## 4 Results and Discussion
Consequently, the MAE increased to 33 with the standard deviation equal to 34 (see Table 1). This result indicates that using a pretrained neural network is indeed beneficial, especially in a biomedical domain as highlighted in the past [62]. Nevertheless, even though the performance of the CNN-based regressor without transfer learning dropped, it was still better than most of the machine-learning-based regressors. This is another indicator of the superiority of the end-to-end training of a single model instead of hand-crafted feature engineering with an adaptive model on top of it. Analyzing Figure 6 (the model without transfer learning) and Figure 7 (the model with transfer learning) it is apparent that transfer learning has a huge impact on the final performance. Interestingly, both models have their worst prediction on the image containing 323 cells (the model with transfer learning achieved an error equal 70, and the model without transfer learning obtained error equal 135). More generally, both models' accuracy decreases in images with more cells, although this effect is stronger for the CNN without transfer learning, as can be seen in the scatterplots in Figures 6 and 7. Looking at Figure 8 we can notice the images with the highest cell counts of the test set, and the corresponding average loss over all models. Some images show artifacts, which may have affected the models' performance. For instance, Image A shows some black artifact in the top right corner, while image B shows some light-colored circular line, and a dark-colored circle in the top right corner. More importantly, all images show at least some degree of cell clumping, and some show overlapping cells. It is most likely not a coincidence that the images with the highest average error have cell clumping and overlapping cells present (Figure 8, images F & H). Apparently, these issues were hard to deal with for both the ML-pipeline and the CNN-regressor, but mostly for the former. Since manual feature extracting methods usually represent images using a limited number of feature types (such as edge, corner or shape detection), problems may arise when the input changes such that the feature extractor's requirements are not satisfied anymore. In the case of the HOG, choosing the right kernel size may be tightly coupled with the cell size, and to obtain larger gradients it may require strong differences in pixel intensity between the inside- and outside of cell areas (which is less present with cell clumping and cell overlapping). The Frangi filter may also perform less well when artifacts are present [71], and similar to the HOG, it also performs better with stronger differences in pixel intensities for cell borders [51]. The CNN, on the other hand, did not require any assumptions of the data and was able to learn features automatically, and the CNN with transfer learning (TL) did so even better than the version without. Although the latter had to spend some training epochs learning low-level features, the CNN with TL could transfer this from its training on ImageNet across domains to our task. This head start meant that deeper layers were able to learn more abstract features, such as entire cells. Possibly this made the model better at distinguish cells from one another, even in the cases where cells were clumped or overlapping.