Cells are the basic unit of biological tissues. State analysis of cells is an important subject in medicine. Researchers study the shape, life cycle, position, speed, trajectory and other information of cells by observing the morphology of cells. For the research of cells’ behavior, it is necessary perform quantitative analysis of cells, such as cell size measurement, cell counting, and cell tracking, etc. The accuracy of cell segmentation operation will affect the results cell counting and cell tracking.

With the advancement of microscopic imaging technology, researchers can easily obtain a large number of high-quality cell images, which also provides a basis for cell analysis. However, data analysis of medical cell images usually encounters the following difficulties:(1)

Cell images have low resolution and are difficult to segment. Therefore, cell images usually require preprocessing.

The acquisition cost of cell images is higher than that of ordinary images, so training samples may be insufficient.

Due to the richness, heterogeneity and complexity of cell images, it is difficult to manage, process and analyze them. With the development of image processing technology based on computer vision, automatic analysis of biomedical images has become possible and has gradually become the key to the development of cell biology. In this article, morphological methods will be used for quality enhancement and edge segmentation of overlapping cell images.

The purpose of cell image segmentation is to simplify cell images and extract interesting information from them, and to provide a basis for subsequent image analysis and understanding. Image segmentation is the process of dividing an image into several meaningful areas. The cell image segmentation algorithm can realize cell segmentation and detection, and prepare for cell tracking and cell counting.

Current imaging tools and medical image processing and analysis platforms are developing rapidly, such as Cell Profiler [1] and Image J [2], which integrate a large number of modular image processing algorithms, which can process images in batches and provide extended interfaces.

At present, thousands of image segmentation algorithms have been proposed, but the development of cell segmentation algorithms is relatively lagging. Most cell segmentation algorithms are designed for specific types of cells. Therefore, there is currently no universal cell segmentation algorithm.

In order to find the most suitable segmentation method for the target cell image and improve the accuracy of cell segmentation and classification, it is necessary to fully understand the characteristics of various algorithms and the characteristics of cell images, and comprehensively consider the factors of cell structure. The hardware platform, the running speed of the algorithm, the segmentation accuracy of the algorithm, the generalization ability of the algorithm, the training speed of the sample, the difficulty of making the sample, etc.

Common segmentation algorithms include threshold segmentation methods [3–6], region-based segmentation methods [7–9], active contour-based segmentation methods [10,11], graph theory-based segmentation methods [12–14] and images segmentation method based on deep learning [15–17] etc.

Based on the Otsu algorithm, Cseke [18] maximized the intra-class variance between the black, gray, and white regions in the cell image through a recursive method, and automatically selected the segmentation threshold to achieve cell segmentation. However, this method cannot divide the cytoplasm.

Rezatofighi et al. [19] used Gram-Schmidt orthogonalization to enhance the color vector of the cell area, and then determined the segmentation threshold according to the gray histogram, and segmented the nucleus, and finally used the Snake algorithm to segment the cytoplasm.

Hou et al. [20] used an improved Snake model to segment and repair overlapping cells.

Arteta et al. [21] proposed a cell segmentation method based on MSER detection, which has achieved good results in many types of cell detection tasks, but cannot obtain accurate cell edges.

Dimopoulos et al. [22] proposed a cell segmentation algorithm based on MPCS, which uses a circle detection algorithm based on Hough transform to detect seed regions. Although the algorithm can obtain more accurate cell edges, the detection results are very unstable.

In 2012, Mohapatra et al. [23] proposed cell segmentation based on linked networks. The algorithm classifies the color of the pixels in the cell image and divides the cells into nucleus and cytoplasm.

Huang et al. [24] used co-occurrence matrix and morphological information to extract 85 texture and morphological features, then used PCA for feature dimension reduction, and K-Means for five-category classification. The classification accuracy of this method for neutrophils is relatively low.

Wang et al. [25] used color information conversion, distance conversion and GVF Snake method to extract cells, and used SVM to classify the cells.

Gu et al. [26] used cell edge phase angle information and linear interpolation to subdivide the cytoplasm, but this method is not suitable for cell images with severe cell overlap.

Ding et al. [27] used a sub-level algorithm for image segmentation of overlapping cells.

Hou et al. [28] used mathematical morphology to segment bone marrow cells.

Wang et al. [29] used the regional growth method to achieve the segmentation of breast cells.

Ruberto et al. [30] proposed a limit corrosion algorithm, which repeatedly corrodes the overlapping cells through morphological corrosion until the seed point disappears. After the seed point image is obtained, the segmentation operation is performed through the watershed segmentation algorithm [31] to obtain the cell segmentation image.

Hou et al. [32] used distance transformation to convert the pixel information of adhering cells into position information, and then segmented the cells through watershed transformation to obtain segmented images. The distance transformation algorithm is likely to cause over-segmentation problems.

Qu et al. [33] used the chain code theory to convert the boundary information of the image into chain code information, and then looked for possible pits as separation points, and finally separated the overlapping cells. The contour tracking algorithm will cause under-segmentation.

In summary, there are some algorithms for overlapping cell segmentation, but their segmentation effect needs to be further improved.

