## 3 The Proposed Transferable Texture Convolutional Neural Network (TTCNN) Method
### Contrast Enhancement  
Improving the contrast is an important preliminary step in the diagnostic process [59]. Due to the lack of illumination, the contrast of the source mammogram image is low. The histogram equalization method appears to be a more efficacious way of enhancing the low contrast images. The modified CLAHE [59] is implemented to adjust the contrast and maintain the standard brightness of the input image. This contrast enhancement methodaffects small parts of the image (mosaics). The histogram in the output part harmonizes the identified histogram because the contrast of each mosaic is emphasized, rather than the absolute mammogram image. After leveling, use linear interpolation to connect adjacent tiles and remove artificial boundaries. CLAHE uses a custom clipping threshold to limit the enhancement of histogram clipping. The clipping level diminishes the noise level and sets the contrast level to enhance the histogram. We use 0 to 0.01 for this activity. Firstly, we divide the input image into correlated areas that do not overlap. The total number of image tiles is \(R\times S\). The histogram of the non-overlapping correlation area is calculated as the level of gray present in the image matrix. Equation (1) calculated the contrast limit histogram of the relevant area that does not overlap according to the clipping limit as follows. \[In_{avg}=\frac{S_{p}\times S_{q}}{S_{gray}}, \tag{1}\]  
where \(In_{avg}\) is the average number of pixels, \(S_{gray}\) is the number of related gray levels that do not overlap, \(S_{p}\) and \(S_{q}\) is the number of pixels in dimensions that do not overlap \(p\) and \(q\). The clipping limit is given in Equation (2) as:  
\[In_{LC}=S_{clipping}\times I_{av}, \tag{2}\]  
where \(In_{LC}\) is the clipping limit, \(S_{clipping}\) is the normalized clipping limit in the range of [0, 1]. If the number of pixels is greater than \(In_{LC}\), the pixels will be clipped. The remaining average pixels are allocated in each gray level as follows:  
\[In_{avg,gray}=\frac{S_{pcw}}{S_{gray}}, \tag{3}\]  
where \(S_{pcw}\) denotes the integer number of pixels after truncation. Move the remaining pixels till all the pixels are connected. The pixel redistribution is given in Equation (4) as:  
\[In_{pace}=\frac{S_{gray}}{S_{tp}}, \tag{4}\]  
where \(S_{tp}\) is the number of remaining clipped pixels. Also, using the Rayleigh transformation in each part, the intensity values are rectified in Equation (5) as:  
\[In_{q}=In_{mi}+\sqrt{2\zeta^{2}ln\bigg{(}\frac{1}{1-C_{in}}\bigg{)}I_{pace}}, \tag{5}\]  
where \(C_{in}\) represents the cumulative probability which develops the transfer function, \(In_{mi}\) is the lower limit of the pixel value, and \(\zeta\) is the scale parameter. The value of each intensity, the output probability density is given by Equation (6) as:  
\[In_{e}=\frac{(In_{q}-In_{mi})}{\zeta^{2}}.exp\bigg{(}-\frac{(In_{q}-In_{mi})^{ 2}}{2\zeta^{2}}\bigg{)}for\leavevmode\
obreak\ In_{q}\geq In_{mi}. \tag{6}\]  
Increasing the value of \(\zeta\) will significantly improve the contrast of the image, but will increase the saturation value and the noise level. Linear contrast stretching can be used to rearrange the output of the resulting transfer function to reduce the effects of sudden changes. The expansion of the linear contrast can be demonstrated in Equation (7) as:  
\[In_{x}=\frac{I_{e}-w_{mi}}{w_{ma}-w_{mi}}, \tag{7}\]  
where \(I_{e}\) is the transfer function obtained, \(w_{mi}\) and \(w_{ma}\) are the minimal and maximum transfer functions value respectively. \(In_{x}\) is used to extract the source image to acquire an image with enhanced contrast. Contrast enhancement refined the edges of the input image. Figure 3 shows the contrast enhancement of the input image. In Figure 3a, the source mammogram image having a tumor is not visible as the tumor in the breast image has no sharp edges.