RiIG Modeled WCP Image-Based CNN Architecture and Feature-Based Approach in Breast Tumor Classiﬁcation from B-Mode Ultrasound

: This study presents two new approaches based on Weighted Contourlet Parametric (WCP) images for the classiﬁcation of breast tumors from B-mode ultrasound images. The Rician Inverse Gaussian (RiIG) distribution is considered for modeling the statistics of ultrasound images in the Contourlet transform domain. The WCP images are obtained by weighting the RiIG modeled Con-tourlet sub-band coefﬁcient images. In the feature-based approach, various geometrical, statistical, and texture features are shown to have low ANOVA p -value, thus indicating a good capacity for class discrimination. Using three publicly available datasets (Mendeley, UDIAT, and BUSI), it is shown that the classical feature-based approach can yield more than 97% accuracy across the datasets for breast tumor classiﬁcation using WCP images while the custom-made convolutional neural network (CNN) can deliver more than 98% accuracy, sensitivity, speciﬁcity, NPV, and PPV values utilizing the same WCP images. Both methods provide superior classiﬁcation performance, better than those of several existing techniques on the same datasets.


Introduction
Breast cancer in women is an important health problem for both developed and developing countries. A recent report by the Cancer Statistics Center of the American Cancer Society shows that among the estimated new cancer cases in 2020, the number of cases of breast cancer is 1,806,590. It also shows that around 606,520 cancer deaths are anticipated only in the United States, of which breast cancer contributes to around 279,100 (approximately 46%) [1].
Breast ultrasound (US) imaging is one of the most promising tools to distinguish and classify breast tumors among the other imaging techniques such as mammograms, MRIs, etc. Ultrasonic images are constructed by dispersing pulses of ultrasound into human tissue using a probe. In US imaging, the pulses echo off the body tissues having several reflection properties which are recorded and exhibited as an image. The B-mode or brightness mode image, in turn, shows the acoustic impedance of a cross-section of tissue in two dimensions.
Plenty of studies have been carried out and are still running to achieve higher accuracy in automatically differentiating malignant breast tumors from benign ones. In 2002, K. Horsch et al. [2] used the depth-to-width ratio of the region of a lesion, the normalized radial gradient, autocorrelation in the depth of lesion region, and minimum side difference of the lesion boundary for the detection of breast tumors. In 2007, Wei-Chih Shen et al. [3] presented a computer-aided diagnostic (CAD) system where a few geometric features such as shape, orientation, margin, lesion boundary, echo pattern, and posterior acoustic feature • This paper demonstrates the suitability of Rician inverse Gaussian (RiIG) distribution [25] for statistical modeling of the Contourlet transformed breast ultrasound images. Further, it shows that the RiIG distribution is better than the well-known Nakagami distribution in capturing the statistics of Contourlet transformed breast ultrasound images in breast tumors classification.

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The suitability of WCP images in classifying breast tumors is investigated for the first time employing three different publicly available datasets consisting of 1193 B-mode ultrasound images and shows that a very high degree of accuracy can be obtained in breast tumor classification using traditional machine-learning-based classifiers as well as deep convolutional neural networks (CNN). • A new deep CNN architecture is proposed for the classification of breast tumors based on RiIG modeled WCP images for the first time. It is also shown that the efficacy of the CNN architecture is superior to the classical feature-based method.

Normalization
The normalization is performed on each image using the formula z = {x − µ(x)}/σ(x) to bring the pixel values to zero mean and unit variance, where x and z represent the image pixels before normalization and after normalization, respectively. Moreover, the µ and σ denote the mean and the standard deviation of pixel values, respectively. Then the pixel values were clipped to keep them within [−3,3]. Here, the significance for taking −3 to 3 values into account is that few features like heterogenicity are measured considering those negative pixels. Applying the normalization process, most of the pixel intensities that were too far from the mean intensity were treated as anomalies and thus removed as shown in Figure 1.

