# Unsupervised Cyclic Siamese Networks Automating Cell Imagery Analysis
## 3 Methodology
### Synthetic Data  
We propose a novel learning scheme in Section 3.3.2 that deals with synthetic data with known ground truth (i.e., the cell count) and a Siamese architecture that can abstract from the fact that the auxiliary data are synthetic. In addition to the common data set enrichment, generating proxy data allows us to create a wide variety of synthetic samples, which are inspired by the natural data, but not limited by their amount or variety. By enriching the training procedure with synthetic data, we extinguish the need for natural labeled data. Synthetic data are easily obtained in this setting because the architecture does not require that the images are rendered realistically in all respects, such as morphological details. The 128 \(\times\) 128 working resolution of the architecture makes the synthetic data generation undemanding, while maintaining sufficient intricacy of visual features such as overlapping (see Figure 3 left). For the specialized training procedure described below, we do not need to synthetically create images that are indistinguishable from natural ones, unlike current data augmentation schemes, such as proposed in the \begin{table}
\begin{tabular}{c c c} \hline \hline
**Data Set Name** & **No. of** & **No. of Bright-Field Images** \\  & **Phase-Contrast Images** & **No. of Bright-Field Images** \\ \hline Nat & Nat-PC & Nat-BF \\ Nat-U-Tr & 3.152 & 2.469 \\ Nat-L-Te & 792 & 514 \\ \hline Syn & Syn-PC & Syn-BF \\ Syn-L-Tr & 3.152 & 2.469 \\ Syn-L-Te & 792 & 514 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Overview of all data sets used. Nat-U-Tr contains natural, unlabeled training data; Nat-L-Te natural, labeled test data; Syn-L-Tr synthetic, labeled training data, and Syn-L-Te contains synthetic, labeled test data. For reasons described in Section 3.2, synthetic data have been generated in a 1:1 ratio to natural data. Nat-PC refers to all natural phase-contrast images (i.e., Nat-L-Te and Nat-U-Tr) and Nat-BF refers to all natural bright-field images, respectively. Syn-PC and Syn-BF denote the groups of training and test data for phase-contrast and bright-field data accordingly, and, lastly, Nat and Syn denote the full set of natural and synthetic data. work [41]. This would require a considerate amount of engineering [37], i.e., human expert labor, exactly what we aim to mitigate. We rely merely on modeling simple ellipsoidal shapes to embody cells, ignoring details of the texture and the intricate morphology of real suspension cells. We imposed this limitation on ourselves to suggest that the learning procedure presented below should also work with other types of image data and is neither tailor-made for exactly these microscopy technologies nor requires extensive manual work to generate the most realistic synthetic data possible. In Section 3.3, we show that this approach is adequate for training our architecture described. We ensured that the distribution of cell counts in the auxiliary data was sufficiently close, but not necessarily identical to that of the natural data sets. This allows for an unlimited amount of labeled training data, with only the processing time being the limiting factor for the potential to use enormous amounts of proxy data, not the availability of such. One problem remains, however, which is how to actually improve the regression performance on natural data. Using a large ratio of synthetic data compared to natural data would entail a separation of the two types of data in the inner representation of the network, resulting in high accuracy on the synthetic data, but low accuracy on the natural data (see Section 4). To prevent this separation, two major functionalities are proposed and have been implemented, described in more detail in the following paragraph. The auxiliary data generator is highly adjustable and produces imagery with a given distribution of cells.