## 2 Materials and Methods
### Datasets
#### 2.1.5 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  
Figure 5: Comparison of Nakagami and RilG statistical modeling for image classification purposes by Nakagami and RilG Contourlet Parametric (CP) images with percentile probability plot (pp-plot) portraying Nakagami, RilG, 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 RilG 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 RilG CDF follows the empirical CDF more precisely than Nakagami CDF. It also indicates the RilG distribution is more suitable for parametric modeling of the breast ultrasound images.  
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.