# A Hierarchical Feature-Based Methodology to Perform Cervical Cancer Classification
## 2 Materials and Methods
### Biological versus Computational Features
The Threshold Adjancency Statistics (TAS) [46] features were also considered in the classification. They are used to differentiate images of distinct subcellular localization quickly and with high accuracy. The Zernike moment [47] features were extracted and considered in the proposed methodology because they measure how the mass is distributed in the region. Finally, the Gray Level Co-occurrence Matrices [44] are texture features extracted that consider the pixels' spatial relation. Figure 3 shows a sample image for each type of lesion present in the CRIC database, and Table 2 presents some feature values extracted from the images in Figure 3. These features are area, eccentricity (eccent. ), circularity (circ. ), maximum intensity (max. int. ), and contrast. We extracted features inspired by the ones that a cytopathologist would use to perform the classification, manually. Morphological features such as area, perimeter, extent, and eccentricity are important because they are related to the nuclear size, which characterizes one of the fundamental biological criteria for differentiating abnormal cells from normal ones. For example, ASC-US interpretation requires that the cells in question demonstrate nuclei approximately 2.5 to 3 times the area of the nucleus of a normal intermediate squamous cell (approximately 35 \(\upmu\)m\({}^{2}\)) or twice the size of a squamous metaplastic cell nucleus (approximately 50 \(\upmu\)m\({}^{2}\)). The cells interpreted as ASC-H are the size of metaplastic cells with nuclei that are up 2.5 times larger than normal. Nuclear enlargement more than three times the area of normal intermediate nuclei characterizes LSIL. HSIL often contains relatively small basal-type cells with nuclear augmentation. The characteristic cells of \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Lesion** & **b** & **Eccent.** & **Circ.** & **Max. int.** & **Contrast** \\ \hline Normal (Figure 3a) & 516 & 0.497 & 0.824 & 0.439 & 0.040 \\ ASC-US (Figure 3b) & 2719 & 0.422 & 0.871 & 0.723 & 0.087 \\ LSIL (Figure 3d) & 8228 & 0.708 & 0.811 & 0.799 & 0.072 \\ ASC-H (Figure 3c) & 2248 & 0.627 & 0.789 & 0.885 & 0.061 \\ HSIL (Figure 3e) & 1539 & 0.715 & 0.854 & 0.531 & 0.122 \\ SC (Figure 3f) & 823 & 0.952 & 0.462 & 0.354 & 0.075 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Feature values extracted from images in Figure 3.  
Figure 3: Types of CRIC lesions: **(a)** Normal **(b)** ASC-US **(c)** LSIL **(d)** ASC-H **(e)** HSIL **(f)** SC. carcinoma (SC) vary markedly in the area but usually show karyomegaly. Table 2 shows that the area feature has a behavior as observed by cytopathologists, in which the normal cell has the smallest area value and there is an increase in the value according to its lesion. Another biologically relevant feature is the nuclear membrane shape, as abnormal cells have different degrees of irregularity. ASC-US shows minimal variation in the nuclear shape, while LSIL presents a contour of nuclear membrane ranging from smooth to very irregular with notches. ASC-H and HSIL show irregular nuclear contour, with anisokaryosis of HSIL being more pronounced. Carcinoma cells may show very marked nuclear pleomorphism (bizarre forms). As a whole, abnormal cells may have multinucleation, or variations in the circular shape of a normal cell's nucleus. This work considered morphological features related to these characteristics (nuclear contour and multinucleation), such as circularity, eccentricity, and minor and major axis. Table 2 shows eccentricity and circularity values that provide examples of features used in this work to measure the nuclear membrane's shape as they would typically be analyzed by cytopathologists. The eccentricity measures the nuclei irregularity, while the circularity value represents how circular the nuclei are. Analyzing the images in Figure 3, the less circular nucleus is the SC, and it has the smallest value for the feature (0.462). Simultaneously, the most irregular nucleus is also the SC, and it has the biggest eccentricity value (0.952).