## 4 Experiment and Results
Our main goal was to achieve a precision of 10 \(\upmu\)m (average size of thyroid cells in zebrafish according to [14]), and to illustrate this, a shade around the gt with this width is added. From this image, one can see that this goal is mainly achieved for the middle elements, while the elements in the beginning and the end are differingly stronger. Elements at the beginning and the end are linked to a very low or very high voltage and so to the clearest distortion in the input image for the CNN. It is possible that learning features in the middle of a range is easier for the CNN, and this might depend on the camera parameters used and the possible occurrence of over saturation at the end of the range. However, due to the test loss of 6.5 \(\upmu\)m (_MAE_), our CNN obviously shows a good performance inside the desired range of tolerance. The statistical results on the test datasets are summarized in Table 1. Here, the accuracy of the results on the test dataset consisting of four elements is also reported. Each estimation, which differs less than 10 \(\upmu\)m from the ground truth value, is considered as a correct estimation. After several weeks and some lens adjustment, another dataset from the same setup and also consisting of 41 data elements was recorded to investigate the performance of the network on data after the AL was influenced by environmental circumstances such as changing ambient temperature and pressure. We used four random elements of this dataset for testing with the trained network and reached a test loss of 213.36 \(\upmu\)m (\(MAE\)), see Table 1. As shown in Figure 5b (blue circles), the estimations do not match the corresponding gt values anymore. This is caused by the intentional misalignment of the setup, leading to different gt values compared to the first dataset. Here, the elements from the test dataset are marked in black. The test elements were not included in the training or validation process. We used transfer learning [32] to improve the performance, and again, data augmentation was used to extend the dataset. As in the first training process, Gaussian noise was added to the images, but here, the noise was sampled from a normal distribution with a standard deviation of 10 counts. This enables the extension of the training and validation data to 3219 images. In the method of transfer learning, a trained CNN is again trained with a slightly different dataset on top. This enables the CNN to recognise input elements with small discrepancy compared to the first dataset. After 87 epochs of transfer learning with heavier data augmentation than in the first training, the CNN achieved a test loss of about 8.15 \(\upmu\)m (\(MAE\)). The whole process of transfer learning was conducted with the second dataset, which was recorded several weeks after the first dataset. The validation loss while training is provided in Figure 4. The improvement in correctness of the network estimations can also be seen in Figure 5b, where the estimations after transfer learning are displayed with green circles and the test elements are marked in black. It is obvious that some pattern of estimation distribution from before transfer learning are still visible in the estimations after transfer learning. By comparing the mean difference (\(MAE\)) of gt and estimation before transfer learning (213 \(\upmu\)m) and after transfer learning (8 \(\upmu\)m), a huge improvement is shown. Furthermore, the standard deviation (\(STD\)) of the difference also decreased from 62 \(\upmu\)m before transfer learning to 2 \(\upmu\)m afterwards. The transfer learning process took 16 min on the above-described system. As an exemplary application, a scan through a fluorescent specimen was performed. In Life Sciences, the investigation of fluorescent specimen by using confocal microscopy is a principal task [33]. To prepare a fluorescent sample fluorescent beads were placed onto a mirror, followed by a microscope slide where on top again fluorescent particles were located. A scheme of this sample is shown in Figure 6a.