## 1 Introduction
Nuclei are segmented using a mean shift method, and three size-and shape-based features of cells namely (i) area, (ii) diameter equality, and (iii) concavity dominance are extracted to differentiate between single and overlapped cells using step-by-step conditional filtering. [PERSON] et al. [16] proposed a method for detecting overlapping nuclei in microscopic red blood cell images prior to performing a splitting process. First, an image is binarized using an automatic thresholding approach, then three features,  
Figure 1: The existence of pleural effusion in the pleura cavity [1]. namely (i) convex hull, (ii) area, and (iii) elongation, are extracted. The pre-labeled value of each feature through parameter-tuning is used to determine overlapping nuclei. [PERSON] et al. [13] reported on a pre-determination scheme to identify overlapping nuclei using shape-based classification. Five shape features that is (i) solidity, (ii) convexity, (iii) eccentricity, (iv) area, and (v) variance are extracted for each nucleus and fed as input to an SVM classifier to classify single and overlapping cell nuclei. Four different types of image set: oil cells, yeast cells, blood cells and curvularia cells, are used to evaluate the method and obtain a classification accuracy of 86%, 90%, 88%, and 88% respectively. [PERSON] et al. [17] proposed an unsupervised data-clustering method to determine the presence of overlapping cell nuclei from Pap smear cervical images. The nuclei borders are firstly outlined using a morphological operation. Three shape-based features and two minima based features are extracted and used as inputs to a fuzzy clustering method to discriminate between single and overlapping nuclei. The method is evaluated using 290 nuclei and obtains an F-score of 79.1%, a recall of 67.4%, and precision of 95.7%. The methods in [14; 15; 16] are parameter-dependent and limited to objects with a great variation of size and shape. The method proposed in [13] is based only on shape and size features. In the case of cytology pleural effusion images, the forms of overlapping nuclei vary greatly. Thus, it can be deduced that considering only size and shape features may not be sufficient for discriminating between overlapping and single nuclei. The method presented in [17] takes into account not only shape features but also local minima based features and judges for the presence of overlapping nuclei using an unsupervised clustering method, which yields acceptable performance. However, the method is designed specifically for cervical cells. It cannot be taken for granted that this method will provide good results with pleural effusion cells. The originators of the aforementioned method did not take into consideration the textural pattern difference between single and overlapping nuclei despite the fact that the texture pattern between single and overlapping nuclei varies greatly. Moreover, supervised learning techniques could greatly help to attain a more accurate detection rate [18]. For our method, we extract a new combination of 16 geometric (i.e., size and shape) and 10 textural features and select the most relevant features from a total of 26 that are then used in identifying overlapping nuclei in CPE images. Using the selected features, five supervised learning methods, namely naive Bayes (NB), support vector machine (SVM), K nearest neighborhood (KNN), decision tree (DT), and random forest (RF), are examined for the classification of single and overlapping nuclei. It should also be noted that our study objective is focused on accurately detecting overlapping nuclei to improve the extraction of each nucleus. Our proposed method is not a separation algorithm for overlapping nuclei or an extraction algorithm for interregional contours of overlapping nuclei.