## 2 Proposed Methods
### Feature Extraction
}^{2P_{1}-1}\operatorname{C}_{d \mu}(u,v)\) & & & \\  & Where \(G_{5}(u)=\sum\limits_{ \begin{subarray}{c}\tau\end{subarray} }^{P_{1}-1} \operatorname{C}_{d\mu}(u,v)\operatorname{C}_{d\mu}(u,v)\) & & \(\sum\limits_{ \begin{subarray}{c}\tau\end{subarray} }^{P_{1}-1} \operatorname{C}_{d\mu}(u,v)\) & \(HU-\sum\limits_{ \begin{subarray}{c}\tau\end{subarray} }^{P_{1}-1} \operatorname{C}_{d\mu}(u,v)\) & \(\operatorname{Log}(G_{5}(u))\) \\  & \(HVV=\sum\limits_{ \begin{subarray}{c}\tau\end{subarray} }^{P_{1}-1} \operatorname{C}_{d\mu}(u,v)\operatorname{Log}(G_{5}(u))\) & \(HUV=-\sum\limits_{ \begin{subarray}{c}\tau\end{subarray} }^{P_{1}-1} \operatorname{C}_{d\mu}(u,v)\operatorname{Log}(G_{5}(u))\) & \((U,Shape-Based Features  
Visual features of lesions are known as shape attributes or features. Such as, triangular shape or circular shapes, diameter of the boundary or perimeter of the border of object etc. Shape attributes can be partitioned into two groups; one is based on the object boundary, and the second is based on features of region. Various features of the shape can be computed including area, which is the number of pixels of the breast lesion and the perimeter of tumor is obtained by computing total number of boundary pixels around the lesion. Usually the lesion features such as area, perimeter, minor axis, and major axis cannot be employed independently for lesion classification. Such features are affected by the size of the lesion. Apart from that, features that are scale-invariant such as elongation, compactness, rectangularity, solidity, roundness, eccentricity, and convexity can be obtained and employed. Formulas used to extract shape features are documented in Table 3 [39]. Illustration of some features such as area, major axis, and minor axis are shown in Figure 6 for more clarity. GLCM uses the arrangement of grey levels and their positions; its statistical characteristics allow faster identification of several varieties of lesions whereas, shape-based features contain all significant properties of an object in a compact descriptor. Employing only one feature type limits the depiction power of the object in terms of classification performance. Their combination constructs a distinct descriptor of feature presenting an optimum representation of the lesion. Thus, texture feature along with the shape-based features documented in Table 4, are merged to develop a hybrid feature set. The hybrid feature set is the concatenation of the GLCM and shape-based features, to provide a total of 27 features. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Feature** & **Formula** & **Description** \\ \hline Elongation & \(1-\frac{Minor Axis}{Major Axis}\) & Used to measure the object length. \\ \hline Roundness & \(\frac{4*n*Area}{(convex_{center})^{2}}\) & Method to show the level of determination lesion. \\ \hline Solidity & \(\frac{Area}{convex_{center}}\) & Used to measure the density of the lesion. \\ \hline Rectangularity & \(\frac{Area}{Major Axis}\) & Method to explain resemblance of lesion shape \\  & \(\frac{Area}{Major Axis}\) & with rectangular shape. \\ \hline Compactness & \(\frac{4*n*Area}{(perimeter)^{2}}\) & The ratio between the lesion area with circle area. \\ \hline Convexity & \(\frac{Convex_{center}}{Perimeter}\) & This technique is the perimeter ratio between convex full of lesion and the lesion itself. \\ \hline Eccentricity & \(\frac{\sqrt{Major Axis}^{2}-Minor Axis}{Major Axis}\) & The proportion of distance between the ellipse \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Formula of shape-based features. Figure 6: (**a**) Area of breast lesion; (**b**) minor axis and major axis.