# A Novel Evolution Strategy of Level Set Method for the Segmentation of Overlapping Cervical Cells
###### Abstract
The LSM-based approach is more suitable for completely automated cervical cell segmentations, because it is less dependent on seeds initialization and parameter configuration. As an effective method for object delineation, LSM was first proposed by [34]. In the development of LSM, scientists contributed some classic works. For instance, after the original snake model was proposed in [35], a geometrically flexible and topologically changeable snake model was introduced independently [36; 37] by partial differential equation (PDE) and has been successfully applied in two- and three-dimensional spaces. After [PERSON] [38] first proposed a functional framework for image segmentation based on the variation method and [PERSON] [39] first introduced the Heaviside and Delta functions to represent the length and area of the region delineated by level set function (LSF), [PERSON] [40] proposed a successful region-based LSM known as the C-V model. Moreover, based on the previous works [38; 41], [PERSON] [42] first proposed an edge-based LSM with a prior shape. [PERSON] [43] proposed a new LSM (DRLSE) without periodic reinitialization LSF as signed distance function (SDF). DRLSE is used in the baseline method [33] to speed up the contour evolution. LSM can be used to detect the textural edges like Canny edge detector [44], because its adaptive topology changes can fit multiple target contours at the same time. The LSM can even control non-closed curves in three-dimensional space by means of the codimension two-level set method (CTLSM), which was first carried out by [45] and developed by [46]. In addition, the LSM has been successfully applied in image segmentation tasks [25; 47; 48; 49]. [PERSON] [33] proposed an algorithm for cervical cells segmentation based on multiple level set functions, which has been regarded as the baseline and comparative algorithm by a lot of literature [26; 28; 50; 51; 52; 53; 54]. However, it has a problem that the poorly initialized level set function never converges to the cell boundaries. With the rapid improvement of the graphic processing unit (GPU), CNNs (convolutional neural networks) have been widely used in the field of medical image segmentation. However, these methods mainly focus on clinical parameters, such as the volume and shape obtained from organ and structure segmentation for quantitative analysis and organ substructure obtained from lesion segmentation for histopathological diagnosis [55]. After the U-net was introduced by [PERSON] [56], U-net-like architecture convolutional neural networks have achieved good results in semantic segmentation tasks, such as the segmentations of organs, tissues or lesions areas in CT, X-ray and MR medical images. In contrast, cervical cell segmentation is more like an instance segmentation task that attempts to delineate all cells from Pap images to separated instances. Although CNN-based methodologies, such as Mask R-CNN [57], have good performances for instance segmentation, they are not suitable for the automated and complete cervical cells segmentation, because the overlapping regions in pairs of overlapping cells cannot be separated. In the latest proposed panoptic segmentation task, which combines semantic with instance segmentation, nonoverlapping is clearly declared in the seminal work [58]. Therefore, CNN-based segmentation methods are difficult to use to achieve end-to-end cervical cell segmentation. This means classical image processing strategies are essential for CNN-assisted methods [22; 59] that are successfully used in the segmentation of overlapping cervical cells. Moreover, the other obstacle for cervical cell segmentation by CNNs is a lack of datasets, and the CNN-based segmentation methods are particularly dependent on datasets. In this paper, we propose a novel method to automatically segment the cytoplasm of touching and overlapping cells in Pap images. Our proposed method is capable of fully segmenting cervical cells compared with the method that can only segment isolated cells or segment regions of cellular clumps [60; 61].