## 4 Results and Discussion  
We present the results for machine learning-based regressors in Figure 5 and for our proposed CNN-based regressor in Figures 6 and 7. We gather all results (average \(\pm\) standard deviation) in Table 1 where raw images are used as inputs (IMG), or images are processed using HOG or Frangi filtering. We notice that there are large differences in performance among the machine learning approaches with a feature extraction or without. The best-performing regressor is the Ridge Regression with the HOG features. The performance of RR + Frangi is slightly worse, but it seems to be statistically indistinguishable. The NNR performed the worst, with an MAE of 107 using the images as features, and 98 and 111 using the HOG and Frangi, respectively. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**MAE \(\pm\) std** & **IMG** & **HOG** & **Frangi** \\ \hline SVR & \(88\pm 65\) & \(94\pm 69\) & \(86\pm 64\) \\ RR & \(88\pm 71\) & \(41\pm 37\) & \(45\pm 52\) \\ NNR & \(107\pm 101\) & \(98\pm 96\) & \(111\pm 101\) \\ XGB & \(86\pm 81\) & \(85\pm 79\) & \(81\pm 79\) \\ GTB & \(75\pm 58\) & \(82\pm 55\) & \(67\pm 51\) \\ \hline Our w/o TL & \(32\pm 33\) & x & x \\ Our w/TL & \(12\pm 15\) & x & x \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Results of applying various feature extraction methods in combination with different regressors vs. our approach. Figure 5: Various boxplots showing the results of applying regressors on: (**Left**) just the image as input, and on extracted features using (**Middle**) HOG and (**Right**) Frangi filtering. Figure 6: A boxplot and a scatterplot showing the results of our CNN-based regressor on the test set without transfer learning applied. Figure 7: A boxplot and a scatterplot showing the results of our CNN-based regressor on the test set with transfer learning applied. Its standard deviation was close to 100 for all three feature extractors, hereby making this approach too unreliable to use in a practical setting. Interestingly, for some regressors (SVR, NNR) applying a feature extractor does not decrease the error, or it could even increase the MAE value. In some cases (NNR, XGB) the performance is almost the same. When looking at the average error of all ML-based regressors for each feature extractor, we see that using just the images gives an MAE of 88, using HOG 81, and using Frangi 78. So, although the best-performing model (RR) uses HOG as features, the average performance of all ML-based regressors was best when using Frangi features. These results clearly indicate how difficult it is to select a proper pair of a feature extraction method and a regressor. The performance of the machine learning-based regressors is rather mediocre. First, the average of the best-performing model is around 40 that is rather high from a practical point of view. Second, the standard deviation is also high, at around 35. This means that in many cases the error is above 50 or even more. Moreover, all other regressors achieved error above 70 that place them as completely unreliable and impractical approaches. A possible explanation of this outcome is the small training sample. Our deep-learning-based approach with transfer learning, on the other hand, achieved an error around 12, with the standard deviation equal to 15 (see Table 1). Only in a few cases, the error was large (>30). Interestingly, the model performed worst when there were more than 300 cells present in an image. In that case the error was more than 60, more than 3 standard deviations away from the mean absolute error of 12. That being said, the MAE of 12 indicates the great practical potential of the proposed CNN-based regressor. This result is especially promising because even human-based counting is a noisy process that could result in a discrepancy of a similar magnitude (\(\sim\)10). To achieve a confirmation of whether transfer learning is indeed useful, we also trained the presented CNN-based regressor without pretraining.