Region of Interest (ROI) Segmentation
The B-mode images stored in database-I, database-II, and database-III are in vario sizes where the highest resolution of them is 600 × 600 pixels. However, almost 50% those images contained a large amount of shadowing effect. Therefore, a shadow red tion operation is performed using adaptive median filtering to minimize the unwan portion of the image for the smooth detection of the region of interest (ROI), which

Region of Interest (ROI) Segmentation
The B-mode images stored in database-I, database-II, and database-III are in various sizes where the highest resolution of them is 600 × 600 pixels. However, almost 50% of those images contained a large amount of shadowing effect. Therefore, a shadow reduction operation is performed using adaptive median filtering to minimize the unwanted portion of the image for the smooth detection of the region of interest (ROI), which is depicted in [29]. It should be noted that almost all the background information and lesion size must be preserved to ensure that no features will be suppressed with the shadow reduction operation. Next, the lesion boundary (ROI) is outlined. This process requires a binary input image, specified as a 2-D logical or numeric matrix. For that, the normalized image is subjected to binarization using MATLAB function 'imbinarize'. Images after binarization and ROI segmentation are shown in Figure 2. The lesion boundary region is automatically outlined using MATLAB functions 'bwboundaries' and 'visboundaries', and those functions are developed using the Moore-Neighbor tracing algorithm modified by Jacob's stopping criteria [30]. The nonzero pixels of that binary image belong to an object and zero-valued pixels constitute the background.

Contourlet Transform
The traditional Discrete Wavelet Transform (DWT) domain has limited directi information as only along with horizontal, vertical, and diagonal dimensions. On other hand, the Contourlet transform has a variety of arbitrary shapes and contours are not limited to three dimensions. The Contourlet transform is executed on the norm ized B-mode images which decouple the multiscale and the directional decomposit using a filter bank [7].
The conceptual theme of a Contourlet transform is the decoupling operation comprises a multiscale decomposition executed as pyramidal decomposition by a La cian pyramid and a following directional decomposition by engaging a directional f bank. Fundamentally, the Contourlet transform is constructed by the grouping of nea wavelet coefficients, since they are locally correlated to ensure the smoothness of the tours. Therefore, a sparse expansion is obtained for natural images by first applyin multi-scale transform, followed by a local directional transform to gather the nearby b functions at the same scale into linear structures. Thus, it establishes a wavelet-like tr form for edge detection and then a local directional transform for contour segment de tion. The overall result is similar to an image expansion using basic elements that are m likely contour segments, and thus the name Contourlets. Performance compariso DWT and Contourlet transform in terms of a better descriptor of contour segments shown in Figure 3. It is observed that, for DWT, the contour detection is performed w limited three dimensions, and the detection becomes fader with the increase of decom sition levels. On the other hand, for Contourlet transform, contour detection with a w range of 32 dimensions and detection become smoother with the increase of pyram

Contourlet Transform
The traditional Discrete Wavelet Transform (DWT) domain has limited directional information as only along with horizontal, vertical, and diagonal dimensions. On the other hand, the Contourlet transform has a variety of arbitrary shapes and contours that are not limited to three dimensions. The Contourlet transform is executed on the normalized B-mode images which decouple the multiscale and the directional decompositions using a filter bank [7].
The conceptual theme of a Contourlet transform is the decoupling operation that comprises a multiscale decomposition executed as pyramidal decomposition by a Laplacian pyramid and a following directional decomposition by engaging a directional filter bank. Fundamentally, the Contourlet transform is constructed by the grouping of nearby wavelet coefficients, since they are locally correlated to ensure the smoothness of the contours. Therefore, a sparse expansion is obtained for natural images by first applying a multi-scale transform, followed by a local directional transform to gather the nearby basis functions at the same scale into linear structures. Thus, it establishes a wavelet-like transform for edge detection and then a local directional transform for contour segment detection. The overall result is similar to an image expansion using basic elements that are more likely contour segments, and thus the name Contourlets. Performance comparison of DWT and Contourlet transform in terms of a better descriptor of contour segments are shown in Figure 3. It is observed that, for DWT, the contour detection is performed with limited three dimensions, and the detection becomes fader with the increase of decomposition levels. On the other hand, for Contourlet transform, contour detection with a wide range of 32 dimensions and detection become smoother with the increase of pyramidal decomposition levels. In DWT coefficient images, the tumor shadowing effect is not visualized whereas in Contourlet transformed coefficient images the shadowing effect is visualized. Moreover, from the literature [7], the Contourlet transform can provide a better description, arbitrary shapes, contours, and more directional information. In addition, the directional decomposition levels contain a variety of directions which is not fixed, and the directional sub-bands increase along with the increase of the pyramidal decomposition levels.

