## 2 Appendix Segmentation with Double-Layered Outlier Rejection FCM
### Double-Layered Outlier Rejection FCM (DORFCM)
#### 2.3.2 Layer-2 Learning (Step 5 to Step 7)
Likewise, Table 3 summarizes the performance comparison between ORFCM and DORFCM among 88 cases that both methods locate the target object successfully. As one can see, the outlier rejection effect is significant. The effect of double-layered learning with outlier rejection strategy is shown in \[w_{si}^{(t)}=\frac{\sum_{s=1}^{cc}(q_{si})^{m}u_{ik}}{\sum_{i=1}^{cc}(q_{si})^{ m}} \tag{6}\]0 The standard ORFCM is implemented as the lower layer (layer-1) of our proposed DORFCM. With the input image Figure 7a, the number of clusters is initialized as 4 by analyzing the histogram as shown in Figure 7b and the segmentation result is shown as Figure 7c. For DORFCM, after lower layer learning, we can remove noise pixels that have lower membership rate and regulating intensities of similar pixels; thus, the histogram of layer-2 (higher layer) looks like Figure 7d thus DORFCM can avoid misguidance of ORFCM that is sensitive to outlier pixels. In the results, DORFCM shows better quantization as shown in Figure 7e. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Accuracy** & **Precision** & **Recall** \\ \hline DORFCM & 84.20\% & 83.40\% & 85.80\% \\ DFCM & 80.80\% & 80.90\% & 80.20\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Outlier effect performance comparison (91 cases). Figure 6: Comparison of DFCM, ORFCM, and DORFCM. (**a**) Input, (**b**) DFCM, (**c**) ORFCM, and (**d**) DORFCM. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Accuracy** & **Precision** & **Recall** \\ \hline DORFCM & 84.82\% & 83.78\% & 86.04\% \\ ORFCM & 81.23\% & 78.56\% & 80.53\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Double layered learning effect comparison (88 cases). ## 4 Conclusions

Abdominal ultrasound examination is the preferred first-hand modality for the diagnosis and management of the patients with clinically suspected appendicitis, especially in emergency and for pediatric or pregnant women patients. However, the sonographic diagnostic criteria for appendicitisitis, such as diameter, compressibility, wall thickness, and hyperaemia, rely on complete identification or visualization of the appendix. Unfortunately, the sonographic appendix visualization rate can vary significantly with respect to the experience of the examiners. It becomes even more challenging when abdominal ultrasound could not correctly visualize the inflamed appendix. In this paper, we propose a robust automatic segmentation method for identifying inflamed appendix from abdominal ultrasound images. FCM based pixel clustering approach has shown better performance than edge detection methods, but FCM is sensitive to the existence of outlier thus outlier rejection method is necessary for the robustness. We apply this outlier rejection FCM to the double-layered learning structure in that the first layer clustering result become the input of the second layer outlier rejection FCM with modified learning parameters and cluster center update rule. This double-layered learning mitigates the tendency of local maximum that FCM can fall into. Thus, our proposed DORFCM is a hybrid method to combine outlier-rejection strategy for efficient noise removal and double-layered learning structure for mitigating misguidance of optimization from single ORFCM learning method in inflamed appendix detection. In experiment with 100 real world inflamed sonographic images, the proposed method (DORFCM) extracts target objects in almost all (98 out of 100) cases and traditional FCM, standard ORFCM and DFCM extracts only 83, 88, and 91 cases, respectively. Furthermore, when we take a human expert's object identification as the ground truth, DORFCM scores better in all criteria, accuracy, precision, and recall, than DFCM and single layered ORFCM significantly in pixel area computation. Thus, DORFCM shows outlier rejection effect and double layered learning effect in our experiment and, thus, we may claim this approach is more robust than standard methods. Figure 7: Effect of double layered learning structure.