## 3 Proposed Methodology
### Proposed Multi-Fractal Dimension
#### 3.5.1 Training Stage  
In this stage, the derived ROI is grouped into five blocks and the noise from each generated block is removed using EWBFEM. The features are extracted from each enhanced block after grouping and enhancing blocks from mammogram images. The first block is selected, and binary images are produced from the selected block based on thresholding values (Figure 4). Traditional histogram is used to compute the threshold value. The first technique can display pixel numbers for each gray value, which is within the scope of the image grayscale. The image histogram demonstrates the number of pixels for each gray value in the image range of 0 to 255. Common gray values within any image are represented by crests within the histogram that are commonly composed of nearly uniform regions. A low number of common values in the histogram is represented by valleys. The vacant districts inside the histogram show that the gray values are absent from the pixels inside the image containing these unfilled locales. Transformation from grey to binary images is possible when thresholding techniques are used. The threshold value can be determined in any threshold technique. The interval intensity amongst the proposed threshold values can be computed to determine uniformly distributed threshold values. The following algorithm demonstrates the binarization steps of the multi-thresholding image that uses the histogram technique. The threshold value was used in Algorithm 1 to generate a binary image. The histogram presents the range of greyscale values, and the algorithm generates the number of thresholds using the interval value. Equation (7) is used to measure the interval \(S\). \[S=Max-Min/(N+1) \tag{7}\]  
The \(S\) value will be calculated using maximum and minimum values of the color image in the first step. The threshold value will be calculated using the threshold counter (R) (\(S=6\)) and minimum values of the color image at the second step. The five thresholds are 16, 32, 48, 64, and 80. ```
Step 1: Calculate the intensity interval (S) between the intensity thresholds. Step 2: Calculate thresholds For R = 1 to N  T (R) = Min + S : R End
```  
**Algorithm 1** Calculate the threshold value:  
Lastly, the selected block from the ROI was transferred to binary images. After converting the image into a binary image with values 0 and 1, regions with the pixel value  
Figure 4: Training stage of feature extraction for each enhanced block. of 1 correspond to regions that contain the information of possible masses. However, normal breast tissue corresponds to regions with the pixel value of 0. Twenty-five different binary images were produced from the selected block after producing 25 thresholds and then applying them to the selected block. Chosen object pixels were acquired depending on binary images. The binary image will be divided into blocks based on FD. FD of the existing object in the binary image is calculated using Equation (6). Box-counting algorithm can be used to assess FD when the binary image is used as the object representation. The first step is to divide the image into a grid containing squares with the size \(\epsilon\times\epsilon\). The number of squares of size \(\epsilon\times\epsilon\) N(\(\epsilon\)) comprising at least one object pixel is then determined. The last step is plotting \(\epsilon\) versus N on a log-log plot, whereby least squares fitting is applied to get the straight line. The slant of this line is the FD fractal measurement. The proposed method can effectively obtain the M-FD based on various binary images. As illustrated in Figure 4, ROI was divided into five blocks. Twenty-five different threshold values are produced for each block based on Algorithm 1. Twenty-five images are generated for each block, depending on the produced threshold values. The box-counting technique is used for calculating the FD for each binary image. Based on this, 25 FDs will be produced for each block. GA is then used as the feature selection technique to reduce the number of FDs to 10.