Contourlet Parametric (CP) Image
The Rician Inverse Gaussian (RiIG) distribution is proposed by Eltoft et al. [25]. It is a mixture of Rician distribution and Inverse Gaussian distribution. The PDF of RiIG distribution is given by The Rician Inverse Gaussian (RiIG) distribution is proposed by Eltoft et al. [25]. It is a mixture of Rician distribution and Inverse Gaussian distribution. The PDF of RiIG distribution is given by where α, β and δ are the three parameters of this PDF. α controls the steepness of the distribution; β regulates the skewness; β < 0 suggests skewed to the left; β > 0 suggests skewed to the right, and δ is a dispersion parameter similar to the variance in the Gaussian distribution. The symbol r denotes the corresponding image which is subjected to the model by RiIG distribution. Moreover, γ = δ 2 − β 2 ; I 0 (.) is the modified Bessel function of the first kind, and K 3/2 (.) is the modified Bessel function of the second kind. A few realizations of the RiIG PDFs for a few selected values of the parameters are shown in Figure 4.  The Contourlet Parametric (CP) image is constructed from the RiIG parameter (δ map, which is attained by employing a square sliding window to process the Contourle coefficient image. This process is depicted in [14], where the author used this process to construct Nakagami parametric images with the image parameters being calculated for each image. It should be noted that in [14,31,32], the parametric images are obtained in the spatial domain, whereas we generated the images in the Contourlet transform domain The results observed in previous studies recommend that the most appropriate sliding window for constructing the parametric image is a square with a side length equal to three times the pulse length of the incident ultrasound. In this study, the parametric imaging employed a 13 × 13 pixel sliding window within the Contourlet sub-band coefficient im age to analyze each local RiIG parameter (δ). The employed sliding window size should be larger than the speckle and should discriminate variations of the local structure in tu mors. The window was moved through the entire Contourlet sub-band coefficient image in steps of 1 pixel, with the local RiIG parameter (δ) assigned as the new pixel located a the center of the window at each position. This process yielded the RiIG parametric image as the map of RiIG parameter δ values. The suitability of the RiIG statistical model over the Nakagami statistical model is shown in Figure 5 by CP images and percentile proba bility plot (pp-plot) [33][34][35]. The Contourlet Parametric (CP) image is constructed from the RiIG parameter (δ) map, which is attained by employing a square sliding window to process the Contourlet coefficient image. This process is depicted in [14], where the author used this process to construct Nakagami parametric images with the image parameters being calculated for each image. It should be noted that in [14,31,32], the parametric images are obtained in the spatial domain, whereas we generated the images in the Contourlet transform domain. The results observed in previous studies recommend that the most appropriate sliding window for constructing the parametric image is a square with a side length equal to three times the pulse length of the incident ultrasound. In this study, the parametric imaging employed a 13 × 13 pixel sliding window within the Contourlet sub-band coefficient image to analyze each local RiIG parameter (δ). The employed sliding window size should be larger than the speckle and should discriminate variations of the local structure in tumors. The window was moved through the entire Contourlet sub-band coefficient image in steps of 1 pixel, with the local RiIG parameter (δ) assigned as the new pixel located at the center of the window at each position. This process yielded the RiIG parametric image as the map of RiIG parameter δ values. The suitability of the RiIG statistical model over the Nakagami statistical model is shown in Figure 5 by CP images and percentile probability plot (pp-plot) [33][34][35].

