# A Novel Evolution Strategy of Level Set Method for the Segmentation of Overlapping Cervical Cells
## 4 Results and Discussion
### Quantitative Evaluation of Our Segmentation Results
#### 4.2.2 Quantitative Comparison with The-State-of-The-Art Methods  
The results of the cytoplasm segmentation for overlapping cells in Pap images based on train-45 and test-90 datasets compared with the state-of-the-art methods are shown in Tables 4 and 5, including the methods of the ISBI-2014 challenge winner, [PERSON] et al. [30], as well as their newly proposed method [31] and the baseline method [33]. In these two tables, the superior results are indicated by the bold numbers. Specifically, our proposed method achieves the best performance on the segmentation precision indicated by the DC value that achieves the highest value (90.4%) with almost up to 2% improvement over the average values (88.6%) of the other methods on the test-90 dataset and highest value (92.3%) with almost up to 3% improvement over the average value (89.7%) on the train-45 dataset. Moreover, our proposed method has the best object-based detection performance on the train-45 dataset, indicated by the lowest \(\text{FN}_{\text{O}}\), which achieved 10.4% with up to an almost 7% reduction over the average value of 17.3%. In addition, our \(\text{FP}_{\text{P}}\) is the lowest on the test-90 dataset, which further shows that our proposed method has the highest segmentation precision over the other methods. Although the method [26] obtained a lower \(\text{FP}_{\text{P}}\) on the train-45 dataset, it is not an accurate method for delineation of the cytoplasm boundaries due to the absence of outstanding DC and \(\text{FP}_{\text{P}}\). Similarly, in the absence of outstanding DC and \(\text{FP}_{\text{P}}\), a much higher \(\text{TP}_{\text{P}}\) alone as obtained by [PERSON] [28; 60] on both of the train-45 and test-90 datasets cannot indicate a promising performance on the segmentation precision. [PERSON] [51] obtained the lowest \(\text{FN}_{\text{O}}\) on the test-90 dataset, but their segmentation precision had no advantage, for the reason reported in [21].  
In summary, our proposed method achieves the highest DC, lower \(\text{FP}_{\text{P}}\) and reasonable \(\text{TP}_{\text{P}}\) compared with the other methods. What is more, it can avoid extensive parameter tuning, such as [30; 32; 33; 34; 35; 36; 37; 50; 51; 52], which relied on manual selection in an arbitrary parameter set for multiple-level set functions.  
Figure 9: Mean Dice coefficient (**a**), mean true positive rate (**b**), mean false positive rate (**c**) and object\(-\)based false negative rate (**d**) as a function of number of cells and overlap ratio.  
The methods used in this comparison, except for the other winner [PERSON] [27] in the ISBI-2014 challenge, were all designed to delineate the cervical cells in Pap images, aiming to segment realistic cytoplasm boundaries. The authors of [27] obtained unrealistic geometric segmentation by the edges of a Voronoi diagram partitioning the overlapped pairs of cells with no respect of the realistic searching for the actual cell boundaries [73]. Although FP\({}_{\text{P}}\) in [27] was the lowest, we still made the second-lowest results (bold number in Table 5). This is not only because of the unrealistic geometric segmentation [27] described above but also that we consider the lower FP\({}_{\text{P}}\) alone cannot reflect the performance on segmentation accuracy, since the FP\({}_{\text{P}}\) would be zero if each nucleus was selected as the segmentation for the cytoplasm of each cell, supposing each nucleus was lying inside its cytoplasm.