# Unsupervised Cell Segmentation and Labelling in Neural Tissue Images
## 2 Methods
### Object Segmentation Phase  
In this work, an image \(I\) is represented as a function \(I:\{1,\dots,M\}\times\{1,\dots,N\}\mapsto\mathbb{R}^{n}\), where \(M,N\in\mathbb{N}\) represent the number of rows and columns in the image. The specific pixel-wise information represented by an element in \(\mathbb{R}^{n}\) is far from standardised in the context of medical imaging; different imaging techniques might capture different biological facts or simply represent them in diverse manners. We denote the set of images whose pixels take values in a given set \(A\) as \(\mathbb{I}_{A}\); for instance, \(\mathbb{I}_{[0,1]}\) refers to the set of binary images, while \(\mathbb{I}_{\mathbb{R}^{n}}\) stands for the set of images with vectorial, real-valued information.  
The Object Segmentation (OS) phase is a mapping \(s:\mathbb{I}_{\mathbb{R}^{n}}\mapsto\mathbb{I}_{[0,1]^{n}}\) whose goal is to discriminate the items of potential interest to the application from the background. This discrimination must be done on the basis of the visual information in the image, e.g., colour, colour transitions in RGB images or intensity in grayscale images.  
Although many different techniques can be fit into the description of the OS phase, thresholding techniques are most commonly used. Straightforward options are [PERSON]'s method [22] (for bimodal histograms) or [PERSON]'s method [23] (for unimodal ones). There exist a wide variety of other methods that might serve similar purposes, e.g., binarization techniques [24; 25]. Depending on the unwanted factors (blurring, noise, etc.), the OS phase might also involve a denoising or sharpening procedure. Bilateral filtering [26], anisotropic diffusion [27] and related techniques [28] are sensible alternatives in this regard, since they perform adaptive smoothing with a sharpening effect. While these techniques can improve the results of the OS phase, they can also incur a significant burden in parameterization [29]. Another recurrent problem in cell screening is the presence of colliding or overlapping cells, which are not trivially discriminated by automatic methods. A primary alternative in these cases is the use of object detection methods designed for blob-like structures [30]. A secondary alternative, not based on filtering, is the use of superpixel maps [31] as the initial oversegmentation. Superpixels are normally able to  
Figure 1: Visual representation of the USRL schema workflow: (**a**) the original USRL schema input image; (**b**) the output resulting from the object segmentation phase; (**c**) the refinement output of (**b**), eliminating unwanted objects and noise; (**d**) the final labelled image, where each class comes with an associated colour.  
provide an initial discrimination between nearby objects according to their shape and tone, hence avoiding the joint segmentation of very close objects.  
The key to determining the best procedures for the OS phase is understanding the need for the auditability of the process. The procedures at this phase should not, in principle, use information other than visual (tonal) information. Furthermore, decisions should be made in a local (pixel) or semi-local (neighbouring region) scope. Finally, in order to maintain the auditability of the multi-phase process, this should involve a minimal number of parameters, especially if such parameters have a non-evident interpretation.