Figure 5. Comparison of Nakagami and RiIG statistical modeling for image classification purposes by Nakagami and RiIG
Contourlet Parametric (CP) images with percentile probability plot (pp-plot) portraying Nakagami, RiIG, and empirical Cumulative density functions (CDFs). Here, we can see that the Nakagami CP image has a lot of black spots which act as artifacts and obscure the tumor region, making it harder for the feature extraction algorithms to work properly. The RiIG CP image on the right side does not have any black spot, and thus, it is easier for the algorithms to extract the necessary features. From the pp-plots, it is seen that the RiIG CDF follows the empirical CDF more precisely than Nakagami CDF. It also indicates the RiIG distribution is more suitable for parametric modeling of the breast ultrasound images.

Weighted Contourlet Parametric (WCP) Image
To obtain the WCP images, the CP images are multiplied with their corresponding Contourlet sub-band coefficients. All the parameter values of those CP images are being weighted by performing multiplication operations with their corresponding Contourlet sub-bands. Therefore, these images can be denoted as "Weighted Contourlet Parametric (WCP)" images. The region of interest (ROI) (i.e., lesion region) is determined for the different sizes of WCP images by employing the Unitarian Rule to ensure that the ROI would be as similar to the same coordinates with the predetermined corresponding parent Bmode image [14]. To reduce the computational complexity for constructing WCP images, six Contourlet sub-bands are carefully chosen as the most suitable (the suitability of chosen six sub-bands is illustrated with ANOVA p-values in Table 2) for feature extraction among other sub-bands from pyramidal decomposition levels 2, 3, and 4 in Contourlet transform where those levels contain 8, 16, and 32 directional sub-bands, respectively. It should be noted that the number of directional sub-bands increases along with pyramidal sub-bands with a relation of 2 (n+1) .  Here, we can see that the Nakagami CP image has a lot of black spots which act as artifacts and obscure the tumor region, making it harder for the feature extraction algorithms to work properly. The RiIG CP image on the right side does not have any black spot, and thus, it is easier for the algorithms to extract the necessary features. From the pp-plots, it is seen that the RiIG CDF follows the empirical CDF more precisely than Nakagami CDF. It also indicates the RiIG distribution is more suitable for parametric modeling of the breast ultrasound images.

Weighted Contourlet Parametric (WCP) Image
To obtain the WCP images, the CP images are multiplied with their corresponding Contourlet sub-band coefficients. All the parameter values of those CP images are being weighted by performing multiplication operations with their corresponding Contourlet sub-bands. Therefore, these images can be denoted as "Weighted Contourlet Parametric (WCP)" images. The region of interest (ROI) (i.e., lesion region) is determined for the different sizes of WCP images by employing the Unitarian Rule to ensure that the ROI would be as similar to the same coordinates with the predetermined corresponding parent B-mode image [14]. To reduce the computational complexity for constructing WCP images, six Contourlet sub-bands are carefully chosen as the most suitable (the suitability of chosen six sub-bands is illustrated with ANOVA p-values in Table 2) for feature extraction among other sub-bands from pyramidal decomposition levels 2, 3, and 4 in Contourlet transform where those levels contain 8, 16, and 32 directional sub-bands, respectively. It should be noted that the number of directional sub-bands increases along with pyramidal sub-bands with a relation of 2 (n+1) .
If we consider pyramidal level-5 along with directional sub-bands-64, then it will increase the computational complexity which is depicted in Table 3. Moreover, we have satisfactory results with pyramidal decomposition level-4; thus, in this paper, image analysis is done up to level-4. These most suitable sub-bands are pyramidal level-2 directional level-4 (P2D4), pyramidal level-2 directional level-8 (P2D8), pyramidal level-3 directional level-8 (P3D8), pyramidal level-3 directional level-16 (P3D16), pyramidal level-4 directional level-16 (P4D16), and pyramidal level-4 directional level-32 (P4D32); these are shown in Figure 6. The main reason behind the selection of these sub-bands is because these particular sub-bands provide the highest resolution for the images, which is important for the feature extraction as well as the CNN for the classification process. From these six sub-bands the six CP images are calculated at first. After obtaining the CP images, each CP image is converted to WCP images by getting weight. In Figure 7 the Contourlet coefficients at decomposition level P4D32 of the normalized images of Figure 2A,D, corresponding CP images, and WCP images are shown where it is observed that the tumor region is visualized more clearly in WCP images than CP images.