Mathematical morphology was proposed in 1964 by Tan et al. [34]. Mathematical morphology is based on set-based algebra, and its main research content is to quantitatively analyze the morphological and structural characteristics of objects. Mathematical morphology is a new method used in the fields of image processing and pattern recognition. At present, mathematical morphology has become a very important and most valuable research field in digital image processing, and has been successfully applied to fingerprint recognition, medical microscopic image analysis, traffic detection, robot vision and other fields.

Mathematical morphology has a complete foundation of mathematical theory. The most notable feature is that it can be directly used to process the geometric structure of the image surface. Compared with spatial domain or frequency domain algorithms, mathematical morphology algorithms have obvious advantages in image processing and analysis. For example, in the process of image restoration, a morphological filter based on mathematical morphology can effectively reduce the noise in the image, while using prior recognition of features and morphological operators to retain important information in the image.

Mathematical morphology can be used to process binary images. The gray value in a binary image has only two values, 0 and 1, which are used as background pixels and target pixels, respectively. Binary morphological processing is the process of transforming structural elements in an image and completing operations such as intersection and union. In binary morphology, the two basic operations of erosion and dilation can be combined to produce many other actual morphological operations.

Before using mathematical morphology to process binary images, it is necessary to design a structural element to collect the information in the image. Structural elements can usually be represented by some small and relatively simple sets, such as of spherical, linear, rectangular, etc. Different image processing results can be obtained by selecting structural elements of different scales or shapes.

A program is compiled to perform overlapping cell separation operations on the cell image shown in Fig. 1.

First, the cell image is transformed by Top-hat and Bot-hat transformation, and the result is shown in Fig. 5.

Then the cell image is converted into a binary image, and the result is shown in Fig. 6.

Small isolated blocks are eliminated in the cell image, including scatter dots on the cells and noise in the background. The result is shown in Figs. 7 and 8.

Tiny noises in the cell image such as lines are eliminated with an erosion operation, as shown in Fig. 9.

A dilation operation is performed on the cell image to smooth the cell edge, as shown in Fig. 10.

The cell image is ready to start cell edge segmentation after a majority operation is executed and small blocks are deleted, as shown in Fig. 11.

The cell image is separated into two images according to the area size. The area of normal cells is moderate, as shown in Fig. 12, while the area of overlapping cells is larger, as shown in Fig. 13.

Next the potential dividing points of overlapping cells are found. Since the cells are round, all the connecting parts of the overlapping cells must be concave, as point A in Fig. 13. Fig. 14 shows an enlarged view of point A. However, not all recessed areas are the connecting parts of the overlapping cells, as point B in Fig. 13. Fig. 15 shows an enlarged view of point B. Therefore, it is necessary to select a suitable depression angle threshold to determine whether a pixel in the cell image is the connection point of the overlapping cells.

For the dividing point of overlapping cells, perform cell segmentation along the midline, as shown in Fig. 16. Note that there may be a dividing line with a large deviation in direction. For the overlapping cells after segmentation, it is also necessary to perform erosion and dilation operations to smooth their boundaries. The result is shown in Fig. 17.

Overlapping cells may be divided into multiple pieces. Note that too small an area may be noise and should be deleted. Divide the segmentation target into two parts according to the size of the area, and the area with a larger area needs to be segmented continuously, as shown in Fig. 18. The smaller area belongs to normal cells and should not be divided, as shown in Fig. 19.

The dividing process proceeds until no cells can be divided, as shown in Figs. 20–23.

Fig. 23 shows that no cells were divided in the 5th dividing process.

Perform the erosion operation on the final cell image and remove blocks less than 2000, as shown in Figs. 24 and 25.

A dilation operation is excuted to smooth remaining cells, as shown in Fig. 26.

Combine the result of dilation operation with the cell area confirmed and saved to obtain the final cell image, as shown in Figs. 27–29.

In order to verify the effectiveness of the algorithm proposed in this paper, it is compared with the segmentation results of the distance transformation algorithm and the limit corrosion algorithm. Since the proposed algorithm does not obtain accurate cell edges, the accuracy of cell counting is used as an evaluation measure for cell segmentation. The proposed algorithm is applied to the segmentation and counting of 300 cell images. The segmentation accuracy rates of cells with overlapping degrees of 0%, 15%, 30%, 45%, and 60% were respectively counted, as shown in Tab. 2.

It can be seen from Tab. 2 that the accuracy of the three overlapping cell image segmentation and counting methods decreases as the degree of overlap increases. When the degree of cell overlap is low, the segmentation accuracy of the algorithm proposed in this paper is higher than the counting accuracy of the distance transformation algorithm and the limit corrosion algorithm. When the degree of cell overlap is high, the segmentation accuracy of the proposed algorithm is similar to the other two algorithms.

This paper proposes a cell image segmentation algorithm based on morphology, which uses morphological operations such as erosion and dilation to accurately segment and count cell images. The experimental results show that when the proposed algorithm is applied to segment lightly or moderately overlapping cells, the accuracy is very high. And when it is used to segment heavily overlapping cells, the effect is normal. However, it must be pointed out that since the algorithm in this paper eliminates part of the edge information in the process of cell segmentation, further processing is needed to obtain accurate cell edge information.