## 4 Feature Extraction  
After detecting the nucleus and cytoplasm area in the cell, we extracted different features, which will be used in the diagnostic process for detecting the cancer cells. The main problem that faces any CAD systems for early diagnosis of lung cancer is associated with the ability of the CAD system to discriminate between normal and abnormal cells (cancer cells). Thus, using the appropriate features we can reduce or eliminate the number of misclassifications. In the literature, different features have been proposed depending on the adopted decision method. In our proposed CAD system, we used the following features: Nucleus to Cytoplasm (NC) ratio, perimeter, density, curvature, circularity and eigen ratio. The first feature is the NC ratio, which is computed by dividing the nucleus area (total number of the pixels in the nucleus region) over the cytoplasm area (total number of pixels in the cytoplasmic region), as follows:  
\[\text{NC ratio}=\frac{\text{Area (Nucleus)}}{\text{Area(Cytoplasm)}}\times 100 \tag{3}\]  
Therefore, based on medical information, the morphology, the size, and the growing correlation of the nuclei and their corresponding cytoplasm regions, reflect the diagnostic situation of the cell life cycle, bearing in mind that cancerous cells are characterized by oversized nucleus-relatively to the cytoplasm. Figure 5a shows samples of extracted nuclei and cytoplasm. Figure 5b depicts the nucleus and cytoplasm extraction where the black and white areas represent the nucleus and the cytoplasm respectively. Figure 5c shows the nucleus area. The second feature is the nucleus perimeter defined by:  
\[P(\text{Nucleus})=\int_{t}\sqrt{x^{2}(t)+y^{2}(t)dt} \tag{4}\]  
where \(x(t)\) and \(y(t)\) are the parameterized contour point coordinates. In the discrete case, \(x(t)\) and \(y(t)\) are defined by a set of pixels in the image. Thus, Equation (4) is approximated by:  
\[P(\text{Nucleus})=\sum_{t}\sqrt{(x_{t}-x_{t-1})^{2}+(y_{t}-y_{t-1})^{2}} \tag{5}\]  
Figure 5d depicts the perimeter area in color red for the nuclei cell in Figure 5c. \begin{table}
\begin{tabular}{c c c c} \hline
**Performance/Algorithm** & **HNN** & **Gray Mean Shift** & **Gray-Space Mean Shift** \\ \hline Sensitivity & 73.77\% & 92.7\% & 93.40\% \\ Accuracy & 65.01\% & 85.43\% & 87.11\% \\ \hline \end{tabular}
\end{table} 
Table 2: Performance of the nucleus segmentation algorithms. The third feature representing the density is based on the darkness of the nucleus area after staining with a certain dye, thus it is based on the mean value of the nucleus region. The mean value represents the average intensity value of all pixels that belong to the same region, and in our case, each mean value is represented as a vector of RGB components, and is calculated as follows for a given nucleus:  
\[\text{Mean}(\text{Nucleus})=\frac{\sum_{i=1}^{N}\text{Intensity}(i)}{\text{ Area}(\text{Nucleus})} \tag{6}\]  
where \(i\) is the intensity color value and \(N\) is the total number of the pixels in the nucleus area. Figure 6 shows the mean intensity values for both benign and malignant cells. As can be seen, all the values that are greater than or equal to the threshold value \(0\) are classified as benign cells (color red) and, the other values which are less than \(0\) are classified as malignant (color blue), BD and MD refer to the benign and malignant density respectively. In our system \(0=128\). Nevertheless, some overlapping does exist, where very few malignant cells are classified as benign cells (FN) and vice versa. In this situation, we cannot consider the intensity feature alone. The fourth feature is the curvature, which is delineated by the rate of change in the edge direction. This rate of change characterizes the points in a curve which are known as corners where the edge direction changes rapidly [18]. A lot of significant information can be extracted from these points. The curvature at a single point in the boundary can be defined by its adjacent tangent line segments.