Feature Extraction
A large set of ultrasound features does not necessarily guarantee the precise classification of breast tumors; rather, it sometimes degrades the performance of the classifier. Moreover, most of the time it would require a high configuration system for all the computation. In this work, several statistical, geometrical, and texture features are investigated on B-mode US image, B-mode parametric image, Contourlet transformed image, parametric version of Contourlet transformed (CP) image, and weighted parametric version of Contourlet coefficient (WCP) image. The prior features were employed on the B-mode US image, share wave elastography, parametric version of US image, and mammogram images in various earlier works but never on the weighted parametric version of Contourlet coefficient images. To ascertain the feasibility and to assess the dissimilarity of the extracted features, ANOVA p-value analysis has also been performed where the p-values are less than 0.1 for all the features utilized in this work, which proves that the features are useful and non-redundant. The features are summarized in Table 4 with corresponding references and p-values.

Feature Extraction
A large set of ultrasound features does not necessarily guarantee the precise classification of breast tumors; rather, it sometimes degrades the performance of the classifier. Moreover, most of the time it would require a high configuration system for all the

Feature Extraction
A large set of ultrasound features does not necessarily guarantee the precise classification of breast tumors; rather, it sometimes degrades the performance of the classifier. Moreover, most of the time it would require a high configuration system for all the

