# Evolutionary 3D Image Segmentation of Curve Epithelial Tissues of _Drosophila melanogaster_
## 1 Introduction
### Related Works  
Machine learning is defined as the development of intelligent systems that learn to solve complex problems automatically from experience [16]. Their approaches for segmentation classify in two groups: unsupervised and supervised. The first approach is based on finding a reference criterion that can be used to optimise the parameters of a segmentation algorithm [17]. For instance, [PERSON] et al. [18] applied a modified version of the search algorithm of the cuckoo for segmenting bidimensional microscopic images of the hippocampus in an unsupervised way. To do that, they optimised segmentation methods based on thresholding, even though they found unsatisfactory results for low levels of thresholds. In addition, [PERSON] et al. [19] applied the search algorithm of the firefly based on swarm intelligence to segment biological images in two dimensions. To achieve that, they also optimised a threshold segmentation. Furthermore, [PERSON] et al. [20] designed a novel version of mean-shift clustering algorithm to segment bidimensional images in an unsupervised way. The algorithm proposed a new online seed optimisation policy and early stopping as conditions to achieve a better computational speed. By contrast with the previous examples, supervised approaches use a training data to learn how to segment the images [17]. The disadvantage of supervised approaches is the creation of training data, as it requires consistency among the researchers dedicated to sample and it requires a time-consuming methodology. For instance, [PERSON] et al. [21] applied different optimisation algorithms, such as genetic algorithms, hill climbing and coordinate descent to segment images in two dimensions in a supervised way, using the ground data as fitness function. In addition, [PERSON] et al. [22] designed a combination of a deep learning algorithm and segmentation algorithms to automatically segment biological images in 2D. The deep learning model learned to predict the locations of cells, which were used to find a threshold to initiate the seed of the watershed algorithm. Most of the approaches to automatically segment biological images are supervised [23; 24; 25; 26; 27; 28]. Frequently their applications have been limited to segmentations in two dimensions due to the fact that three-dimensional data sets are difficult to obtain in some biological fields, where the availability of raw images is limited or where the segmentation is particularly difficult [29; 30]. However, the necessity of studying biological tissues in a context of three-dimensionality has been proved, for example, to unveil the presence of a novel cellular shape necessary to pack efficiently monolayer epithelial tissues in curvature conditions: the scutoids [31], or to analyse the composition of other complex tissues, such as multilayer epithelia, where tetradacehedral cells predominate [32]. Consequently, some three-dimensional biological studies cannot progress as fast as they expect, and they still need to optimise the segmentation process manually or through classical approaches, which may cause significant delays. Thus, it is vital to optimise this process automatically, to achieve automatic segmentation, which would accelerate their science. This article presents an implementation of an evolutionary algorithm proposed to optimise three-dimensional segmentation in a semi-supervised way. Our implementation uses a three-dimensional region growing segmentation algorithm called LimeSeg, whose parameters are optimised through the measurement of segmented cells. It has been applied to three different data sets of confocal images (each data set contains several images to represent only one sample of a tissue) taken from the model organism, _Drosophila melanogaster_: salivary glands, embryos and egg chambers. Classically, all of them have been widely used to analyse the different biological events in which epithelial cells are involved: division, migration, apoptosis, differentiation, polarity, cancer, wound healing and much more [33; 34; 35; 36; 37].