# Optimizing Cervical Cancer Diagnosis with Feature Selection and Deep Learning
## 2 Materials and Methods
### Feature Extraction  
A feature vector serves as a parametric representation of objects within an image, making its development a crucial phase in every classification system. Thus, accurate feature selection can significantly enhance classification performance. This section introduces a collection of features that characterize cells on LBC slides and reflect their morphological aspects. For effective feature extraction, it is essential to identify the features that distinguish between uterine cervix cell conditions. Table 1 describes these features, using a normal cell (NSIL) as the reference. Based on this description, we propose the following 27 morphological features:  
* **Nucleus size (N)**--is defined as the sum of all nuclei pixels in the nucleus. * **Cell size (C)**--is calculated as the total number of pixels of the cell in the segmented image. * **Nucleus/cell ratio (NCr)**--this feature was calculated as a ratio of the nucleus size and the cell size, providing insights into nuclear enlargement, a hallmark of malignancy: \[NCr=\frac{N}{C}.\] (4)  
Figure 3: Segmentation of a cell and its nucleus. * **Nucleus perimeter (\(Np\))--**we define \(Np\) as the length of the nuclear boundary of a nucleus \(N\) that is approximated by a length of the polygonal approximation of the boundary [34]. * **Cell perimeter (\(Cp\))--**similar to \(Np\), cell diameter is defined as the length of the cell membrane of a cell \(C\) that is approximated by the polygonal approximation length of the membrane. * **Nucleus/cell perimeter ratio (\(Nc\))--**this feature was calculated as a ratio of nucleus diameter and cell diameter: \[NCpr=\frac{Nd}{Cd}.\] (5)
* **Min Axis (\(MinA\))--\(MinA\)** is calculated as a shortest Euclidean distance between extreme points of the segmented region both for nucleus and a cell. * **Min Axis ratio (\(MinAr\))--**represents a ratio between Min Axis for nucleus and a cell
* **Max Axis (\(MaxA\))--\(MaxA\)** is calculated as a largest Euclidean distance between extreme points of the segmented region both for nucleus and a cell. * **Max Axis ratio (\(MaxAr\))--**determined as a ratio between \(MaxA\) for the nucleus and a cell. * **Nucleus Aspect Ratio (\(Nar\))--**to compute the aspect ratio, the bounding box (\(BB\)) of a nucleus is obtained. Feature is calculated as a ratio between width (\(BB_{w}\)) and height (\(BB_{h}\)) of the bounding box. * **Cell Aspect Ratio (\(Car\))--**this feature is similar to \(Nar\). Here, the bounding box is determined according to the cell image rather than the nucleus. * **Nucleus/cell Aspect Ratio (\(NCar\))--**here, we calculate the ratio of \(Nar\) and \(Car\). * **Extent (\(Ext\))--**extent is a feature that represents the amount of space that the nucleus or a cell occupies with respect to its bounding box. We calculate this feature according to Equation (6). It provides information about how compact or irregular a shape is. \[Ext=\frac{area}{BB_{w}*BB_{h}},\] (6) where \(area\) represents the size of a nucleus or a cell. * **Nucleus/cell extent (\(NCExt\))--**is a ratio of nucleus extent and cell extent. * **Solidity (\(So\))--**solidity measures the smoothness or irregularity of the nucleus boundary. It represents the number of pixels occupied by the object but with respect to its convex hull (\(CH\)). Solidity is defined by Equation (7). \[extent=\frac{area}{Area(CH)},\] (7) where \(area\) represents the size of a nucleus or a cell and \(Area(CH)\) is an area of \(CH\). * **Nucleus/cell solidity (\(NCs\))--**defined as a ratio between \(NSol\) and \(CSol\)
* **Equivalence diameter (\(Eq\))--**equivalence diameter is simply a diameter of a circle which area is the same as \(N\) or \(C\). * **Equivalence diameter ratio (\(NCEa\))--**is a ratio between equivalence diameter of the nucleus and the equivalence diameter of a cell. * **Orientation (\(Or\))--**this feature is known as an axis of the least second moment and provides the information about the angle between the row axis when the coordinate system is placed and the centroid of the nucleus/cell.