## 1 Introduction
This method was known to be poor as early as the 60s [6] and newer and better performing algorithms have been developed since. One of the seminal developments in this field is [PERSON]'s method [7] which improved upon previous thresholding algorithms by developing a non-parametric and unsupervised method for selecting the threshold. In [PERSON]'s method, the threshold is chosen by minimizing the intra-class variance of the foreground and background pixels. Although [PERSON]'s method was a great development, it suffers from several limitations including noise and small object size. A modification to [PERSON]'s method to address issues with noisy images called the two-dimensional [PERSON]'s method was published in 1991 [8]. It improved performance on noisy images by comparing pixel intensity variance within a pixel's neighborhood rather than globally. A difficulty with image segmentation comes from brightness gradients across images. A single threshold is not enough to deal with this problem. Adaptive thresholding, where a new threshold is calculated for every pixel is therefore necessary for this task. An algorithm developed in 2007 [9], uses the integral image to calculate the average pixel intensity around a pixel and if the intensity is a certain threshold below the average, it is set to black, otherwise it is set to white. The advantage of this algorithm is it performs well on images with spatial variation of illumination, and it is very fast to compute. Interactive segmentation algorithms are also a popular set of methods for image segmentation. These include tools such as the Lasso tool in Adobe Photoshop, as well as Lazy Snapping [10] and Grabcut [11]. Lazy Snapping and Grabcut are accurate tools that involved user input to help locate the general area of the boundary. In the case of Grabcut, a bounding box was drawn by the user around the object of interest, and iterative graph cuts employed by the algorithm would segment the object inside the bounding box. Meanwhile for Lazy Snapping, lines would be drawn by the user to indicate the general area of the foreground and background and graph cuts would place a deformable edge around the object, allowing the user to correct any errors. A similar user interface is involved in [12], which requires the user to scribble different regions of interest in an image. The advantage of these tools was mainly ease of use, but the interactive nature did not make them useful in high-throughput settings such as biomedical imaging. A class of segmentation algorithms using active contours were developed in the 80s, 90s and 2000s. [PERSON] et al. introduced the Snakes active contour algorithm in 1988 [13]. The Snakes algorithm uses energy minimization to fit deformable splines to the contours of objects in images. They were able to solve problems that had up to that point eluded accurate segmentation, especially in images with a lot of noise. The Snakes algorithm, however, was not completely automatic and required user input to move splines out of local minima. Extensions to this work involved improvements to the types of active contours that were used, the energy definition and the energy minimization algorithms used [14; 15]. The watershed algorithm, developed by [16] is a segmentation algorithm with a very intuitive explanation. It looks at an image as a topographical relief map. The image is 'flooded' at the local minima in the image and the places where different sources of water touch are used as segmentation boundaries. [PERSON] improved the algorithm by introducing markers as sources for flooding, avoiding the issues with having flooding from all regional minima [17]. By indicating the sources of flooding with early approximations of the objects of interest, watershed segmentation performs very well and is often included in segmentation and tracking pipelines even now [18; 19]. Many algorithms have been presented for the cell segmentation problem over the past decade.