# Automatic Breast Tumor Screening of Mammographic Images with Optimal Convolutional Neural Network
## 3 Experimental Results
### Testing of the First Convolutional Layer and Determination of the Window Type  
As seen in Table 5, three types of convolution windows in the first convolutional layer, including fractional-order windows, Sobel windows, and Histeq windows, are used perform the 2D spatial convolutions [35; 36; 47; 49; 50; 51; 52]. Figure 6a shows the original image and image enhancement results of these three types of convolution windows. Figure 6b shows the pixel grayscale value distribution map after the image is magnified. Compared with the original image grayscale value (0-255) distribution map, the convolution result of the first derivative-based Sobel convolution window [49] has a smoothing effect and is anti-noise but requires a considerable amount of calculations while performing convolutions; moreover, this window type produces a thicker edge contour, which results in lower accuracy in identifying the position of the target object. We can use a second-order-based convolutional window for feature enhancement, but this window is fairly susceptible to noise and thus unsuitable for obtaining the edge contour of the target; this type of window is generally used for binarization applications. The Histeq convolution (histogram regularization) [50] yields a histogram of the number of times each grayscale value appears. This histogram can describe the statistical information of the grayscale values of the image and allows the direct observation of the characteristics of the image, such as its brightness and contrast. It is primarily used for image segmentation and adjustment of grayscale values in the image. As shown in Figure 6b, the non-zero value of the histogram has a wide and uniform distribution, which indicates that the contrast of the image is high. The pixel value of the image may be readjusted to a value between 0 and 255 by using linear, piecewise linear, and nonlinear transformation functions [53]. These transformation functions are primarily used to magnify the contrast of the original image. The overall grayscale value distribution map shifts to the right, and the contrast of the image increases, thereby minimizing the effort required to highlight the outline of the malignant tumor, as shown in Figure 6a. However, this method is susceptible to factors such as illumination, viewing angle, and noise. The Histeq (histogram normalization) function [50] can automatically determine the grayscale transformation function and yield an output image with a uniform histogram. It is primarily used for contrast adjustments over a small range but could amplify background noise. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & **1 st Convolutional** & **2 nd Convolutional** & **3 rd Convolutional** & **Stride/** & **Maximum** & \\  & **Window and** & **Window and** & **Window and** & **Padding** & **Pooling** & **Stride** \\  & **Window Size** & **Window Size** & **Window Size** & **Window Size** & **Window** & \\ \hline
1 & Fractional Order, \(3\times 3,2\) & \(3\times 3\)or \(5\times 5,16\) & \(3\times 3\)or \(5\times 5,16\) & \(1/1\) & \(2\times 2,16\) & 2 \\ \hline
2 & Sobel (First Order), \(3\times 3,2\) & \(3\times 3\)or \(5\times 5,16\) & \(3\times 3\)or \(5\times 5,16\) & \(1/1\) & \(2\times 2,16\) & 2 \\ \hline
3 & Histeq, \(3\times 3,2\) & \(3\times 3\)or \(5\times 5,16\) & \(3\times 3\)or \(5\times 5,16\) & \(1/1\) & \(2\times 2,16\) & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Different convolutional layer models for feature enhancement and extraction (Models #1–#3). When fractional-order spatial convolution is conducted in 2D space, the overall grayscale value distribution moves to the right, which increases the contrast of the image and filters out noise. Thus, it shows better performance than the Sobel convolutional operation. Therefore, in the first convolutional layer, this study selects a \(3\times 3\) fractional-order convolution window for the first convolutional layer.