## 3 Methodology
### Nuclei Segmentation  
Nuclei segmentation is an important task for most microscopic image analysis employed in disease diagnosis, and also in the determination of overlapping nuclei. Accurate extraction of nuclei regions  
Figure 5: Individual components of RGB of CPE image: (**a**) Original CPE image, (**b**) red component, (**c**) green component, and (**d**) blue component. Figure 6: The visual results of the preprocessing step: (**a**) after applying histogram stretching on green channel, and (**b**) after applying CLAHE on resulting image from histogram stretching. can result in the good performance of subsequent processes. In most CPE images, cell nuclei appear as the darker regions, along with blood cells and artifacts, and are relatively low in gray-level intensity. On the other hand, background and cytoplasm regions are high in gray-level intensity. Image gray-level intensity variation is depicted as the surface plot in Figure 7, wherein the dark-bluish intensity valleys represent cell nuclei regions. By benefiting from this priori-knowledge of brightness and intensity variation inside an image, we consider gray level intensity-based image segmentation methods to extract the cell nuclei. Thresholding methods are the simplest and most used approaches to gray level intensity-based image segmentation. Currently, there are numerous thresholding based segmentation methods, e.g., [PERSON]'s thresholding method, the adaptive thresholding method, maximum entropy thresholding, and so on. Maximum entropy thresholding does not require specific prior knowledge and can deal with images which have non-ideal bimodal histogram. Therefore, we employed a maximum entropy thresholding method to extract cell nuclei from CPE images which have non-uniform gray level distribution. Another motivation for using the maximum entropy method to select the optimal threshold in our study was that it has been widely and successfully used in many real applications of medical image analysis [22; 23; 24] Maximum entropy thresholding is one of the global thresholding methods which is proposed by [PERSON] in 1948, [25; 26]. Similar to the Otsu method, maximum entropy thresholding selects the optimal threshold by maximizing the information measure between objects and their backgrounds. In our study, maximum entropy thresholding based nuclei segmentation was performed using five steps. In the first step, we computed the entropy function on the 1D histogram of a gray level image. The second step was to compute the probability distribution of the object and the background. Suppose \(i\) is the gray level intensity of a pixel in an image so \(i=[0,1...T-1,T,t+1...255]\), and the probability of each gray level \(i\) can be calculated as:  
\[P_{i}=\frac{n_{i}}{n} \tag{1}\]  
where the total number of pixels in an image is denoted as \(n\), and the number of pixels that have a gray level \(i\) is denoted as \(n_{i}\). Let \(roi\) and \(b\) respectively be the region of interest (ROI) and the background of an image; thus, the probabilities of \(roi\) and \(b\) are defined in Equations (2) and (3):  
\[P_{roi}=\sum\
olimits_{i=0}^{T-1}P_{i} \tag{2}\]  
\[P_{b}=\sum\
olimits_{i=T}^{255}P_{i} \tag{3}\]  
The third step was to compute the entropies of ROI and the background, which can be computed as follows:  
\[E_{roi}(T)=\sum\
olimits_{i=0}^{T-1}\frac{P_{i}}{P_{roi}}log_{2}\frac{P_{i}}{P _{roi}} \tag{4}\]  
\[E_{b}(T)=-\sum\
olimits_{i=T}^{255}\frac{P_{i}}{P_{b}}log_{2}\frac{P_{i}}{P_{ b}}, \tag{5}\]  
Therefore, the entropy of the gray level image segmented by threshold \(t\) is:  
\[E(t)=E_{roi}(t)+E_{b}(t) \tag{6}\]  
The principle of maximum entropy is applied to select \(t\), which maximizes \(E\).