Proposed Classification Schemes
The proposed classification schemes, WCP feature-based scheme, and WCP CNNbased scheme are illustrated in Figure 8. To assess the performance of the algorithmextracted WCP feature-based method, seven classifiers are considered as shown in Figure 8. On the other hand, in the CNN-based classification process, previously mentioned seven classifiers are utilized at the last layer of the CNN. All the classifiers employed in this study are implemented in MATLAB (the toolbox and default parameters). From the results, described in Section 3, it is seen that applying RiIG modeled WCP images provided the highest accuracy by the SVM classifier. After determining the RiIG based WCP images were the most suitable choice, they were provided to a CNN with all the seven classifiers applied to the outermost layer, to determine which classifier will provide even higher accuracy. For that reason, our proposed classification scheme consists of a CNN network where RiIG based WCP images are provided as inputs. Neural networks generally require a lot of samples for training, much more than the 250 images of database-I, 163 images of database-II, and 647 images of database-III. For that reason, the number of samples was increased by augmentation to 2000 for three databases with an equal number of malignant and benign cases, forming three large databases consisting of 6000 images. Since six sub-bands were selected for each B-mode image, the number of total images increased to 6000 × 6 = 36,000 Contourlet coefficient images. From Figure 6, it can be easily seen that the images obtained from different Contourlet sub-band coefficients all have different sizes. As a CNN would require all the images to have the same sizes, all the images were resized to 224 × 224, and then, the corresponding six sub-band images were stacked together to form 6000 3D stack images of size 224 × 224 × 6. The CNN network employed for this work is a modified version of the custom CNN network provided in [41]; the differences between that network and the proposed network have an input of 224 × 224 × 6 3D image stack, and the features extracted from the outermost layer (the Global Average Pooling layer) were provided to seven different classifiers. The inspiration for not using a pre-trained network for the WCP images is, as we claimed, that the pre-trained networks were built for 3-channel visual images with spatial dimensions, and, they were not compatible with our 3D stack of transform domain coefficient images. The architecture of the proposed CNN network configuration is depicted in Table 5 and shown in Figure 9.
tween that network and the proposed network have an input of 224 × 224 × 6 3D image stack, and the features extracted from the outermost layer (the Global Average Pooling layer) were provided to seven different classifiers. The inspiration for not using a pretrained network for the WCP images is, as we claimed, that the pre-trained networks were built for 3-channel visual images with spatial dimensions, and, they were not compatible with our 3D stack of transform domain coefficient images. The architecture of the proposed CNN network configuration is depicted in Table 5 and shown in Figure 9.     For training, a ratio of 90-10% is used where 10% of the un-augmented database images (i.e., only original database images) are randomly selected for blind testing, and the remaining 90% (i.e., remaining original database images and their corresponding augmented images) are used for training so that there is no overlap between the testing and training samples. If the test data are selected from augmented data, the accuracy can be significantly biased due to leakage and can be higher than the real test. As there are not many tests or original data, it is more appropriate to separate the testing images from the whole database for testing purposes and the rest of the database is utilized to generate training data with augmentation. A 10-fold cross-validation scheme is also employed along with an exhaustive grid search method using the average validation accuracy as a metric to determine the hyper-parameters of the neural network. This network employs the Adam optimization technique [42] and a batch size and learning rate of 64 and 0.01, respectively. The training data are applied to the CNN network through 40,000 iterations. The performance of the proposed method is measured using the performance indices like accuracy, sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV), etc. Later, the confusion matrices are obtained by measuring true-positive (TP), true-negative (TN), false-positive (FP), and false-negative (FN), respectively, where positive stands for a malignant tumor, and negative stands for a benign tumor. The results are discussed in Section 3. For training, a ratio of 90-10% is used where 10% of the un-augmented database images (i.e., only original database images) are randomly selected for blind testing, and the remaining 90% (i.e., remaining original database images and their corresponding augmented images) are used for training so that there is no overlap between the testing and training samples. If the test data are selected from augmented data, the accuracy can be significantly biased due to leakage and can be higher than the real test. As there are not many tests or original data, it is more appropriate to separate the testing images from the whole database for testing purposes and the rest of the database is utilized to generate training data with augmentation. A 10-fold cross-validation scheme is also employed along with an exhaustive grid search method using the average validation accuracy as a metric to determine the hyper-parameters of the neural network. This network employs the Adam optimization technique [42] and a batch size and learning rate of 64 and 0.01, respectively. The training data are applied to the CNN network through 40,000 iterations. The performance of the proposed method is measured using the performance indices like accuracy, sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV), etc. Later, the confusion matrices are obtained by measuring true-positive (TP), true-negative (TN), false-positive (FP), and false-negative (FN), respectively, where positive stands for a malignant tumor, and negative stands for a benign tumor. The results are discussed in Section 3.

