# Toward Automatic Cardiomyocyte Clustering and Counting through Hesitant Fuzzy Sets
## 2 Related Work  
Existing methods for counting cardiomyocytes are mostly manual or semi-automated operations, such as the blood cell counting plate [25], the trypan blue staining count [26], and the visual field counting method [27]. Manual counting not only takes a long time but also incurs human errors. Therefore, an automatic counting system is highly desired. Semi-automated approaches exist to record the cardiomyocytes state (e.g., frequency scaling, morphological changes) in the culture of cardiomyocytes. In [28], the cardiomyocyte motion field is calculated in real time by GPU acceleration, and the autotrophic model is used to analyze the contraction frequency of cardiomyocytes. In [29], a microelectrode-array (MEA)-based dual-function cardiomyocytes biosensor system explores the impedance detection function, monitors the rhythmic beat of cardiomyocytes, and simultaneously records the extracellular potential. Unfortunately, both of the above approaches show significant errors. Under normal circumstances, the observation of cardiomyocytes mainly depends on ordinary light microscopy. Therefore, the state of the practice of observation and statistics of cardiomyocytes are still largely dependent on manual approaches, including recording the cultivation of cardiomyocytes, extracting and clustering the target objects, counting the number of cells, and so forth. However, there are few automatic and efficient cardiomyocytes occuring methods built upon efficient algorithms and computer systems. The state of the practice of automatic counting in this area is for red blood cells due to its unique shape. In the following part, we will review important work in counting cells. Previous literature mainly focused on red blood cells. In [30], an automatic mosaic method is proposed to improve the reliability of live/dead cell counts by representing the entire red blood cell as a grid mosaic. In [31], an approach is proposed to improve the accuracy of cell counting by learning the parameter set of each application to reduce the error during fine-tuned filtering. For counting red blood cells, mathematical morphology and Otsu threshold method [32] are proposed to determine the round red blood cells, non-circular red blood cells, and overlapping red blood cells. For grayscale images [33], estimating the minimum and maximum number of red blood cells can be achieved by obtaining red blood cell, masking small circle transformation, and then detecting and counting the cells with the iterative soft threshold after removing conflicting red blood cells. Another approach [34] is to simulate human visual system by a computer-aided system and automatically detect red blood cells and white blood cells in the image. There are also many methods using artificial intelligence and machine learning to perform red blood cell counts. In [35], supervised learning and optimal clustering are employed along with spatial color classification to separate overlapping cells and count the number of fetal and maternal red blood cells. Classification of red blood cell images using spectral angle mapping (SAM) [36] is proposed; SAM leverages support vector machine (SVM) and establishes a standard red blood cell model for matching the red blood cells. The approach proposed by [37] takes convolution lexical learning and coding for red blood cell detection and counting in holographic lens imaging. Two types of single-frame processing based on machine learning [38] are proposed for lensless red blood cell counting, i.e., based on extreme learning machines and convolutional neural networks. Existing methods of counting white blood cells include [39], which detects more accurate regional boundaries by using gradient-based region growth and neighborhood effects after region segmentation. Each region is classified according to its shape, size, color, and texture features using different fuzzy and non-fuzzy techniques, respectively. Cell counting methods for non-red blood cells are also available.