## 3 Results  
### ACDC Performance  
In this section, we present the results obtained with ACDC on the VU dataset and the 2018 DSB training dataset [37; 46]. Figure 7 shows an example of results obtained on VU and DSB datasets, where the detected cells are displayed with different colors to highlight the separation among overlapping and merging cells. We note that the analyzed images are characterized by a considerable variability in terms of cell density. Figure 8 shows a representative case for both the VU and DSB datasets, where the results of ACDC are slightly different from the gold standard. In the case of the VU dataset (Figure 8a), it is clear that some groups of small cells, characterized by very similar intensity values without strong discontinuities are detected by ACDC as a single connected-component (orange arrows). On the contrary, for the 2018 DSB dataset (Figure 8b), ACDC is capable of accurately separating groups of cells that were erroneously delineated as single connected-components in the gold standard (green arrows); moreover, the spurious speckles included in the 2018 DSB gold standard (highlighted by blue dashed boxes), are not detected by ACDC since these very small regions are characterized by hypo-intense fluorescence levels. Figure 7: Examples of cell nuclei segmented by ACDC considering sub-images of Figure 1a,b (**a**,**b**), and the whole images in Figure 2a,b (**c**,**d**). The cell nuclei images were over-imposed onto the original fluorescence images with alpha-blending (\(\alpha=0.4\)). The assessment of cell count was quantified by means of the Pearson coefficient to measure the linear correlation between the automated and manual cell counts. The accuracy of the achieved segmentation results was evaluated by using the DSC and the IoU metrics. Table 1 reports the results--by also comparing the performance of ACDC with and without bilateral filtering--achieved on the VU and 2018 DSB datasets, which are supported by the scatter plots in Figure 9 that reports the results concerning the case of the bilateral filter. The achieved high \(\rho\) coefficient values confirm the effectiveness of the proposed approach, according to a validation performed against the manual cell counting, which is considered as the gold standard. Figure 8: Comparison of the gold standard cell nuclei segmentation (magenta contour in the left images) against the automated result obtained by ACDC (segmented nuclei over-imposed onto the original fluorescence images with alpha-blending in the right images): (**a**) VU dataset, where the orange arrows denote errors in the split of clustered cell nuclei; (**b**) DSB dataset, where the green arrows denote groups of cells that were erroneously delineated as unique connected-components in the gold standard and the blue dashed boxes represent spurious speckles that are not detected by ACDC. A strong positive correlation between the cell counts computed automatically by ACDC and the manual measurements was observed for both datasets analyzed in this study. In particular, in the case of the VU dataset, the automated cell counting is strongly consistent with the corresponding manual measurements, by denoting also a unity slope, as shown in Figure 9a. In the case of the DSB dataset (Figure 9b), the identity straight-line reveals a negative offset in the ACDC measurements. This finding means that the cell counts achieved by ACDC slightly under-estimated the gold standard in approximately 55% of cases. Besides the high variability of the fluorescence images included in the DSB dataset, this systematic error often depends on the gold standard binary masks, where the cell nuclei are not always precisely separated (since the DSB challenge was focused on the segmentation task), and consider also partial connected-components of cell nuclei smaller than 40 pixels located at the cropped image borders. Notice that no ACDC setting was modified, so some very small partial cell components were removed according to the morphological refinements based on the connected-component size.