## 4 Experimental Results
In evaluating A1 and A2, we disregarded the accuracy of the traced boundaries. Therefore, some errors are allowed in a certain margin between the auto detected and manually traced boundaries; that is, the detection focuses only on the rough relative position between the traced boundaries and real WBCs. Therefore, the results are better than the results in the overall evaluation. D denotes the average Hausdorff distance between the auto detected and manually traced boundaries. Several experts are requested to manually trace the boundaries of WBC. We treated the average result of the experts as the ground truth and then applied the Hausdorff distance between the auto detected and manually traced boundaries to describe their contact ratios. A smaller D corresponds to better performance. D has a close relationship with the recognition accuracy of the entire system because the features extracted from the detected WBCs strongly rely on the segmentation results, whereas D describes the segmentation performance:  
\[\text{A1}=\frac{\text{{The}}\;number\;of\;correctly\;detected\;WBCs}{Total\;number \;of\;detected\;WBCs}\times\text{100\%}, \tag{7}\]  
\[\text{A2}=\frac{\text{{Total}}\;number\;of\;detected\;WBCs}{Total\;number\;of\; WBCs\;that\;exist\;in\;all\;images}\times\text{100\%}, \tag{8}\]  
\[\left\{ \begin{matrix}\text{E1}=1-\text{A1}\\ E2=1-\text{A2}\end{matrix} \right., \tag{9}\]  
where E1 denotes the false detection ratio and E2 denotes the leak detection ratio. The proposed method achieves a high overall accuracy for cytoplasm segmentation. Table 1 shows that the proposed method obtains low false and leak detection ratios and that the traced boundaries of the proposed method achieves high accuracy. The segmentation results for single WBC of the proposed method are compared with the original images and the manual segmentation results in Figure 14. The proposed method also performs well when multiple WBCs exists in one image, as shown in Figure 15.  
Figure 14: Comparison of the proposed method and the manual method on single WBC segmentation. Figure 15: Comparison of the proposed method and the manual method on multiple WBC segmentation. \begin{table}
\begin{tabular}{c c c c} \hline
**Parameter** & **Region Growing** & **Snake** & **Proposed Method** \\ \hline A1 & 88.4\% & 90.3\% & 94.6\% \\ A2 & 89.2\% & 87.4\% & 95.1\% \\ D & 60.62 & 30.62 & 19.13 \\ \hline \end{tabular}
\end{table} 
Table 1: Performance evaluation. The performance of the proposed method, region growing method, watershed method and snakes' method was also evaluated via the parameter: OR, UR, ER and RDE [16, 23, 24]. OR denotes the over-segmentation rate, UR denotes the under-segmentation rate, and ER denotes the overall error rate. They are often used to evaluate the performance of segmentation methods. [PERSON] _et al_. [16] and [PERSON] _et al_. [23] have given a clear definition. RDE denotes the relative distance error, which is firstly proposed by [PERSON] _et al_. [24] to evaluate the segmentation results. Assume that \(e_{1},e_{2},e_{3},...,e_{n_{e}}\) are the pixels of E, and \(t_{1},t_{2},t_{3},...,t_{n_{t}}\) are the pixels of T, in which E denotes the segmentation results, T denotes the ground truth, and \(n_{e},n_{t}\) denote the number of pixels of E and T, respectively. The definition of RDE is illustrated as follows:  
\[RDE=\frac{1}{2}\bigg{(}\sqrt{\frac{1}{n_{e}}\sum_{i=1}^{n_{e}}d_{e_{i}}^{2}}+ \sqrt{\frac{1}{n_{e}}\sum_{j=1}^{n_{e}}d_{t_{j}}^{2}}\bigg{)}, \tag{10}\]  
where \(d_{e_{i}}=min\{distance\big{(}e_{i},t_{j}\big{)}|j=1,2,...n_{t}\}\), \(d_{t_{j}}=min\{distance\big{(}e_{i},t_{j}\big{)}|i=1,2,...n_{e}\}\), and \(distance\big{(}e_{i},t_{j}\big{)}\) denotes the Euclidean distance between \(e_{i}\) and \(t_{j}\)[16]. Table 2 shows the evaluation of the four methods via the average error measure of OR, UR, ER and RDE. The proposed method is only slightly worse than the region growing method in UR evaluation. It shows similar attributes to the watershed method in OR evaluation, however it is better in other indexes.