## 3 Results and Discussion
### The EYB Eyes Image Results
#### 3.1.2 The Scale Space with a Curvature-Based Method Results  
In the following experiment, we evaluated the scale-space method from Equations (13) and (17). There were four octaves (\(O\)) and three levels in each octave (\(L\)). Moreover, the scale space (\(SS\)) was then combined with the curvature-based methods in Equations (18)-(20), resulting in a total of 12 variables of \(O\) and \(L\) from \(SS\) and the \(K\), \(H\), \(X\), and \(N\) curvatures. The accuracy results appear in Figure 3. The best results were derived from \(O=0\) and \(O=1\), while starting from \(O=2\), the accuracy results decreased. The performance decreased due to the smaller size of the convoluted images and wider Gaussian width in \(O=2\) and \(O=3\). The sizes of the images in \(O=1\), \(O=2\), and \(O=3\) were \(59\times 15\), \(29\times 7\), and \(14\times 3\) pixels, respectively. The widths of the Gaussian filters for \(L=1\), \(L=2\), and \(L=3\) were \(1.23\), \(1.97\), and \(2.77\), respectively. Consequently, due to the inferior results starting from \(O=2\), Table 4 displays the results of the curvature-based scale-space method only from \(O=0\) and \(O=1\). Overall, the scale space accuracy results from \(O=0\) performed better than those from \(O=1\), except for combinations of \(SS+H\) (scale space with mean curvature) and \(SS+X\) (scale space with the max principal). The results reached the peak at \(O=1\) and \(L=1\) from \(SVM\)-\(1\). Details from Table 3 also show that \(SVM\)-\(1\) produced superior results compared with \(1\)-\(NN\) and \(SVM\)-\(2\)  
Figure 3: The accuracy results (%) from (**a**) \(1\)-\(NN\), (**b**) \(SVM\)-\(1\), and (**c**) \(SVM\)-\(2\). The results were evaluated for 12 octave \(O\) and level \(L\) variables from \(SS\) and 5 curvature-based scale spaces (\(SS\), \(SS+K\), \(SS+H\), \(SS+X\), and \(SS+N\)). We successfully improved the accuracy of the scale-space method by combining it with a curvature-based method. The best accuracies were 76.04% and 74.65%, respectively, from \(SS+X\) and \(SS+H\). They improved the previous scale-space method accuracy by 7.84%. Figure 4 shows the results from \(SS+K\), \(SS+H\), \(SS+X\), and \(SS+N\). From Figure 4, we can observe why the combination of \(SS+H\) (Figure 4b) and \(SS+X\) (Figure 4c) performed well. They were richer in features compared with \(SS+K\) (Figure 4a) and \(SS+N\) (Figure 4d). The scale space with a curvature-based method effectively captured the prominent feature at \(O=1\), while the mean and max principal curvature characterized this feature to be more distinctive. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Classifier**} & \multirow{2}{*}{**Method**} & \multicolumn{6}{c}{**Octave-Level (O-L)**} \\ \cline{3-8}  & & **0-1** & **0-2** & **0-3** & **1-1** & **1-2** & **1-3** \\ \hline \multirow{4}{*}{1-\(\text{NN}\)} & \(SS\) & 54.84 & 54.10 & 50.41 & 48.36 & 45.90 & 43.32 \\  & \(SS+K\) & 41.24 & 43.89 & 45.90 & 25.32 & 29.10 & 29.29 \\  & \(SS+H\) & 63.20 & 64.49 & 63.32 & 53.78 & 52.35 & 51.89 \\  & \(SS+X\) & 63.85 & 64.06 & 64.70 & 57.58 & 56.43 & 51.77 \\  & \(SS+N\) & 66.41 & 65.35 & 65.46 & 46.38 & 45.88 & 42.86 \\ \hline \multirow{4}{*}{_SVM-1_} & \(SS\) & 69.59 & 69.59 & 69.12 & 68.20 & 67.28 & 66.82 \\  & \(SS+K\) & 47.93 & 53.92 & 57.60 & 49.77 & 42.40 & 36.41 \\  & \(SS+H\) & 64.06 & 64.52 & 65.44 & 74.65 & 64.98 & 60.37 \\  & \(SS+X\) & 65.44 & 64.06 & 63.13 & 76.04 & 72.81 & 64.98 \\  & \(SS+N\) & 67.74 & 66.82 & 66.82 & 60.83 & 50.23 & 45.16 \\ \hline \multirow{4}{*}{_SVM-2_} & \(SS\) & 49.31 & 40.55 & 40.55 & 24.42 & 25.81 & 18.89 \\  & \(SS+K\) & 35.02 & 38.71 & 35.48 & 22.12 & 26.73 & 35.02 \\ \cline{1-1}  & \(SS+H\) & 43.78 & 59.91 & 54.38 & 35.48 & 32.26 & 26.27 \\ \cline{1-1}  & \(SS+X\) & 43.78 & 36.41 & 36.87 & 29.49 & 29.03 & 33.18 \\ \cline{1-1}  & \(SS+N\) & 53.00 & 52.53 & 48.85 & 33.18 & 33.64 & 33.64 \\ \hline \hline \end{tabular}
\end{table}