# Automatic Tortuosity Estimation of Nerve Fibers and Retinal Vessels in Ophthalmic Images
## 4 Experimental Results
### Nerve Fibers Tortuosity Grading  
As shown in Table 2, in this work, we calculate the tortuosity classification results for each level and the overall tortuosity level on both fiber dataset. For both the in-house CCM-A and public CCM-B datasets, the segmentation is manually done by ophthalmologists. In order to make a comparative study, we compared three methods: Annanziata [1], Kexp and Kexp+. The Annunziata method calculates ACR, TD, SCC, AC and WAC in Table 1 respectively, and get several features for an image. Finally, several features are fused by weighted average strategy, and the tortuosity of the image is classified into different levels by Multinomial Logistic Ordinal Regression. Kexp is our approach, but it does not include enhancement step. Kexp+ is our proposed method, which includes enhancement step.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & & \multicolumn{6}{c}{**CCM-A Dataset**} & \multicolumn{6}{c}{**CCM-B Dataset**} \\ \cline{3-11}  & & _Level-1_ & _Level-2_ & _Level-3_ & _Level-4_ & **Overall** & _Low_ & _Mid_ & _High_ & **Overall** \\ \hline \multirow{3}{*}{Annumziata [1]} & Sen & 0.718 & 0.644 & 0.660 & 0.707 & 0.663 & 0.783 & 0.743 & 0.761 & 0.766 \\  & Spec & 0.867 & 0.790 & 0.783 & 0.857 & 0.806 & 0.904 & 0.860 & 0.864 & 0.912 \\  & Acc & 0.858 & 0.780 & 0.759 & 0.843 & 0.790 & 0.877 & 0.826 & 0.847 & 0.848 \\ \hline \multirow{3}{*}{Kexp based SVM} & Sen & 0.731 & 0.654 & 0.669 & 0.713 & 0.675 & 0.811 & 0.758 & 0.786 & 0.784 \\  & Spec & 0.878 & 0.802 & 0.794 & 0.865 & 0.816 & 0.914 & 0.865 & 0.887 & 0.921 \\  & Acc & 0.865 & 0.788 & 0.775 & 0.853 & 0.797 & 0.909 & 0.833 & 0.870 & 0.868 \\ \hline \multirow{3}{*}{Kexp+ based SVM} & Sen & 0.742 & 0.674 & 0.683 & 0.734 & 0.715 & 0.824 & 0.765 & 0.790 & 0.810 \\  & Spec & 0.898 & 0.819 & 0.811 & 0.881 & 0.852 & 0.929 & 0.873 & 0.891 & 0.929 \\ \cline{1-1}  & Acc & 0.881 & 0.799 & 0.793 & 0.864 & 0.820 & 0.914 & 0.841 & 0.883 & 0.882 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison results of tortuosity classification on CCM-A and CCM-B.  
In Table 2, the comparison results of tortuosity classification show that our proposed Kexp+ on enhanced images show better performance than the [PERSON]'s both on CCM-A and CCM-B datasets. The evaluation metrics are wSen, wSpec, and wAcc scores. For the overall result, the kexp+ achieved the wAcc with 0.820 and 0.882 on the two datasets respectively, while the [PERSON]'s approach are 0.790 and 0.848. The Kexp+ also outperforms the better classification results with regard to the wSen and wSpec in overall. In this experiment, we also further compare the reusls level-by-level according to the tortuosity. Among different levels, we found that the level-1 column, level-4 column in CCM-A dataset and the low level column in CCM-B have the good classification results. The more levels are divided, the worse the classification results are. For [PERSON]'s method, the wAccs of level-1, level-4 and low level are 0.858, 0.843 and 0.877, while the results of Kexp+ are 0.881, 0.864, and 0.914. In the group of low-level in CCM-B, two images were wrongly classified. Because of the interference of pathological features, some nerve fibers could not be traced completely.