Experimental Results
In the proposed classification scheme, for the classical feature-based classification approach, the classification performances are investigated on B-mode US image, parametric (P) image, Contourlet transformed image, parametric version of Contourlet transformed image, weighted parametric version of Contourlet transformed image, etc. The results are shown in Table 6, where it is evident that the application of statistical modeling and Contourlet transform improves the accuracy of the classification. Here, it can be seen that the features extracted from the B-mode image provide the least amount of accuracy. For B-mode images without any statistical modeling or Contourlet transform applied on them, the highest accuracies obtained for database-I, database-II, and database-III were 92%, 92.05%, and 92.15%, respectively, all of them obtained using the KNN classifier. Applying Nakagami and RiIG statistical modeling on the B-mode images improves the accuracies of the classification, the highest being 93.5%, 93.25%, and 92.55% for databases I, II, and III, respectively, obtained from the SVM classifier. Applying Contourlet transform on the B-mode images also proved to be effective in increasing the accuracies, the highest being 93%, 92.65%, and 93.05%, for databases I, II, and III, respectively, using the SVM classifier. From the results, it is seen that applying either technique on the B-mode images improves the classification performance. In the case of CP images, where both the techniques are applied together, the highest classification accuracies increased to 93%, 93.15%, and 93.55% for databases I, II, and III, respectively, all of them obtained from the SVM classifier. In the case of our proposed WCP images, the highest accuracies increased further to 97.5%, 97.55%, and 97.95% for databases I, II, and III, respectively, and all were obtained from the SVM classifier. Here, it could be easily seen that the RiIG statistical model provided better performance for all seven classifiers compared to the Nakagami statistical model for all types of images in database-I, database-II, and database-III, proving RiIG to be more suitable for the statistical modeling of the B-mode images. As it was shown that the RiIG modeled WCP images provided the best result for the feature engineering method, the CNN method was applied on RiIG modeled WCP images only. From the results, it could be easily seen that CNN-based feature extraction provided more accuracy than algorithmbased feature extraction. For the CNN-based approach, the highest accuracies obtained for databases I, II and III were 98.05%, 98.35%, and 98.55%, respectively, all of them obtained from the KNN classifier. From Table 6, it is evident that the proposed RiIG based WCP image is the most suitable choice for the classification of breast tumors in both the feature extraction-based approach and CNN-based approach. Moreover, the CNN-based approach provides higher accuracy over the feature extraction-based approach. The confusion matrices of 10-fold cross-validation result for the proposed CNN-based approach employing the KNN classifier are shown in Table 7 along with performance indices such as accuracy, sensitivity, specificity, positive predictive value (PPV), and negative predictive value (NPV) by measuring true positive (TP), true negative (TN), false positive (FP), and false-negative (FN), where positive stands for malignant tumor and negative stands for a benign tumor. It is observed that for all three databases, the values of accuracy, sensitivity, specificity, PPV, and NPV are greater than 98%.

WCP Image Analysis with Database-I WCP Image Analysis with Database-II
proach. The confusion matrices of 10-fold cross-validation result for the p based approach employing the KNN classifier are shown in Table 7 alo mance indices such as accuracy, sensitivity, specificity, positive predictiv and negative predictive value (NPV) by measuring true positive (TP), true false positive (FP), and false-negative (FN), where positive stands for m and negative stands for a benign tumor. It is observed that for all three values of accuracy, sensitivity, specificity, PPV, and NPV are greater than

Discussion
In the previous section, it was shown that the best classification accur using the CNN-based approach with the RiIG-based WCP images. A co other works is presented in Table 8. The work of P. Acevedo et al. [5] yield CNN-based approach provides higher accuracy over the feature extraction-based approach. The confusion matrices of 10-fold cross-validation result for the proposed CNNbased approach employing the KNN classifier are shown in Table 7 along with performance indices such as accuracy, sensitivity, specificity, positive predictive value (PPV), and negative predictive value (NPV) by measuring true positive (TP), true negative (TN), false positive (FP), and false-negative (FN), where positive stands for malignant tumor and negative stands for a benign tumor. It is observed that for all three databases, the values of accuracy, sensitivity, specificity, PPV, and NPV are greater than 98%.

Discussion
In the previous section, it was shown that the best classification accuracy is achieved using the CNN-based approach with the RiIG-based WCP images. A comparison with other works is presented in Table 8. The work of P. Acevedo et al. [5] yielded an accuracy WCP Image Analysis with Database-III proach. The confusion matrices of 10-fold cross-validation result for the proposed based approach employing the KNN classifier are shown in Table 7 along with p mance indices such as accuracy, sensitivity, specificity, positive predictive value and negative predictive value (NPV) by measuring true positive (TP), true negative false positive (FP), and false-negative (FN), where positive stands for malignant and negative stands for a benign tumor. It is observed that for all three databas values of accuracy, sensitivity, specificity, PPV, and NPV are greater than 98%.

