## 3 Results
### ACDC Performance
The agreement between ACDC and the manual cell counting measurements can be graphically represented also by using a Bland-Altman plot [73], as reported in Figure 10 for both datasets. The Bland-Altman analysis allows for a better data visualization by showing the pairwise difference between the measurements obtained with the two methods, against their mean value. In this way, we can assess any possible relationship between the estimation errors and easily detect any outlier (i.e., observations outside the 95% limits of agreement). Figure 10 reveals that ACDC achieved reproducible results also by considering the whole range of the cell counts concerning the analyzed cell microscopy images; only about the 4% and 6% of outliers are observed in the ACDC results achieved on the VU and DSB datasets, respectively. This confirms the observations on the scatter plots \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & **Dataset** & **Pearson Coeff. (\(p\)-Value)** & **DSC (\%)** & **IoU (\%)** & **Exec. Time (s)** \\ \hline ACDC (without bilateral filter) & VU & \(\rho=0.99\)\((p=2.5\times 10^{-74})\) & \(75.86\pm 5.98\) & \(61.45\pm 7.47\) & \(3.98\pm 0.10\) \\ ACDC (with bilateral filter) & VU & \(\rho=0.99\)\((p=6.6\times 10^{-74})\) & \(76.84\pm 6.71\) & \(62.84\pm 8.58\) & \(7.49\pm 0.30\) \\ \hline ACDC (without bilateral filter) & DSB & \(\rho=0.96\)\((p=1.1\times 10^{-175})\) & \(87.34\pm 6.89\) & \(77.97\pm 9.49\) & \(0.07\pm 0.05\) \\ ACDC (with bilateral filter) & DSB & \(\rho=0.96\)\((p=2.6\times 10^{-169})\) & \(88.64\pm 7.41\) & \(80.37\pm 10.58\) & \(0.12\pm 0.09\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Evaluation metrics on cell counting and segmentation achieved by ACDC (with and without bilateral filtering) on the analyzed time-lapse microscopy - VU and 2018 DSB datasets, comprising 46 and 301 images, respectively. The results for the DSC and IoU metrics, as well as the execution time measurements, are expressed as mean value \(\pm\) standard deviation. Figure 9: Scatter plots depicting ACDC results compared to the gold standard in terms of cell nuclei counting in the case of: (**a**) time-lapse fluorescence images from the VU dataset; (**b**) small fluorescent nuclei images from the DSB dataset. The equality line through the origin is drawn as a dashed line. in Figure 9; neither systematic discrepancy between the measurements nor bias can be observed in the VU dataset, while a negative bias is visible in the case of the DSB dataset. The analysis of the DSC and IoU mean values reported in Table 1, calculated on the VU images, reveals a good agreement between the segmentation results achieved by ACDC and the gold standard. The standard deviation values confirm the high variability encountered in the input datasets. In particular, in the case of the VU images, this evidence strongly depends on the density of the cells represented in the input image. As a matter of fact, the DSC and IoU metrics is highly affected by the size of the foreground regions with respect to the background. This behavior is confirmed by the results achieved on the DSB dataset, where the IoU values are considerably higher than those achieved on the VU images, even though the Pearson coefficient is slightly lower in this case. Accordingly, the high standard deviation for the DSB dataset is due to the intrinsic variety of the images--in terms of image size, zoom factor, and specimen type--included in this dataset (see Section 2.1.2). In general, the bilateral filtering allows us to achieve better segmentation performance, while no appreciable difference was found in the \(\rho\) values. Therefore, we incorporated the bilateral filtering into the ACDC pipeline tested in the experiments. The mean execution times concerning the segmentation tests are shown in Table 1. These experiments were run on a personal computer equipped with a quad-core Intel Core 7700 HQ (clock frequency 3.80 GHz), 16 GB RAM, and Ubuntu 16.04 LTS operating system.