## 2 Materials and Methods
### Proposed Classification Schemes  
The proposed classification schemes, WCP feature-based scheme, and WCP CNN-based scheme are illustrated in Figure 8. To assess the performance of the algorithm-extracted 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 \(\times\) 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 \(\times\) 224, and then, the corresponding six sub-band images were stacked together to form 6000 3D stack images of size 224 \(\times\) 224 \(\times\) 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 \(\times\) 224 \(\times\) 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. \begin{table}
\begin{tabular}{c c} \hline \hline
**Feature with Reference** & \(p\)**-Values** \\ \hline Hypoechogenicity [36; 37] & 0.0022 \\ Microbiobulation [36; 37] & 0.0031 \\ Homogeneous Echoes [36; 37] & 0.0032 \\ Heterogeneous Echoes [36; 37] & 0.0040 \\ Taller Than Wide [36; 37] & 0.0044 \\ Microcalcification [38; 39] & 0.0054 \\ Texture [38; 39] & 0.0069 \\ Shape Class [3] & 0.0145 \\ Echo Pattern Class [3] & 0.0155 \\ Margin Class [3] & 0.0162 \\ Orientation Class [3] & 0.0165 \\ Lesion Boundary Class [3] & 0.0166 \\ Tiled Ellipse Radius [40] & 0.0312 \\ Tilted Ellipse Perimeter [40] & 0.0344 \\ Tilted Ellipse Area [40] & 0.0347 \\ Tilted Ellipse Compactness [40] & 0.0355 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The features utilization considering WCP images with ANOVA \(p\)-values.