Discussion
In the previous section, it was shown that the best classification accuracy is ach using the CNN-based approach with the RiIG-based WCP images. A comparison other works is presented in Table 8. The work of P. Acevedo et al. [5] yielded an acc

Discussion
In the previous section, it was shown that the best classification accuracy is achieved using the CNN-based approach with the RiIG-based WCP images. A comparison with other works is presented in Table 8. The work of P. Acevedo et al. [5] yielded an accuracy of 94% with an F1 score of 0.942 using Database-I. Shivabalan et al. [20] also used the same Database-I and reported an accuracy of 94.5% with an F1 score of 0.945. Therefore, the accuracy level obtained by the proposed method using the same Database-I about 98.25% with an F1 score of 0.982 is significantly better. In another work, Hou et al. [21] used the Database-II and reported an accuracy of 94.8%. Shin et al. [22] reported an accuracy of 84.5% using the same Database-II combined with other databases. Byra et al. [23] reported an accuracy of 85.3% with an F1 score of 0.765 using Database-II. Qi et al. [24] illustrated an accuracy of 94.48% with an F1 score of 0.942 using Database-II. On the other hand, the proposed method using Database-II gives an accuracy of 98.35% with an F1 score of 0.984, which is significantly better. The method of Ka Wing Wan et al. [43] provides accuracies of 91%, with an F1 score of 0.87 with a CNN, and 90%, with an F1 score of 0.83 using a Random Forest classifier for the Database-III. Moon et al. [44] reported an accuracy of 94.62% with an F1 score of 0.911, using the same Database-III. In contrast, the accuracy and F1 score for the proposed method are superior. Furthermore, the proposed CNN-based approach is applied for classification on the Database-III with 80% training and 20% testing ratio with the same validation approach as in [43,44]. This experiment provides an accuracy of 96.45%, a sensitivity 93.09%, a specificity 98.14% with an F1 score of 0.946, still superior to those of [43,44]. The box plots given in Figure 10 indicate the comparison of accuracies of Table 8; these also indicate a consistent performance by the various methods including the proposed method.  Figure 10. Comparison of accuracies of the three databases from Table 8.

Conclusions
In this paper, two new approaches in breast tumors classification are presented, employing RiIG statistical model-based Weighted Contourlet Parametric images obtained from the Contourlet transformed breast US images. In the first approach, various statistical, geometrical, and texture-based features are extracted from RiIG statistical modelbased WCP images, which are then classified employing different classifiers. It is shown Figure 10. Comparison of accuracies of the three databases from Table 8.

Conclusions
In this paper, two new approaches in breast tumors classification are presented, employing RiIG statistical model-based Weighted Contourlet Parametric images obtained from the Contourlet transformed breast US images. In the first approach, various statistical, geometrical, and texture-based features are extracted from RiIG statistical model-based WCP images, which are then classified employing different classifiers. It is shown that by employing the SVM classifier, a very good degree of accuracy can be achieved. Secondly, a new custom CNN-based architecture is proposed to classify WCP images of breast tumors which has shown a better performance than the first approach in terms of accuracy. The proposed CNN architecture can also provide a very high degree of sensitivity, specificity, NPV, and PPV values by employing the KNN classifier. Both the approaches demonstrate better performance in classification as compared to existing methods on publicly available benchmark datasets. In addition, the RiIG distribution is a highly suitable distribution for modeling the statistics of the Contourlet transform coefficients of B-mode Ultrasound images of breast tumors. There are scopes for further improvements by employing the proposed approach in other multi-resolution transform domains and involving other datasets.   [28].

Conflicts of Interest:
The authors declare no conflict of interest.