 100 features.*

and validation data.

**Figure 7.**

**60**

**Figure 6.**

The SVM, ANN, NB and KNN classifiers are used to classify input images into benign or malignant. The sensitivity, accuracy and specificity are shown in **Table 2**. According to the results in **Table 2**, we can see that small number of features (100 features in this case) can achieve best performances in the case of 512x512 ULC size. In addition, we have studied the effect of the ULC size on the obtained results. The accuracy curve of the classification accuracy versus the ULC size is shown in

**Figure 7** represents the variation of the classification accuracy according to different features' number with a fixed ULC size of 512x512. **Figure 8** demonstrates the classification performance of ANN using the confusion matrix for training, test

between the results of the proposed algorithm with previous results, which are reported in the literature. We can see that the proposed CAD system gives better

accuracy results compared to those obtained using the other methods.

*Classification performances vs. the number of features. (ULC size of 512x512).*

To show the efficiency of the presented technique, **Table 3** shows a comparison


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*Abbreviations: ANN, artificial neural network; SVM, support vector machines; NB, Naive Bayes; RF, random Forest; KNN, k-nearest neighbors; M-RCNN and Dee Lab (two deep learning-based instance segmentation Frameworks); Subset of CBIS-DDSM Curated Breast Imaging of DDSM (Digital Database for Screening Mammography).*

### **Table 3.**

*Comparison results of the proposed method with existing methods.*
