## 1 Introduction  
Cancer is a class of diseases characterized by malignant cells, and malignant pleural effusion (MPE) is the excessive accumulation of cancerous effusion in the pleura, as shown in Figure 1[1]. MPE is one of the most aggressive cancerous effusions and a sign of an advanced stage of cancer. It is a common problem for cancer patients, and around half of cancer patients end up developing MPE. MPE can be caused by metastatic cancers or primary cancers (mesothelioma). MPE often implies an advanced stage of cancer and confers a poor prognosis [2; 3]. Thus, fast and accurate diagnosis and prognosis of cancer cells in pleural effusion is a first priority task required so that cytologists can arrange effective treatment plans. Cytology examination is currently considered the gold standard for diagnosing cancerous cells in pleural effusion. Cytologists take a small amount of effusion then fix and stain it on a glass slide using certain staining methods. They then visually examine the cytology slides under a microscope in order to diagnose for abnormality in every single cell [4; 5]. However, classical cytological diagnosis is laborious, tedious, and unreasonably time-consuming. It is also prone to different diagnosis results depending on the observer. Recently, there has been growing interest in automated cell analysis systems which can serve as assistance tools to help cytologists during cytology examinations. They can provide fast, accurate and objective diagnostic results for cell analysis [6; 7]. One of the difficulties found while developing such systems is the presence of overlapping nuclei. Nuclei morphology, e.g., size, shape, and density are the most important features used by cytologists in predicting cell malignancy. For instance, the excessive enlargement of nuclei and their irregular shapes are highly suggestive of malignancy. Accurate delineation of each cell contour is essential for the quantitative analysis of cell morphology. In practice, there is a great deal of overlapping nuclei occurrence in cytological pleural effusion (CPE) images. Although human experts find little difficulty in differentiating between single and overlapping nuclei, it is still a challenging task for automatic systems. Overlapping nuclei in CPE images often appear as dark purple regions, and there is a high degree of resemblance among the nuclei forming the overlapped or clustered regions. Thus, an automatic system may wrongly interpret overlapping nuclei as single nuclei. It is difficult to retrieve and quantitatively analyze features such as nucleus morphology and density if cells are touching, overlapping or clustered. Furthermore, the excessive enlargement of size and irregular shapes of overlapping nuclei regions may lead automatic systems to misclassify them as malignant cells. Thus, overlapping nuclei should be detected and distinguished from single ones prior to nuclei feature learning. Many researchers have reported several methods for delineating the interregional contours of overlapping cell nuclei or for splitting the overlapping nuclei into individual ones. Watershed methods [8; 9] and concavity analysis based methods [10; 11] are the most widely used overlapping-nuclei splitting methods in microscopy image analysis. Recently, [PERSON] et al. reported a rule-based clump isolation method for separating overlapping nuclei [12]. In another study, [PERSON] et al. presented a bottleneck rule method for isolating overlapping cells [13]. These previous studies indicate that there has been a tremendous interest in accurately delineating individual cell nuclei in cell image analysis. Nevertheless, it is crucial to accurately determine the presence of overlapping nuclei prior to the occurrence of any splitting process. Some studies have been devoted to distinguishing overlapping nuclei from single ones. For instance, [PERSON] et al. [14; 15] demonstrated a method for the identification of overlapping nuclei on microscopic images of neuroblastoma.