## 3 Results
### Comparison with Other Cell Imaging Tools and Segmentation Methods  
We compared the performance of ACDC against two pipelines realized with ImageJ v1.53c [8]. Since filtering operations typically represent the initial step used to enhance the subsequent segmentation, in order to assess any performance improvement introduced by low-pass filtering, we implemented the processing pipelines in ImageJ, to perform cell segmentation and counting, with and without a Gaussian filtering. To be more precise, the steps are: (i) Gaussian low-pass filtering; (ii) uneven background removal by  
Figure 10: Bland-Altman plots of the cell counting measurements achieved by ACDC versus the gold standard for the (**a**) VU and (**b**) DSB datasets. Solid horizontal and dashed lines denote the mean and \(\pm\)1.96 standard deviation values, respectively. an histogram-based rolling-ball algorithm; (iii) Otsu global thresholding; (iv) morphological operations including hole-filling; (v) watershed algorithm for cell nuclei separation. The pipelines have been tested on both VU and DSB datasets. Figure 11 shows the results concerning cell counting achieved by ACDC and the two ImageJ pipelines. In the case of the VU dataset (plots a-c), the ImageJ pipelines tend to over-estimate the number of cells in the images; on the contrary, considering the DSB dataset (plots d-f), the results are comparable. The segmentation results shown in Figure 12 present a different scenario. ACDC is generally better than the ImageJ pipelines; we also note that the application of Gaussian filtering in the ImageJ pipelines does not allow us to markedly improve the segmentation outcome. However, over-segmentation can be observed when low-pass filtering is not applied. Table 2 reports the values of DSC and IoU achieved by ACDC and the tested ImageJ pipelines. The highest values for these metrics are obtained by ACDC both in the case of VU and DSB datasets. Moreover, the very high \(\rho\) coefficients indicate that all approaches are effective, when validated against the gold standard. To assess whether the difference in the achieved segmentation performance between ACDC and ImageJ with Gaussian filter is statistically significant, we performed a two-sided Wilcoxon signed rank test on both paired DSC and IoU results [74], with the null hypothesis that the samples come from continuous distributions with equal medians, and considering a significance level of 0.05. The results of the test confirmed that both the achieved DSC and IoU values are statistically different in the case of ACDC and ImageJ with Gaussian filtering (\(p<0.001\) and \(p<0.01\) for the VU and DSB datasets, respectively). As a final test, we considered a recently published work that takes into account the SNP HEp-2 Cell Dataset (SNPHEp-2) [75]. SNPHEp-2 is composed of images acquired using a monochrome high dynamic range microscopy camera, equipped with a plan-Apochromat \(20\times/0.8\) objective lens and an LED illumination source, resulting in a dataset considerably different compared to VU and DSB datasets. Specifically, we compared ACDC against CellProfiler [10], Marker-Controlled Watershed algorithm (MC-Watershed), and Split and Merge Watershed (SM-Watershed) [16]. The DSC and IoU metrics reported in Table 3 are computed against the gold standard automatically obtained by processing the DAPI channel. To obtain a fair comparison with the results presented in [16], we processed the 40 cell images from the homogeneous class used in that work. Even if the SNPHEp-2 dataset consists of cell images with different characteristics with respect to those contained in the VU and 2018 DSB datasets, ACDC achieved better results than CellProfiler, and slightly worse results than MC-Watershed and SM-Watershed approaches, which were specifically tailored to analyze this kind of images (see Table 3).